Appendix N: Derivation of the Logarithm Change of Base Formula
We take loga of each side of this equation which gives us loga by = loga x
MATHEMATICS 0110A CHANGE OF BASE Suppose that we have
So we get the following rule: Change of Base Formula: logb a = logc a logc b. Example 1. Express log3 10 using natural logarithms. log3 10 =.
Change of Base
Logarithms – University of Plymouth
16 jan. 2001 7. Quiz on Logarithms. 8. Change of Bases ... following important rules apply to logarithms. ... Proof that loga MN = loga M + loga N.
PlymouthUniversity MathsandStats logarithms
Secondary V Videos and Notes
Proof of the logarithm change of base rule https://youtu.be/1reblXFlM6I. Logarithm properties: review https://www.khanacademy.org/math/algebra2/.
Secondary V Videos and Notes
6.2 Properties of Logarithms
The proofs of the Change of Base formulas are a result of the other properties studied in this section. If we start with bx logb(a) and use the Power Rule
S&Z . & .
Logarithms - changing the base
This leaflet gives this formula and shows how to use it. A formula for change of base. Suppose we want to calculate a logarithm to base 2. The formula states.
mc logs
Elementary Functions The logarithm as an inverse function
Each of these three properties is merely a restatement of a property of exponents. Smith (SHSU). Elementary Functions. 2013. 18 / 29. Changing the base.
. Logarithms (slides to )
Logarithms.pdf
16 nov. 2017 This law allows a logarithm with a given base to be changed to a new base ... The third law: (Power Rule) log log n a a. x n x. = Proof:.
Logarithms
ln b ∫ ln x dx.
The conventional proof of the integral of a logarithm utilises integration change of base rule and multiplication by a constant rule:.
an alternative proof of the integral of a logarithm
Introduction to Algorithms
I can prove this using the definition of big-Omega: This tells us that every positive power of the logarithm of n to the base b where b ¿ 1
cs lect fall notes
Secondary V Foundations of Algebra
Equations and Inequalities
TopicVideo/NotesOrigins of algebrahttps://youtu.be/_LDR1_PrveoThe beauty of algebrahttps://youtu.be/kpCJyQ2usJ4What is a variable?https://youtu.be/tHYis-DP0oUEvaluating an expression with one variablehttps://youtu.be/AJNDeVt9UOoEvaluating expressions with two variableshttps://youtu.be/S_OX3ByvBScEvaluating expressions with two variables: fractions & decimalshttps://youtu.be/GmD7Czmol0kIntroduction to combining like termshttps://youtu.be/CLWpkv6ccpASimplifying expressionshttps://youtu.be/3NHSwiv_pSECombining like terms: challenge problemhttps://youtu.be/FNnmseBlvaYSimplifying expressions with rational numbershttps://youtu.be/rtNuo7R3scYEquivalent expressionshttps://youtu.be/rHNY01R2VSQWhy dividing by zero is undefinedhttps://youtu.be/SQzjzStU1RQUndefined & indeterminate expressionshttps://youtu.be/lHdlHTsXbZgTopicVideo/NotesLinear equationshttps://youtu.be/1c5HY3z4k8MEquation with fractionshttps://youtu.be/PL9UYj2awDcEquation with the variable in the denominatorhttps://youtu.be/Z7C69xP08d8Equations with parentheseshttps://youtu.be/YZBStgZGyDYEquation with no solutionshttps://youtu.be/uQs100shv-AEquation with infinitely many solutionshttps://youtu.be/Dq0xFgQB9qoInequalities with variables on both sideshttps://youtu.be/SgKBBUFaGb4Inequalities with variables on both sideshttps://youtu.be/XOAn5z8mkvICompound inequalities: ORhttps://youtu.be/0YErxSShF0A
Compound inequalities: ANDhttps://youtu.be/d2cnQ5ahHgEA compound inequality with no solutionhttps://youtu.be/ZF_cZ-GX9PIDouble inequalitieshttps://youtu.be/cvB8b4AACyECompound inequalities: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:compound-inequalities/a/compound-inequalities-review?modal=1Introduction to two-variable linear equationshttps://youtu.be/AOxMJRtoR2ASolutions to two-variable equationshttps://youtu.be/qk69pR91R00Example: solutions to two-variable equationshttps://youtu.be/d3VMo1VWFvcIntroduction to slopehttps://youtu.be/MeU-KzdCBpsPositive & negative slopehttps://youtu.be/EQoNfxToez0Example: slope from graphhttps://youtu.be/R948Tsyq4vAGraphing a line given point and slopehttps://youtu.be/5mgH-_5UJ54Example: slope from two pointshttps://youtu.be/WkspBxrzuZoSlope: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/a/slope-review?modal=1Slope of a horizontal linehttps://youtu.be/CFSHq099Mx0Horizontal & vertical lineshttps://youtu.be/J43CIbKpdWcIntroduction to interceptshttps://youtu.be/LNSB0N6esPUhttps://youtu.be/xiIQQNufFuUIntercepts from an equationhttps://youtu.be/xGmef7lFc5whttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:x-intercepts-and-y-intercepts/a/intercepts-of-lines-review-x-intercepts-and-y-intercepts?modal=1Linear functions word problem: fuelhttps://youtu.be/AAmVITyDXbcIntroduction to slope-intercept formhttps://youtu.be/IL3UCuXrUzEIntroduction to slope-intercept form: noteshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:intro-to-slope-intercept-form/a/introduction-to-slope-intercept-form?modal=1TopicVideo/Notes-intercept of a linex
Intercepts of lines review (-intercepts and -intercepts)xyhttps://youtu.be/Z65mz__8DQ0Examples: slope-intercepthttps://youtu.be/qgsNNqmlLoALinear equation: word problemshttps://youtu.be/w6R8rywmgekGraph from slope-intercept equationhttps://youtu.be/uk7gS3cZVp4Graphing lines from slope-intercept form: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:graphing-slope-intercept-equations/a/graphing-lines-review?modal=1Slope-intercept equation from graphhttps://youtu.be/9wOalujeZf4Writing slope-intercept equationshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:writing-slope-intercept-equations/a/writing-slope-intercept-equations?modal=1Slope-intercept equation from slope & pointhttps://youtu.be/AqFwKecNaTkSlope-intercept equation from two pointshttps://youtu.be/XMJ72mtMn4YConstructing linear equations from contexthttps://youtu.be/hBpI9IfmMKgSlope-intercept form: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:writing-slope-intercept-equations/a/slope-intercept-form-review?modal=1Introduction to point-slope formhttps://youtu.be/K_OI9LA54AAPoint-slope & slope-intercept equationshttps://youtu.be/LtpXvUCrgrMPoint-slope form: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:point-slope-form/a/point-slope-form-review?modal=1Introduction to linear equation standard formhttps://youtu.be/6CFE60iP2Ughttps://youtu.be/86NwKBcOlowConverting from slope-intercept to standard formhttps://youtu.be/XOIhNVeLfWsForms of linear equations: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:summary-forms-of-two-variable-linear-equations/a/forms-of-linear-equations-review?modal=1TopicVideo/NotesSlope and -intercept from equationy
Graphing a linear equation: 5x+2y=20
Functions
TopicVideo/NotesWhat is a function?https://youtu.be/kvGsIo1TmsMExample: Evaluating functionshttps://youtu.be/Id6UovYjd-MExample: Evaluating functions from graphhttps://youtu.be/kzYtx_AqzjMEvaluating discrete functionshttps://youtu.be/Ddw8u7nNmKsExample: evaluating expressions with function notationhttps://youtu.be/uaPm3TpuxbcExample: matching an input to a function's output (equation)https://youtu.be/tJBQZ3PUkPoExample: matching an input to a function's output (graph)https://youtu.be/0Rmmynff5YcExample: two inputs with the same output (graph)https://youtu.be/qSktOkaW6EAEquations vs. functionshttps://youtu.be/l3iXON1xEC4Obtaining a function from an equationhttps://youtu.be/OOim0QPsJ9oFunction notation word problem: bankhttps://youtu.be/HERb3x0aw6cFunction notation word problem: beachhttps://youtu.be/94Gnto5G1PUIntervals and interval notationhttps://youtu.be/UJQkqV2zGv0What is the domain of a function?https://youtu.be/-DTMakGDZAwWhat is the range of a function?https://youtu.be/96uHMcHWD2EExample: domain and range from graphhttps://youtu.be/sXP7VhU1gYEDetermining whether values are in domain of functionhttps://youtu.be/LdbrNNheFg8Examples: finding the domain of functionshttps://youtu.be/4ZWbeESjv4MRecognizing functions from graphhttps://youtu.be/qGmJ4F3b5W8Does a vertical line represent a function?https://youtu.be/_npwsLh0vwsRecognizing functions from tablehttps://youtu.be/5cK86VKoBPwIntroduction to minimum and maximum pointshttps://youtu.be/Hoyv3-BMAGcExample: absolute and relative extremahttps://youtu.be/xmrhZ5ySaD0Increasing, decreasing, positive or negative intervalshttps://youtu.be/KxOp3s9ottgExample: positive & negative intervalshttps://youtu.be/eDv7dk9uNmM
Graph interpretation word problem: temperaturehttps://youtu.be/VtBRkjRua0IIntroduction to average rate of changehttps://youtu.be/oT6LclcJ-I8Example: average rate of change from graphhttps://youtu.be/TEXSW-o8674Example: average rate of change from tablehttps://youtu.be/U1lQbh21y1kAverage rate of change word problem: graphhttps://youtu.be/-6EqUILZ1ywAverage rate of change: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:average-rate-of-change-word-problems/a/average-rate-of-change-review?modal=1Introduction to inverse functionshttps://youtu.be/W84lObmOp8MIntroduction to inverse functions: noteshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/a/intro-to-inverse-functions?modal=1Inputs & outputs of inverse functionshttps://youtu.be/KzaPBzFFLRMGraphing the inverse of a linear functionhttps://youtu.be/KPeS2gdizhQFinding inverse functions: linearhttps://youtu.be/wSiamij_i_kIntroduction to composing functionshttps://youtu.be/wUNWjd4bMmwIntroduction to composing functions: noteshttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/a/introduction-to-function-composition?modal=1Composing functionshttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/a/finding-and-evaluating-composite-functions?modal=1Evaluating composite functionshttps://youtu.be/lxtlwnCV-HMEvaluating composite functions: using tableshttps://youtu.be/FR8JH6IldsEEvaluating composite functions: using graphshttps://youtu.be/oORnGaJp1pkFinding composite functionshttps://youtu.be/_b-2rZpX5z4Evaluating composite functions: advancedhttps://youtu.be/jlID_mIJXi4Example 1: Modeling with composite functionshttps://youtu.be/pIMfRbznxKAExample 2: Modeling with composite functionshttps://youtu.be/LG6g7gxupHgVerifying inverse functions by compositionhttps://youtu.be/8GEGnSEJA2sTopicVideo/Notes
Verifying inverse functions by composition: noteshttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:verifying-inverse/a/verifying-inverse-functions-by-composition?modal=1Verifying inverse functions by composition: not inversehttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:compositeIntroduction to piecewise functionshttps://youtu.be/tedzsRH0JasExample: evaluating piecewise functionshttps://youtu.be/hg2HR9zJFq4Example: graphing piecewise functionshttps://youtu.be/PQiXRrT_14oExample: domain & range of step functionhttps://youtu.be/4n7TIvRHuDsExample: domain & range of piecewise linear functionshttps://youtu.be/rpI-X9Gn5a4Shifting functions: introductionhttps://youtu.be/RttvubuBhAEShifting functions: exampleshttps://youtu.be/MDav5OMpCtoGraphing shifted functionshttps://youtu.be/5DLkB-g8Rr8Reflecting functions: introductionhttps://youtu.be/mR2y_kohZIwExamples: Reflecting functionshttps://youtu.be/0QOnEoQHZ1kFunction symmetry: introductionhttps://youtu.be/4dOQePLgqxEFunction symmetry: introduction, noteshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:symmetry/a/intro-to-symmetry-of-functions?modal=1Even and odd functions: Graphshttps://youtu.be/zltgXTlUVLwEven and odd functions: Tableshttps://youtu.be/eKwJlJUM_d0Even and odd functions: Equationshttps://youtu.be/fTeO-V_VgEcEven and odd functions: Find the mistakehttps://youtu.be/RAksvTJWgxoSymmetry of polynomialshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:symmetry/a/symmetry-of-polynomials?modal=1Scaling functions: introductionhttps://youtu.be/1lt6a77OmLUExamples: Scaling functions verticallyhttps://youtu.be/tRCEBtKLqEwExample: Scaling functions horizontallyhttps://youtu.be/npMMbXm9sR0Identifying horizontal squash from graphhttps://youtu.be/4H5JZnytOfEIdentifying function transformationshttps://youtu.be/ENFNyNPYfZUTopicVideo/Notes
Exponents and Logarithms
Graphing square and cube root functionshttps://youtu.be/PI6IV7K3DbMRadical functions & their graphshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:radical-graphs/a/match-the-formula-of-a-radical-function-to-its-graph?modal=1Example 1: Transforming exponential graphshttps://youtu.be/83gM3ufe1NwExample 2: Transforming exponential graphshttps://youtu.be/ja4WRZ4DrAwGraphing exponential functionshttps://youtu.be/vlSEpdWf2hQhttps://youtu.be/K_PiPfYxtaoExample 1: Graphing logarithmic functionshttps://youtu.be/GpBSbNoon1EExample 2: Graphing logarithmic functionshttps://youtu.be/f_BJC6UwDTETopicVideo/NotesGraphical relationship between and 2
x log 2 xTopicVideo/NotesMultiplying & dividing powers: integer exponentshttps://youtu.be/CZ5ne_mX5_IPowers of products & quotients: integer exponentshttps://youtu.be/dC1ojsMi1yUIntroduction to square rootshttps://youtu.be/mbc3_e5lWw0Understanding square rootshttps://youtu.be/ROIfbUQrSY4Square root of decimalhttps://youtu.be/tRHLEWSUjrQIntroduction to cube rootshttps://youtu.be/87_qIofPwhg5th rootshttps://youtu.be/8wrtyW1RwNkHigher order rootshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/a/higher-order-roots?modal=1Simplifying square rootshttps://youtu.be/cw3mp8oNASkSimplifying square roots: variableshttps://youtu.be/qFFhdLlX220Simplifying square-root expressionshttps://youtu.be/3MijXB91DVoSimplifying square roots: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/a/simplifying-square-roots-review?modal=1
Introduction to exponential functionshttps://youtu.be/6WMZ7J0wwMIGraphing exponential functionhttps://youtu.be/9SOSfRNCQZQExponential vs. linear growthhttps://youtu.be/_vlXdx-CqM0Exponential expressions word problems: numericalhttps://youtu.be/L70UJVjc-bcExponential expressions word problems: algebraichttps://youtu.be/Z3YVZzCEi_AGraphs of exponential growthhttps://youtu.be/6rX2VNybXEEIntroduction to exponential decayhttps://youtu.be/v4IdaXvyE7UGraphing exponential growth & decayhttps://youtu.be/RVv0Jgi3PbwWriting exponential functionshttps://youtu.be/UgLfAb_aFt4Writing exponential functions from tableshttps://youtu.be/Qst1UVtq8pEWriting exponential functions from graphshttps://youtu.be/gFdh_rE2XgUModeling with basic exponential functions word problemhttps://youtu.be/2iZXFd_ZImALinear vs. exponential growth: from datahttps://youtu.be/721RrH6auoUIntroduction to logarithmshttps://youtu.be/Z5myJ8dg_rMIntroduction to logarithms: noteshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/a/intro-to-logarithms?modal=1Evaluating logarithms: advancedhttps://youtu.be/eTWCARmrzJ0Relationship between exponentials & logarithmshttps://youtu.be/Obch1OP5QyARelationship between exponentials & logarithms: graphshttps://youtu.be/DhW9pz5VfwoRelationship between exponentials & logarithms: tableshttps://youtu.be/Iz6IVf8frjwhttps://youtu.be/BKGx8GMVu88https://youtu.be/oQhp3ndj28YEvaluating natural logarithm with calculatorhttps://youtu.be/Dpo_-GrMpNEIntroduction to logarithm properties: part 1https://youtu.be/PupNgv49_WYIntroduction to logarithm properties: part 2https://youtu.be/TMmxKZaCqe0TopicVideo/Notes and compound intereste
as a limiteIntroduction to logarithm properties: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logsUsing the logarithmic product rulehttps://youtu.be/pkGrXzakRFsUsing the logarithmic power rulehttps://youtu.be/Pb9V374iOasUsing the properties of logarithms: multiple stepshttps://youtu.be/RhzXX5PbsuQProof of the logarithm product rulehttps://youtu.be/FP2arCfAfBYProof of the logarithm quotient and power ruleshttps://youtu.be/yEAxG_D1HDwJustifying the logarithm propertieshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/a/justifying-the-logarithm-properties?modal=1Evaluating logarithms: change of base rulehttps://youtu.be/OkFdDqW9xxMLogarithm change of base rule: noteshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/a/logarithm-change-of-base-rule-intro?modal=1Using the logarithm change of base rulehttps://youtu.be/qtsMgdZ98YgProof of the logarithm change of base rulehttps://youtu.be/1reblXFlM6ILogarithm properties: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/a/logarithm-properties-review?modal=1Solving exponential equations using logarithms: base-10https://youtu.be/R443Db-wJ5oSolving exponential equations using logarithmshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/a/solving-exponential-equations-with-logarithms?modal=1Solving exponential equations using logarithms: base-2https://youtu.be/7Ig6kVZaWoUExponential model word problem: medication dissolvehttps://youtu.be/HnHCQ2X_megExponential model word problem: bacteria growthhttps://youtu.be/IpXL9HIkqUQTopicVideo/Notes
Quadratics
TopicVideo/NotesIntroduction to Polynomialshttps://youtu.be/Vm7H0VTlIcoMultiplying binomialshttps://youtu.be/ZMLFfTX615whttps://youtu.be/JfuisfEdnjkhttps://youtu.be/xH_GllPuymchttps://youtu.be/h6HmHjkA034https://youtu.be/xjkbR7GjgjsBinomial special products: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:special-product-binomials/a/binomial-special-products-review?modal=1Introduction to factors & divisibilityhttps://youtu.be/SjN3_xCJamAhttps://youtu.be/D3a8NnpQ2vUhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/a/factoring-quadratics-leading-coefficient-1?modal=1https://youtu.be/1kfq0aR3ASshttps://youtu.be/eF6zYNzlZKQFactoring simple quadratics: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/a/factoring-simple-quadratics-review?modal=1Introduction to groupinghttps://youtu.be/X7B_tH4O-_sFactoring by groupinghttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-grouping/a/factoring-by-grouping?modal=1Factoring quadratics by groupinghttps://youtu.be/u1SAo2GiX8ASquaring binomials of the form (ax+b)
2 More examples of factoring quadratics as (x+a)(x+b)Special products of the form (ax!b)(ax+b)
Example 2: factoring quadratics as (x+a)(x+b)
Squaring binomials of the form (x+a)
2 Example 1: factoring quadratics: leading coefficient =1Special products of the form (x!a)(x+a)
Factoring quadratics as (x+a)(x+b)
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-grouping/a/factoring-quadratics-leading-coefficient-not-1?modal=1Factoring quadratics: common factor + groupinghttps://youtu.be/R-rhSQzFJL0Factoring quadratics: negative common factor + groupinghttps://youtu.be/d-2Lcp0QKfIIntroduction to difference of squareshttps://youtu.be/HLNSouzygw0Factoring quadratics: difference of squareshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/a/factoring-quadratics-difference-of-squares?modal=1https://youtu.be/jmbg-DKWuc4Factoring difference of squares: analyzing factorizationhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/v/equivalent-expressions-to-differences-of-squares?modal=1Factoring difference of squares: shared factorshttps://youtu.be/xYQR2LNZLeUIntroduction to perfect square factorizationhttps://youtu.be/JX5Zvh6swmoFactoring quadratics: perfect squareshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/a/factoring-quadratics-perfect-squares?modal=1Factoring perfect squareshttps://youtu.be/liRNTieIU_kIdentifying perfect square formhttps://youtu.be/4STGvuoBi5UFactoring perfect squares: negative common factorhttps://youtu.be/XuwldEyWjH0Factoring perfect squares: missing valueshttps://youtu.be/oIslHyWJHEYFactoring perfect squares: shared factorshttps://youtu.be/6jZZ6EeE-j0Strategy in factoring quadratics: part 1https://youtu.be/2hHyY1eyHQsStrategy in factoring quadratics: part 2https://youtu.be/ahPdiNQGXRAFactoring quadratics in any formhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-strategy/a/factoring-quadratics-in-any-form?modal=1TopicVideo/NotesFactoring quadratics: leading coefficient "1
Factoring difference of squares: leading coefficient "1Introduction to parabolashttps://youtu.be/BGz3pkoGPagGraphing quadratics in factored formhttps://youtu.be/EV57jv7JKCsQuadratic word problems: factored formhttps://youtu.be/xVZA6NOQA7ASolving quadratics by taking square rootshttps://youtu.be/RweAgQwLdMsSolving quadratics by taking square roots: noteshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/a/solving-quadratic-equations-by-taking-square-roots?modal=1Examples: solving quadratics by taking square rootshttps://youtu.be/VTlvg4wJ1X0Solving simple quadratics: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/a/solving-simple-quadratics-review?modal=1Introduction to vertex formhttps://youtu.be/_QqhuLixNEkGraphing quadratics: vertex formhttps://youtu.be/7QMoNY6FzvMQuadratic word problems: vertex formhttps://youtu.be/lUA1LYCoIAgSolving quadratics by factoringhttps://youtu.be/2ZzuZvz33X0https://youtu.be/KbFwLvCOBUIQuadratic equations word problem: triangle dimensionshttps://youtu.be/STcsaKuW-24Quadratic equations word problem: box dimensionshttps://youtu.be/vl9o9XEfXtwSolving quadratics by factoring: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratics-solve-factoring/a/solving-quadratics-by-factoring-review?modal=1The quadratic formulahttps://youtu.be/i7idZfS8t8wUnderstanding the quadratic formulahttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/a/quadratic-formula-explained-article?modal=1Example 1: quadratic formulahttps://youtu.be/CLrImGKeuEIExample 2: quadratic formula with negative coefficientshttps://youtu.be/_E3gx_yQhHQTopicVideo/NotesSolving quadratics by factoring: leading coefficient "1
Using the quadratic formula: number of solutionshttps://youtu.be/XUvKjC21fYUProof of the quadratic formulahttps://youtu.be/r3SEkdtpoboQuadratic formula: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/a/quadratic-formula-review?modal=1Discriminant: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/a/discriminant-review?modal=1Completing the squarehttps://youtu.be/bNQY0z76M5ASolving quadratics by completing the squarehttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/a/solving-quadratic-equations-by-completing-the-square?modal=1Example: completing the squarehttps://youtu.be/VvuuRpJbbHEExample: rewriting expressions by completing the squarehttps://youtu.be/sh-MP-dVhD4Example: solving equations by completing the squarehttps://youtu.be/KouDAzYl_bcSolving quadratics by completing the square: no solutionhttps://youtu.be/6agzj3A9IgACompleting the square: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/a/completing-the-square-review?modal=1Finding the vertex of a parabola in standard formhttps://youtu.be/IbI-l7mbKO4Graphing quadratics: standard formhttps://youtu.be/MQtsRYPx3v0Vertex & axis of symmetry of a parabolahttps://youtu.be/dfoXtodyiIAGraphing quadratics: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/a/graphing-quadratics-review?modal=1Introduction to parabola transformationshttps://youtu.be/99v51U3HSCUShifting parabolashttps://youtu.be/ZmVOR6n_fzYScaling & reflecting parabolashttps://youtu.be/AMsbZLxd3lETopicVideo/Notes
Polynomials
TopicVideo/NotesIntroduction to polynomialshttps://youtu.be/Vm7H0VTlIcoThe parts of polynomial expressionshttps://youtu.be/REiDXCN0lGUFinding average rate of change of polynomialshttps://youtu.be/neZeuTgEoMAAdding polynomialshttps://youtu.be/ahdKdxsTj8ESubtracting polynomialshttps://youtu.be/5ZdxnFspyP8Adding and subtracting polynomials: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:poly-add-sub/a/adding-and-subtracting-polynomials-review?modal=1Multiplying monomialshttps://youtu.be/7EplN4Ch98QMultiplying monomials by polynomials: area modelhttps://youtu.be/bkZYILrmFRUMultiplying monomials by polynomialshttps://youtu.be/pD2-H15ucNEMultiplying monomials by polynomials: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/a/multiplying-monomials-by-polynomials-review?modal=1Multiplying binomials by polynomials: area modelhttps://youtu.be/C9m5VEEyno8Multiplying binomials by polynomials https://youtu.be/D6mivA_8L8UMultiplying binomials by polynomials: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:bi-by-poly/a/multiplying-binomials-by-polynomials-review?modal=1Polynomial special products: difference of squareshttps://youtu.be/uNweU6I4IcwPolynomial special products: perfect squarehttps://youtu.be/hw5DE8HSZk0Introduction to factoring higher degree polynomials: part 1https://youtu.be/7y_2jQlnKagIntroduction to factoring higher degree monomials: part 2https://youtu.be/Kze7cw30F60
Taking common factor from binomialhttps://youtu.be/iTn3TTF0IXkTaking common factor from trinomialhttps://youtu.be/MZl6Mna0leQFactoring polynomials by taking a common factorhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:common-factor/a/taking-common-factors?modal=1Factoring higher degree polynomialshttps://youtu.be/AUBX_aHStQYFactoring higher-degree polynomials: common factorhttps://youtu.be/BFW2lHobO4EIdentifying quadratic patternshttps://youtu.be/OcavJJA8UygFactorization with substitutionhttps://youtu.be/js5cP-rq0FIFactoring using the perfect square patternhttps://youtu.be/o-ZbdYVGehIFactoring using the difference of squares patternhttps://youtu.be/tvnOWIoeeaUIntroduction to polynomial identitieshttps://youtu.be/EvNKKyhLSpQAnalyzing polynomial identitieshttps://youtu.be/-6qiO49Q180Polynomial division introductionhttps://youtu.be/3eowXt_LNbghttps://youtu.be/HUdA6LdCRk8https://youtu.be/UquFdMg6Z_UIntro to long division of polynomialshttps://youtu.be/FXgV9ySNuscDividing quadratics by linear expressions (no remainders)https://youtu.be/dRvLVdQ8cw4Dividing quadratics by linear expressions with remaindershttps://youtu.be/-veSAbfer7Qhttps://youtu.be/CDJGU9P_pGUDividing polynomials by linear expressionshttps://youtu.be/G2VBRwXq1q4Dividing polynomials by linear expressions: missing termhttps://youtu.be/QTZ5Dn0t6M4Divide polynomials by monomials with remaindershttps://youtu.be/WqNc6My1aNUDividing polynomials with remaindershttps://youtu.be/pLCmwHsDYqoThe Fundamental theorem of Algebrahttps://youtu.be/d8-LO6FCna0Quadratics & the Fundamental Theorem of Algebrahttps://youtu.be/zNxEVaRbdusTopicVideo/NotesDividing polynomials by (no remainders)x
Dividing quadratics by linear expressions with remainders: missing -termxDivide polynomials by (with remainders)x
Number of possible real roots of a polynomialhttps://youtu.be/_HFTRQRpzFMFactoring using polynomial divisionhttps://youtu.be/I9PiXAbjnMQFactoring using polynomial division: missing termhttps://youtu.be/AkY3DGzrvk8Introduction to the Polynomial Remainder Theoremhttps://youtu.be/MwG6QD352ycRemainder theorem: finding remainder from equationhttps://youtu.be/MHtTP6vc4RUExamples: Remainder theoremhttps://youtu.be/dBOpC_-PDTARemainder theorem: checking factorshttps://youtu.be/JAdNNJynWM4Remainder theorem: finding coefficientshttps://youtu.be/e0lBUViss8EProof of the Polynomial Remainder Theoremhttps://youtu.be/NIazpCER9oMZeros of polynomials introductionhttps://youtu.be/EtzwLlkoAnMZeros of polynomials: plotting zeroshttps://youtu.be/5qQUN1fugXQZeros of polynomials: matching equation to zeroshttps://youtu.be/CtqwiX4wHEYZeros of polynomials: matching equation to graphhttps://youtu.be/f-xluUaAfwoZeros of polynomials with factoring: groupinghttps://youtu.be/w0vTAHIS5B4Zeros of polynomials with factoring: common factorhttps://youtu.be/SONskIMkYdUPositive and negative intervals of polynomialshttps://youtu.be/z3faK7OV3EwMultiplicity of zeros of polynomialshttps://youtu.be/jrFLb9ZoZH0Zeros of polynomials: multiplicityhttps://youtu.be/1ke_xceCevkZeros of polynomials & their graphshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/a/zeros-of-polynomials-and-their-graphs?modal=1Positive & negative intervals of polynomialshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/a/positive-and-negative-intervals-of-polynomials?modal=1Introduction to end behaviour of polynomialshttps://youtu.be/tZKzaF28sOkEnd behaviour of polynomialshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-end-behavior/a/end-behavior-of-polynomials?modal=1TopicVideo/Notes
Right triangles and Trigonometry
Graphs of polynomialshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-graphs-together/a/graphs-of-polynomials?modal=1Graphs of polynomials: challenge problemshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-graphs-together/a/graphs-of-polynomials-challenge-problems?modal=1TopicVideo/NotesTopicVideo/NotesIntroduction to the Pythagorean theorem: part 1https://youtu.be/AA6RfgP-AHUIntroduction to the Pythagorean theorem: part 2https://youtu.be/AEIzy1kNRqoPythagorean theorem word problem: fishing boathttps://youtu.be/JVrkLIcA2qwExample: Pythagorean theoremhttps://youtu.be/O64YFlX1_aIPythagorean theorem word problem: carpethttps://youtu.be/T0IOrRETWhIIntroduction to the trigonometric ratioshttps://youtu.be/Jsiy4TxgIMETrigonometric ratios in right triangleshttps://youtu.be/G-T_6hCdMQcHypotenuse, opposite, and adjacenthttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/a/opposite-adjacent-hypotenuse?modal=1Trigonometric ratios in right triangleshttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/a/finding-trig-ratios-in-right-triangles?modal=1Solving for a side in right triangles with trigonometryhttps://youtu.be/l5VbdqRjTXcSolving for a side in right triangles with trigonometryhttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-a-side/a/unknown-side-in-right-triangle-w-trig?modal=1Introduction to inverse trig functionshttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-an-angle/a/inverse-trig-functions-intro?modal=1Right triangle: word problemhttps://youtu.be/aHzd-u35LuAAngles of elevation and depressionhttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/a/angles-of-elevation-and-depression?modal=1
Right triangle trigonometry: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/a/right-triangle-trigonometry-review?modal=1Triangle similarity & the trigonometric ratioshttps://youtu.be/QuZMXVJNLCoSine & cosine of complementary angleshttps://youtu.be/BLQNL_UGONgUsing complementary angleshttps://youtu.be/yiH6GoscimYTrig word problem: complementary angleshttps://youtu.be/Z5EnuVJawmYSolving for a side with the law of sineshttps://youtu.be/VjmFKle7xIwSolving for an angle with the law of sineshttps://youtu.be/IJySBMtFlnQProof of the law of sineshttps://youtu.be/APNkWrD-U1kSolving for a side with the law of cosineshttps://youtu.be/ZElOxG7_m3cSolving for an angle with the law of cosineshttps://youtu.be/Ei54NnQ0FKsProof of the law of cosineshttps://youtu.be/pGaDcOMdw48Laws of sines and cosines: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solving-general-triangles/a/laws-of-sines-and-cosines-review?modal=1Introduction to radianshttps://youtu.be/EnwWxMZVBegRadians & degreeshttps://youtu.be/z8vj8tUCkxYDegrees to radianshttps://youtu.be/O3jvUZ8wvZsRadians to degreeshttps://youtu.be/z0-1gBy1ykEhttps://youtu.be/sjUhr0HkLUghttps://youtu.be/08zHioOVTd4https://youtu.be/FK6-tZ5D7xMFeatures of sinusoidal functionshttps://youtu.be/s4cLM0l1gd4Amplitude & period of sinusoidal functions from equationhttps://youtu.be/SBqnRja4CW4Amplitude & period of sinusoidal functions from equationhttps://youtu.be/SBqnRja4CW4Midline, amplitude, and period: reviewhttps://www.khanacademy.org/math/trigonometry/trig-function-graphs/period-of-sinusoids/a/midline-amplitude-and-period-review?modal=1Transforming sinusoidal graphs: vertical stretch & horizontal reflectionhttps://youtu.be/0zCcFSO8ouETopicVideo/NotesGraph of y=tanx
Intersection points of and y=sinxy=cosx
Graph of y=sinx
Transforming sinusoidal graphs: vertical & horizontal stretcheshttps://youtu.be/uBVhtGL9y88Sinusoidal function from graphhttps://youtu.be/yHo0CcDVHskTrig word problem: modelling daily temperaturehttps://youtu.be/RX0DY9eRp8gTrig word problem: modeling annual temperaturehttps://youtu.be/mVlCXkht6hgTrig word problem: length of day (phase shift)https://youtu.be/MJBjGnR6vlkhttps://youtu.be/JGU74wbZMLghttps://youtu.be/Idxeo49szW0https://youtu.be/eTDaJ4ebK28Restricting domains of functions to make them invertiblehttps://youtu.be/tCV9VyIIaw0Domain & range of inverse tangent functionhttps://youtu.be/QGfdhqbilY8Using inverse trig functions with a calculatorhttps://youtu.be/MABWdzmZFIQInverse trigonometric functions: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:inverse-trig/a/inverse-trigonometric-functions-review?modal=1https://youtu.be/NC7iWEQ9Kughttps://youtu.be/SdHwokUU8xITrig word problem: solving for temperaturehttps://youtu.be/2pwnr_soZEUTrigonometric equations: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:sinus-models/a/trigonometric-equations-review?modal=1Sine & cosine identities: symmetryhttps://youtu.be/tzQ7arA917ETangent identities: symmetryhttps://youtu.be/k_wJsio68D4Sine & cosine identities: periodicityhttps://youtu.be/h-TPSylHrvETangent identities: periodicityhttps://youtu.be/C3HFAyigqoYReview of trig angle addition identitieshttps://youtu.be/a70-dYvDJZYUsing the cosine angle addition identityhttps://youtu.be/h0SNEO25vIwUsing the cosine double-angle identityhttps://youtu.be/D_smr0GBPvAProof of the sine angle addition identityhttps://youtu.be/R0EQg9vgbQwProof of the cosine angle addition identityhttps://youtu.be/0VBQnR2h8XMTopicVideo/NotesIntroduction to arctanx
Solving and cos!=1cos!=!1
Introduction to arcsinx
Solving sinusoidal equations of the form sinx=d
Introduction to arccosx
Analytic Geometry and Circles
Finding trig values using angle addition identitieshttps://youtu.be/2RbKfRfzD-MUsing trig angle addition identities: finding side lengthshttps://youtu.be/sI789G6FBb4Using trig angle addition identities: manipulating expressionshttps://youtu.be/yV4Xa8XtmrcUsing trigonometric identitieshttps://youtu.be/4OEeVLo5V1oTrig identity referencehttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:using-trig-id/a/trig-identity-reference?modal=1TopicVideo/NotesTopicVideo/NotesDistance formulahttps://youtu.be/nyZuite17PcDistance formula: noteshttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/a/distance-formula?modal=1Midpoint formulahttps://youtu.be/Ez_-RwV9WVoMidpoint formula: noteshttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/a/midpoint-formula?modal=1Distance formula: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/a/distance-formula-review?modal=1Midpoint formula: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/a/midpoint-formula-review?modal=1Dividing line segments: graphicalhttps://youtu.be/0rlNHYHhrWsDividing line segmentshttps://youtu.be/lEGS5ECgFxEIntroduction to parallel & perpendicular lineshttps://youtu.be/V0xounKGEXsParallel & perpendicular lines from graphhttps://youtu.be/6riBTnlI4fwExample 1: parallel lines from equationhttps://youtu.be/T-aCweuimisExample 2: parallel lines from equationhttps://youtu.be/lOWXZFP8VucExample 3: parallel lines from equationhttps://youtu.be/y5yNi08cr6IPerpendicular lines from equationhttps://youtu.be/0671cRNjeKI
Complex Numbers
Example 1: writing equations of perpendicular lineshttps://youtu.be/TsEhZRT16LUExample 2: writing equations of perpendicular lineshttps://youtu.be/8m8hFcFJ-JMProof: parallel lines have the same slopehttps://youtu.be/9ZYoIliBXYEProof: perpendicular lines have opposite reciprocal slopeshttps://youtu.be/HyThzLRuqXoCircles glossaryhttps://youtu.be/U2W7HPyC0cMhttps://youtu.be/jyLRpr2P0MQIntroduction to arc measurehttps://youtu.be/_H4jllna_ecFinding arc measureshttps://youtu.be/GOA9XWEo7QIFinding arc measures with equationshttps://youtu.be/bsDu8VQKwxAArc length from subtended anglehttps://youtu.be/tVcasOt55LcSubtended angle from arc lengthhttps://youtu.be/1BH2TNzAAikArc length as fraction of circumferencehttps://youtu.be/XFI7GK4Nv-sArc length from subtended angle: radianshttps://youtu.be/dtQyiDMoub4Area of a sectorhttps://youtu.be/u8JFdwmBvvQInscribed angleshttps://youtu.be/aNi1-zeEps8Graphing circles from featureshttps://youtu.be/LDjMDIuTWtMFeatures of a circle from its graphhttps://youtu.be/SLyM_-sQwMMFeatures of a circle from its standard equationhttps://youtu.be/JvDpYlyKkNUGraphing a circle from its standard equationhttps://youtu.be/thDrJvWNI8MWriting standard equation of a circlehttps://youtu.be/iX5UgArMyiIFeatures of a circle from its expanded equationhttps://youtu.be/XyDMsotfJhECircle equation: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-circle-expanded-equation/a/circle-equation-review?modal=1TopicVideo/NotesRadius, diameter, circumference & "
TopicVideo/NotesIntroduction to the imaginary numbershttps://youtu.be/ysVcAYo7UPIPowers of the imaginary unithttps://youtu.be/QiwfF83NWNASimplifying roots of negative numbershttps://youtu.be/s03qez-6JMAhttps://youtu.be/rYG1D5lUE4IIntroduction to complex numbershttps://youtu.be/SP-YJe7VldoClassifying complex numbershttps://youtu.be/A_ESfuN1PkgPlotting numbers on the complex planehttps://youtu.be/kGzXIbauGQkThe complex planehttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-plane/a/the-complex-plane?modal=1Adding complex numbershttps://youtu.be/SfbjqVyQljkSubtracting complex numbershttps://youtu.be/tvXRaZbIjO8Distance & midpoint of complex numbershttps://youtu.be/Efoeqb6tC88Multiplying complex numbershttps://youtu.be/cWn6g8Qqvs4Complex number operations: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul/a/complex-number-operations-review?modal=1Introduction to complex number conjugateshttps://youtu.be/BZxZ_eEuJBMComplex number conjugateshttps://youtu.be/dbxJ6LD0344Dividing complex numbershttps://youtu.be/Z8j5RDOibV4Dividing complex numbers: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-div/a/dividing-complex-numbers-review?modal=1Complex numbers & sum of squares factorizationhttps://youtu.be/8TPofjGXDR4Factoring sum of squareshttps://youtu.be/C3QPTCwpIZoAbsolute value of complex numbershttps://youtu.be/yvzyC4VBpUUAbsolute value & angle of complex numbershttps://youtu.be/FwuPXchH2rAComplex number absolute value & angle: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-abs-angle/a/complex-number-absolute-value-and-angle-review?modal=1Polar & rectangular forms of complex numbershttps://youtu.be/8RasCV_LgggTopicVideo/Notes as the principal root of -1i
Vectors
Complex number forms: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-polar/a/complex-number-forms-review?modal=1Dividing complex numbers: polar & exponential formhttps://youtu.be/xOa-l_tXgWAVisualizing complex number multiplicationhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/a/visualizing-complex-multiplication?modal=1Powers of complex numbershttps://youtu.be/dl_9NC_J6yohttps://youtu.be/N0Y8ia57C24Visualizing complex number powershttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/a/visualizing-complex-powers?modal=1Complex number polar form: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/a/complex-number-polar-form-review?modal=1Solving quadratic equations: complex rootshttps://youtu.be/dnjK4DPqh0kTopicVideo/NotesComplex number equations: x
3 =1TopicVideo/NotesIntroduction to vectors and scalarshttps://youtu.be/ihNZlp7iUHERecognizing vectorshttps://youtu.be/n8Ic2Oj-zvARecognizing vectors practicehttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vectors-intro/a/recognizing-vectors?modal=1Equivalent vectorshttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vectors-intro/v/equivalent-vectors-examples?modal=1Example 1: components of vectorshttps://youtu.be/BmDph4uNfPIExample 2: components of vectorshttps://youtu.be/v7ZZ1ctT1k0Vector magnitude from graphhttps://youtu.be/-U53eHKCLcgVector magnitude from componentshttps://youtu.be/qMZnsj4ZO9g
Vector magnitude from initial & terminal pointshttps://youtu.be/jfaSZhNFEOEScalar multiplication of vectorshttps://youtu.be/JuTvjQgpUMQAnalyzing scalar multiplicationhttps://youtu.be/kLLsJXc1E1EAdding & subtracting vectorshttps://youtu.be/VgqsM-XdBD0Graphically adding & subtracting vectorshttps://youtu.be/BsBH8nAv5l4Graphically subtracting vectorshttps://youtu.be/coDfeoi2zcQAdding vectors algebraically & graphicallyhttps://youtu.be/8QihetGj3pgCombined vector operationshttps://youtu.be/TdhbEonaHrcVector operations: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vec-ops/a/vector-operations-review?modal=1Introduction to unit vectorshttps://youtu.be/9ylUcCOTH8YExample: finding unit vector with given directionhttps://youtu.be/jCkhbKFZgLkExample: finding unit vector with given directionhttps://youtu.be/jCkhbKFZgLkExample: scaling unit vectorshttps://youtu.be/OFBI_rNDZE0Direction of vectors from components: 1st & 2nd quadrantshttps://youtu.be/A3OuFLHum6wDirection of vectors from components: 3rd & 4th quadrantshttps://youtu.be/EX0Ha42WQ24Vector forms: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:magnitude-direction/a/vector-forms-review?modal=1Vector components from magnitude & directionhttps://youtu.be/MkFbisCyjFcVector components from magnitude & direction: advancedhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:component-form/a/vector-component-form-no-direction-angle?modal=1Vector magnitude and direction: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:component-form/a/vector-magnitude-and-direction-review?modal=1Adding vectors in magnitude & direction form: part 1https://youtu.be/6Kw2nIwWYL0TopicVideo/Notes
Coins Sections
Adding vectors in magnitude & direction form: part 2https://youtu.be/SjY5UytlTTsVector addition & magnitudehttps://youtu.be/0t8W4JFpP2MVectors word problem: pushing a boxhttps://youtu.be/9A8wM1UMLyoVectors word problem: tug of warhttps://youtu.be/KNklNvGof8oVectors word problem: hikinghttps://youtu.be/cf1-CwrDwrATopicVideo/NotesTopicVideo/NotesIntroduction to conic sectionshttps://youtu.be/0A7RR0oy2hoIntroduction to ellipseshttps://youtu.be/lvAYFUIEpFIEllipse standard equation from graphhttps://youtu.be/_JrQF8RkaioEllipse graph from standard equationhttps://youtu.be/h5dIVNjVjXgEllipse features: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/a/ellipse-features-review?modal=1Ellipse equation: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/a/ellipse-equation-review?modal=1Foci of an ellipse from equationhttps://youtu.be/QR2vxfwiHAUEllipse foci: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-foci/a/ellipse-foci-review?modal=1Introduction to focus & directrixhttps://youtu.be/pe8Dm_FUpdUEquation of a parabola from focus & directrixhttps://youtu.be/okXVhDMuGFgFocus & directrix of a parabola from equationhttps://youtu.be/w56Vuf9tHfAParabola focus & directrix: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:parab-focus-directrix/a/parabola-focus-directrix-review?modal=1Introduction to hyperbolashttps://youtu.be/pzSyOTkAsY4Example 1: vertices & direction of a hyperbolahttps://youtu.be/oO3nWnJppqg
Example 2: vertices & direction of a hyperbolahttps://youtu.be/hnVFThmLW5QExample: graphing hyperbolashttps://youtu.be/hl58vTCqVIYFoci of a hyperbola from equationhttps://youtu.be/S0Fd2Tg2v7MProof of the hyperbola foci formulahttps://youtu.be/HPRFmu7JsKUEquation of a hyperbola not centered at the originhttps://youtu.be/lGQw-W1PxBERepresenting a line tangent to a hyperbolahttps://youtu.be/c_8QQbVQKU0Common tangent of circle & hyperbola: part 1https://youtu.be/MhLfun2VaskCommon tangent of circle & hyperbola: part 2https://youtu.be/0imeUgSxR10Common tangent of circle & hyperbola: part 3https://youtu.be/RomnHMWSLoECommon tangent of circle & hyperbola: part 4https://youtu.be/eGo8C2JshzsCommon tangent of circle & hyperbola: part 5https://youtu.be/rPoqpQcgNv4Intersection of circle & hyperbolahttps://youtu.be/6g3DPg2HqGwTopicVideo/Notes
Secondary V Foundations of Algebra
Equations and Inequalities
TopicVideo/NotesOrigins of algebrahttps://youtu.be/_LDR1_PrveoThe beauty of algebrahttps://youtu.be/kpCJyQ2usJ4What is a variable?https://youtu.be/tHYis-DP0oUEvaluating an expression with one variablehttps://youtu.be/AJNDeVt9UOoEvaluating expressions with two variableshttps://youtu.be/S_OX3ByvBScEvaluating expressions with two variables: fractions & decimalshttps://youtu.be/GmD7Czmol0kIntroduction to combining like termshttps://youtu.be/CLWpkv6ccpASimplifying expressionshttps://youtu.be/3NHSwiv_pSECombining like terms: challenge problemhttps://youtu.be/FNnmseBlvaYSimplifying expressions with rational numbershttps://youtu.be/rtNuo7R3scYEquivalent expressionshttps://youtu.be/rHNY01R2VSQWhy dividing by zero is undefinedhttps://youtu.be/SQzjzStU1RQUndefined & indeterminate expressionshttps://youtu.be/lHdlHTsXbZgTopicVideo/NotesLinear equationshttps://youtu.be/1c5HY3z4k8MEquation with fractionshttps://youtu.be/PL9UYj2awDcEquation with the variable in the denominatorhttps://youtu.be/Z7C69xP08d8Equations with parentheseshttps://youtu.be/YZBStgZGyDYEquation with no solutionshttps://youtu.be/uQs100shv-AEquation with infinitely many solutionshttps://youtu.be/Dq0xFgQB9qoInequalities with variables on both sideshttps://youtu.be/SgKBBUFaGb4Inequalities with variables on both sideshttps://youtu.be/XOAn5z8mkvICompound inequalities: ORhttps://youtu.be/0YErxSShF0A
Compound inequalities: ANDhttps://youtu.be/d2cnQ5ahHgEA compound inequality with no solutionhttps://youtu.be/ZF_cZ-GX9PIDouble inequalitieshttps://youtu.be/cvB8b4AACyECompound inequalities: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:compound-inequalities/a/compound-inequalities-review?modal=1Introduction to two-variable linear equationshttps://youtu.be/AOxMJRtoR2ASolutions to two-variable equationshttps://youtu.be/qk69pR91R00Example: solutions to two-variable equationshttps://youtu.be/d3VMo1VWFvcIntroduction to slopehttps://youtu.be/MeU-KzdCBpsPositive & negative slopehttps://youtu.be/EQoNfxToez0Example: slope from graphhttps://youtu.be/R948Tsyq4vAGraphing a line given point and slopehttps://youtu.be/5mgH-_5UJ54Example: slope from two pointshttps://youtu.be/WkspBxrzuZoSlope: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/a/slope-review?modal=1Slope of a horizontal linehttps://youtu.be/CFSHq099Mx0Horizontal & vertical lineshttps://youtu.be/J43CIbKpdWcIntroduction to interceptshttps://youtu.be/LNSB0N6esPUhttps://youtu.be/xiIQQNufFuUIntercepts from an equationhttps://youtu.be/xGmef7lFc5whttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:x-intercepts-and-y-intercepts/a/intercepts-of-lines-review-x-intercepts-and-y-intercepts?modal=1Linear functions word problem: fuelhttps://youtu.be/AAmVITyDXbcIntroduction to slope-intercept formhttps://youtu.be/IL3UCuXrUzEIntroduction to slope-intercept form: noteshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:intro-to-slope-intercept-form/a/introduction-to-slope-intercept-form?modal=1TopicVideo/Notes-intercept of a linex
Intercepts of lines review (-intercepts and -intercepts)xyhttps://youtu.be/Z65mz__8DQ0Examples: slope-intercepthttps://youtu.be/qgsNNqmlLoALinear equation: word problemshttps://youtu.be/w6R8rywmgekGraph from slope-intercept equationhttps://youtu.be/uk7gS3cZVp4Graphing lines from slope-intercept form: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:graphing-slope-intercept-equations/a/graphing-lines-review?modal=1Slope-intercept equation from graphhttps://youtu.be/9wOalujeZf4Writing slope-intercept equationshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:writing-slope-intercept-equations/a/writing-slope-intercept-equations?modal=1Slope-intercept equation from slope & pointhttps://youtu.be/AqFwKecNaTkSlope-intercept equation from two pointshttps://youtu.be/XMJ72mtMn4YConstructing linear equations from contexthttps://youtu.be/hBpI9IfmMKgSlope-intercept form: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:writing-slope-intercept-equations/a/slope-intercept-form-review?modal=1Introduction to point-slope formhttps://youtu.be/K_OI9LA54AAPoint-slope & slope-intercept equationshttps://youtu.be/LtpXvUCrgrMPoint-slope form: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:point-slope-form/a/point-slope-form-review?modal=1Introduction to linear equation standard formhttps://youtu.be/6CFE60iP2Ughttps://youtu.be/86NwKBcOlowConverting from slope-intercept to standard formhttps://youtu.be/XOIhNVeLfWsForms of linear equations: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:summary-forms-of-two-variable-linear-equations/a/forms-of-linear-equations-review?modal=1TopicVideo/NotesSlope and -intercept from equationy
Graphing a linear equation: 5x+2y=20
Functions
TopicVideo/NotesWhat is a function?https://youtu.be/kvGsIo1TmsMExample: Evaluating functionshttps://youtu.be/Id6UovYjd-MExample: Evaluating functions from graphhttps://youtu.be/kzYtx_AqzjMEvaluating discrete functionshttps://youtu.be/Ddw8u7nNmKsExample: evaluating expressions with function notationhttps://youtu.be/uaPm3TpuxbcExample: matching an input to a function's output (equation)https://youtu.be/tJBQZ3PUkPoExample: matching an input to a function's output (graph)https://youtu.be/0Rmmynff5YcExample: two inputs with the same output (graph)https://youtu.be/qSktOkaW6EAEquations vs. functionshttps://youtu.be/l3iXON1xEC4Obtaining a function from an equationhttps://youtu.be/OOim0QPsJ9oFunction notation word problem: bankhttps://youtu.be/HERb3x0aw6cFunction notation word problem: beachhttps://youtu.be/94Gnto5G1PUIntervals and interval notationhttps://youtu.be/UJQkqV2zGv0What is the domain of a function?https://youtu.be/-DTMakGDZAwWhat is the range of a function?https://youtu.be/96uHMcHWD2EExample: domain and range from graphhttps://youtu.be/sXP7VhU1gYEDetermining whether values are in domain of functionhttps://youtu.be/LdbrNNheFg8Examples: finding the domain of functionshttps://youtu.be/4ZWbeESjv4MRecognizing functions from graphhttps://youtu.be/qGmJ4F3b5W8Does a vertical line represent a function?https://youtu.be/_npwsLh0vwsRecognizing functions from tablehttps://youtu.be/5cK86VKoBPwIntroduction to minimum and maximum pointshttps://youtu.be/Hoyv3-BMAGcExample: absolute and relative extremahttps://youtu.be/xmrhZ5ySaD0Increasing, decreasing, positive or negative intervalshttps://youtu.be/KxOp3s9ottgExample: positive & negative intervalshttps://youtu.be/eDv7dk9uNmM
Graph interpretation word problem: temperaturehttps://youtu.be/VtBRkjRua0IIntroduction to average rate of changehttps://youtu.be/oT6LclcJ-I8Example: average rate of change from graphhttps://youtu.be/TEXSW-o8674Example: average rate of change from tablehttps://youtu.be/U1lQbh21y1kAverage rate of change word problem: graphhttps://youtu.be/-6EqUILZ1ywAverage rate of change: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:average-rate-of-change-word-problems/a/average-rate-of-change-review?modal=1Introduction to inverse functionshttps://youtu.be/W84lObmOp8MIntroduction to inverse functions: noteshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/a/intro-to-inverse-functions?modal=1Inputs & outputs of inverse functionshttps://youtu.be/KzaPBzFFLRMGraphing the inverse of a linear functionhttps://youtu.be/KPeS2gdizhQFinding inverse functions: linearhttps://youtu.be/wSiamij_i_kIntroduction to composing functionshttps://youtu.be/wUNWjd4bMmwIntroduction to composing functions: noteshttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/a/introduction-to-function-composition?modal=1Composing functionshttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/a/finding-and-evaluating-composite-functions?modal=1Evaluating composite functionshttps://youtu.be/lxtlwnCV-HMEvaluating composite functions: using tableshttps://youtu.be/FR8JH6IldsEEvaluating composite functions: using graphshttps://youtu.be/oORnGaJp1pkFinding composite functionshttps://youtu.be/_b-2rZpX5z4Evaluating composite functions: advancedhttps://youtu.be/jlID_mIJXi4Example 1: Modeling with composite functionshttps://youtu.be/pIMfRbznxKAExample 2: Modeling with composite functionshttps://youtu.be/LG6g7gxupHgVerifying inverse functions by compositionhttps://youtu.be/8GEGnSEJA2sTopicVideo/Notes
Verifying inverse functions by composition: noteshttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:verifying-inverse/a/verifying-inverse-functions-by-composition?modal=1Verifying inverse functions by composition: not inversehttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:compositeIntroduction to piecewise functionshttps://youtu.be/tedzsRH0JasExample: evaluating piecewise functionshttps://youtu.be/hg2HR9zJFq4Example: graphing piecewise functionshttps://youtu.be/PQiXRrT_14oExample: domain & range of step functionhttps://youtu.be/4n7TIvRHuDsExample: domain & range of piecewise linear functionshttps://youtu.be/rpI-X9Gn5a4Shifting functions: introductionhttps://youtu.be/RttvubuBhAEShifting functions: exampleshttps://youtu.be/MDav5OMpCtoGraphing shifted functionshttps://youtu.be/5DLkB-g8Rr8Reflecting functions: introductionhttps://youtu.be/mR2y_kohZIwExamples: Reflecting functionshttps://youtu.be/0QOnEoQHZ1kFunction symmetry: introductionhttps://youtu.be/4dOQePLgqxEFunction symmetry: introduction, noteshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:symmetry/a/intro-to-symmetry-of-functions?modal=1Even and odd functions: Graphshttps://youtu.be/zltgXTlUVLwEven and odd functions: Tableshttps://youtu.be/eKwJlJUM_d0Even and odd functions: Equationshttps://youtu.be/fTeO-V_VgEcEven and odd functions: Find the mistakehttps://youtu.be/RAksvTJWgxoSymmetry of polynomialshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:symmetry/a/symmetry-of-polynomials?modal=1Scaling functions: introductionhttps://youtu.be/1lt6a77OmLUExamples: Scaling functions verticallyhttps://youtu.be/tRCEBtKLqEwExample: Scaling functions horizontallyhttps://youtu.be/npMMbXm9sR0Identifying horizontal squash from graphhttps://youtu.be/4H5JZnytOfEIdentifying function transformationshttps://youtu.be/ENFNyNPYfZUTopicVideo/Notes
Exponents and Logarithms
Graphing square and cube root functionshttps://youtu.be/PI6IV7K3DbMRadical functions & their graphshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:radical-graphs/a/match-the-formula-of-a-radical-function-to-its-graph?modal=1Example 1: Transforming exponential graphshttps://youtu.be/83gM3ufe1NwExample 2: Transforming exponential graphshttps://youtu.be/ja4WRZ4DrAwGraphing exponential functionshttps://youtu.be/vlSEpdWf2hQhttps://youtu.be/K_PiPfYxtaoExample 1: Graphing logarithmic functionshttps://youtu.be/GpBSbNoon1EExample 2: Graphing logarithmic functionshttps://youtu.be/f_BJC6UwDTETopicVideo/NotesGraphical relationship between and 2
x log 2 xTopicVideo/NotesMultiplying & dividing powers: integer exponentshttps://youtu.be/CZ5ne_mX5_IPowers of products & quotients: integer exponentshttps://youtu.be/dC1ojsMi1yUIntroduction to square rootshttps://youtu.be/mbc3_e5lWw0Understanding square rootshttps://youtu.be/ROIfbUQrSY4Square root of decimalhttps://youtu.be/tRHLEWSUjrQIntroduction to cube rootshttps://youtu.be/87_qIofPwhg5th rootshttps://youtu.be/8wrtyW1RwNkHigher order rootshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/a/higher-order-roots?modal=1Simplifying square rootshttps://youtu.be/cw3mp8oNASkSimplifying square roots: variableshttps://youtu.be/qFFhdLlX220Simplifying square-root expressionshttps://youtu.be/3MijXB91DVoSimplifying square roots: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/a/simplifying-square-roots-review?modal=1
Introduction to exponential functionshttps://youtu.be/6WMZ7J0wwMIGraphing exponential functionhttps://youtu.be/9SOSfRNCQZQExponential vs. linear growthhttps://youtu.be/_vlXdx-CqM0Exponential expressions word problems: numericalhttps://youtu.be/L70UJVjc-bcExponential expressions word problems: algebraichttps://youtu.be/Z3YVZzCEi_AGraphs of exponential growthhttps://youtu.be/6rX2VNybXEEIntroduction to exponential decayhttps://youtu.be/v4IdaXvyE7UGraphing exponential growth & decayhttps://youtu.be/RVv0Jgi3PbwWriting exponential functionshttps://youtu.be/UgLfAb_aFt4Writing exponential functions from tableshttps://youtu.be/Qst1UVtq8pEWriting exponential functions from graphshttps://youtu.be/gFdh_rE2XgUModeling with basic exponential functions word problemhttps://youtu.be/2iZXFd_ZImALinear vs. exponential growth: from datahttps://youtu.be/721RrH6auoUIntroduction to logarithmshttps://youtu.be/Z5myJ8dg_rMIntroduction to logarithms: noteshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/a/intro-to-logarithms?modal=1Evaluating logarithms: advancedhttps://youtu.be/eTWCARmrzJ0Relationship between exponentials & logarithmshttps://youtu.be/Obch1OP5QyARelationship between exponentials & logarithms: graphshttps://youtu.be/DhW9pz5VfwoRelationship between exponentials & logarithms: tableshttps://youtu.be/Iz6IVf8frjwhttps://youtu.be/BKGx8GMVu88https://youtu.be/oQhp3ndj28YEvaluating natural logarithm with calculatorhttps://youtu.be/Dpo_-GrMpNEIntroduction to logarithm properties: part 1https://youtu.be/PupNgv49_WYIntroduction to logarithm properties: part 2https://youtu.be/TMmxKZaCqe0TopicVideo/Notes and compound intereste
as a limiteIntroduction to logarithm properties: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logsUsing the logarithmic product rulehttps://youtu.be/pkGrXzakRFsUsing the logarithmic power rulehttps://youtu.be/Pb9V374iOasUsing the properties of logarithms: multiple stepshttps://youtu.be/RhzXX5PbsuQProof of the logarithm product rulehttps://youtu.be/FP2arCfAfBYProof of the logarithm quotient and power ruleshttps://youtu.be/yEAxG_D1HDwJustifying the logarithm propertieshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/a/justifying-the-logarithm-properties?modal=1Evaluating logarithms: change of base rulehttps://youtu.be/OkFdDqW9xxMLogarithm change of base rule: noteshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/a/logarithm-change-of-base-rule-intro?modal=1Using the logarithm change of base rulehttps://youtu.be/qtsMgdZ98YgProof of the logarithm change of base rulehttps://youtu.be/1reblXFlM6ILogarithm properties: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/a/logarithm-properties-review?modal=1Solving exponential equations using logarithms: base-10https://youtu.be/R443Db-wJ5oSolving exponential equations using logarithmshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/a/solving-exponential-equations-with-logarithms?modal=1Solving exponential equations using logarithms: base-2https://youtu.be/7Ig6kVZaWoUExponential model word problem: medication dissolvehttps://youtu.be/HnHCQ2X_megExponential model word problem: bacteria growthhttps://youtu.be/IpXL9HIkqUQTopicVideo/Notes
Quadratics
TopicVideo/NotesIntroduction to Polynomialshttps://youtu.be/Vm7H0VTlIcoMultiplying binomialshttps://youtu.be/ZMLFfTX615whttps://youtu.be/JfuisfEdnjkhttps://youtu.be/xH_GllPuymchttps://youtu.be/h6HmHjkA034https://youtu.be/xjkbR7GjgjsBinomial special products: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:special-product-binomials/a/binomial-special-products-review?modal=1Introduction to factors & divisibilityhttps://youtu.be/SjN3_xCJamAhttps://youtu.be/D3a8NnpQ2vUhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/a/factoring-quadratics-leading-coefficient-1?modal=1https://youtu.be/1kfq0aR3ASshttps://youtu.be/eF6zYNzlZKQFactoring simple quadratics: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/a/factoring-simple-quadratics-review?modal=1Introduction to groupinghttps://youtu.be/X7B_tH4O-_sFactoring by groupinghttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-grouping/a/factoring-by-grouping?modal=1Factoring quadratics by groupinghttps://youtu.be/u1SAo2GiX8ASquaring binomials of the form (ax+b)
2 More examples of factoring quadratics as (x+a)(x+b)Special products of the form (ax!b)(ax+b)
Example 2: factoring quadratics as (x+a)(x+b)
Squaring binomials of the form (x+a)
2 Example 1: factoring quadratics: leading coefficient =1Special products of the form (x!a)(x+a)
Factoring quadratics as (x+a)(x+b)
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-grouping/a/factoring-quadratics-leading-coefficient-not-1?modal=1Factoring quadratics: common factor + groupinghttps://youtu.be/R-rhSQzFJL0Factoring quadratics: negative common factor + groupinghttps://youtu.be/d-2Lcp0QKfIIntroduction to difference of squareshttps://youtu.be/HLNSouzygw0Factoring quadratics: difference of squareshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/a/factoring-quadratics-difference-of-squares?modal=1https://youtu.be/jmbg-DKWuc4Factoring difference of squares: analyzing factorizationhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/v/equivalent-expressions-to-differences-of-squares?modal=1Factoring difference of squares: shared factorshttps://youtu.be/xYQR2LNZLeUIntroduction to perfect square factorizationhttps://youtu.be/JX5Zvh6swmoFactoring quadratics: perfect squareshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/a/factoring-quadratics-perfect-squares?modal=1Factoring perfect squareshttps://youtu.be/liRNTieIU_kIdentifying perfect square formhttps://youtu.be/4STGvuoBi5UFactoring perfect squares: negative common factorhttps://youtu.be/XuwldEyWjH0Factoring perfect squares: missing valueshttps://youtu.be/oIslHyWJHEYFactoring perfect squares: shared factorshttps://youtu.be/6jZZ6EeE-j0Strategy in factoring quadratics: part 1https://youtu.be/2hHyY1eyHQsStrategy in factoring quadratics: part 2https://youtu.be/ahPdiNQGXRAFactoring quadratics in any formhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-strategy/a/factoring-quadratics-in-any-form?modal=1TopicVideo/NotesFactoring quadratics: leading coefficient "1
Factoring difference of squares: leading coefficient "1Introduction to parabolashttps://youtu.be/BGz3pkoGPagGraphing quadratics in factored formhttps://youtu.be/EV57jv7JKCsQuadratic word problems: factored formhttps://youtu.be/xVZA6NOQA7ASolving quadratics by taking square rootshttps://youtu.be/RweAgQwLdMsSolving quadratics by taking square roots: noteshttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/a/solving-quadratic-equations-by-taking-square-roots?modal=1Examples: solving quadratics by taking square rootshttps://youtu.be/VTlvg4wJ1X0Solving simple quadratics: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/a/solving-simple-quadratics-review?modal=1Introduction to vertex formhttps://youtu.be/_QqhuLixNEkGraphing quadratics: vertex formhttps://youtu.be/7QMoNY6FzvMQuadratic word problems: vertex formhttps://youtu.be/lUA1LYCoIAgSolving quadratics by factoringhttps://youtu.be/2ZzuZvz33X0https://youtu.be/KbFwLvCOBUIQuadratic equations word problem: triangle dimensionshttps://youtu.be/STcsaKuW-24Quadratic equations word problem: box dimensionshttps://youtu.be/vl9o9XEfXtwSolving quadratics by factoring: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratics-solve-factoring/a/solving-quadratics-by-factoring-review?modal=1The quadratic formulahttps://youtu.be/i7idZfS8t8wUnderstanding the quadratic formulahttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/a/quadratic-formula-explained-article?modal=1Example 1: quadratic formulahttps://youtu.be/CLrImGKeuEIExample 2: quadratic formula with negative coefficientshttps://youtu.be/_E3gx_yQhHQTopicVideo/NotesSolving quadratics by factoring: leading coefficient "1
Using the quadratic formula: number of solutionshttps://youtu.be/XUvKjC21fYUProof of the quadratic formulahttps://youtu.be/r3SEkdtpoboQuadratic formula: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/a/quadratic-formula-review?modal=1Discriminant: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/a/discriminant-review?modal=1Completing the squarehttps://youtu.be/bNQY0z76M5ASolving quadratics by completing the squarehttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/a/solving-quadratic-equations-by-completing-the-square?modal=1Example: completing the squarehttps://youtu.be/VvuuRpJbbHEExample: rewriting expressions by completing the squarehttps://youtu.be/sh-MP-dVhD4Example: solving equations by completing the squarehttps://youtu.be/KouDAzYl_bcSolving quadratics by completing the square: no solutionhttps://youtu.be/6agzj3A9IgACompleting the square: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/a/completing-the-square-review?modal=1Finding the vertex of a parabola in standard formhttps://youtu.be/IbI-l7mbKO4Graphing quadratics: standard formhttps://youtu.be/MQtsRYPx3v0Vertex & axis of symmetry of a parabolahttps://youtu.be/dfoXtodyiIAGraphing quadratics: reviewhttps://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/a/graphing-quadratics-review?modal=1Introduction to parabola transformationshttps://youtu.be/99v51U3HSCUShifting parabolashttps://youtu.be/ZmVOR6n_fzYScaling & reflecting parabolashttps://youtu.be/AMsbZLxd3lETopicVideo/Notes
Polynomials
TopicVideo/NotesIntroduction to polynomialshttps://youtu.be/Vm7H0VTlIcoThe parts of polynomial expressionshttps://youtu.be/REiDXCN0lGUFinding average rate of change of polynomialshttps://youtu.be/neZeuTgEoMAAdding polynomialshttps://youtu.be/ahdKdxsTj8ESubtracting polynomialshttps://youtu.be/5ZdxnFspyP8Adding and subtracting polynomials: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:poly-add-sub/a/adding-and-subtracting-polynomials-review?modal=1Multiplying monomialshttps://youtu.be/7EplN4Ch98QMultiplying monomials by polynomials: area modelhttps://youtu.be/bkZYILrmFRUMultiplying monomials by polynomialshttps://youtu.be/pD2-H15ucNEMultiplying monomials by polynomials: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/a/multiplying-monomials-by-polynomials-review?modal=1Multiplying binomials by polynomials: area modelhttps://youtu.be/C9m5VEEyno8Multiplying binomials by polynomials https://youtu.be/D6mivA_8L8UMultiplying binomials by polynomials: reviewhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:bi-by-poly/a/multiplying-binomials-by-polynomials-review?modal=1Polynomial special products: difference of squareshttps://youtu.be/uNweU6I4IcwPolynomial special products: perfect squarehttps://youtu.be/hw5DE8HSZk0Introduction to factoring higher degree polynomials: part 1https://youtu.be/7y_2jQlnKagIntroduction to factoring higher degree monomials: part 2https://youtu.be/Kze7cw30F60
Taking common factor from binomialhttps://youtu.be/iTn3TTF0IXkTaking common factor from trinomialhttps://youtu.be/MZl6Mna0leQFactoring polynomials by taking a common factorhttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:common-factor/a/taking-common-factors?modal=1Factoring higher degree polynomialshttps://youtu.be/AUBX_aHStQYFactoring higher-degree polynomials: common factorhttps://youtu.be/BFW2lHobO4EIdentifying quadratic patternshttps://youtu.be/OcavJJA8UygFactorization with substitutionhttps://youtu.be/js5cP-rq0FIFactoring using the perfect square patternhttps://youtu.be/o-ZbdYVGehIFactoring using the difference of squares patternhttps://youtu.be/tvnOWIoeeaUIntroduction to polynomial identitieshttps://youtu.be/EvNKKyhLSpQAnalyzing polynomial identitieshttps://youtu.be/-6qiO49Q180Polynomial division introductionhttps://youtu.be/3eowXt_LNbghttps://youtu.be/HUdA6LdCRk8https://youtu.be/UquFdMg6Z_UIntro to long division of polynomialshttps://youtu.be/FXgV9ySNuscDividing quadratics by linear expressions (no remainders)https://youtu.be/dRvLVdQ8cw4Dividing quadratics by linear expressions with remaindershttps://youtu.be/-veSAbfer7Qhttps://youtu.be/CDJGU9P_pGUDividing polynomials by linear expressionshttps://youtu.be/G2VBRwXq1q4Dividing polynomials by linear expressions: missing termhttps://youtu.be/QTZ5Dn0t6M4Divide polynomials by monomials with remaindershttps://youtu.be/WqNc6My1aNUDividing polynomials with remaindershttps://youtu.be/pLCmwHsDYqoThe Fundamental theorem of Algebrahttps://youtu.be/d8-LO6FCna0Quadratics & the Fundamental Theorem of Algebrahttps://youtu.be/zNxEVaRbdusTopicVideo/NotesDividing polynomials by (no remainders)x
Dividing quadratics by linear expressions with remainders: missing -termxDivide polynomials by (with remainders)x
Number of possible real roots of a polynomialhttps://youtu.be/_HFTRQRpzFMFactoring using polynomial divisionhttps://youtu.be/I9PiXAbjnMQFactoring using polynomial division: missing termhttps://youtu.be/AkY3DGzrvk8Introduction to the Polynomial Remainder Theoremhttps://youtu.be/MwG6QD352ycRemainder theorem: finding remainder from equationhttps://youtu.be/MHtTP6vc4RUExamples: Remainder theoremhttps://youtu.be/dBOpC_-PDTARemainder theorem: checking factorshttps://youtu.be/JAdNNJynWM4Remainder theorem: finding coefficientshttps://youtu.be/e0lBUViss8EProof of the Polynomial Remainder Theoremhttps://youtu.be/NIazpCER9oMZeros of polynomials introductionhttps://youtu.be/EtzwLlkoAnMZeros of polynomials: plotting zeroshttps://youtu.be/5qQUN1fugXQZeros of polynomials: matching equation to zeroshttps://youtu.be/CtqwiX4wHEYZeros of polynomials: matching equation to graphhttps://youtu.be/f-xluUaAfwoZeros of polynomials with factoring: groupinghttps://youtu.be/w0vTAHIS5B4Zeros of polynomials with factoring: common factorhttps://youtu.be/SONskIMkYdUPositive and negative intervals of polynomialshttps://youtu.be/z3faK7OV3EwMultiplicity of zeros of polynomialshttps://youtu.be/jrFLb9ZoZH0Zeros of polynomials: multiplicityhttps://youtu.be/1ke_xceCevkZeros of polynomials & their graphshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/a/zeros-of-polynomials-and-their-graphs?modal=1Positive & negative intervals of polynomialshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/a/positive-and-negative-intervals-of-polynomials?modal=1Introduction to end behaviour of polynomialshttps://youtu.be/tZKzaF28sOkEnd behaviour of polynomialshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-end-behavior/a/end-behavior-of-polynomials?modal=1TopicVideo/Notes
Right triangles and Trigonometry
Graphs of polynomialshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-graphs-together/a/graphs-of-polynomials?modal=1Graphs of polynomials: challenge problemshttps://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-graphs-together/a/graphs-of-polynomials-challenge-problems?modal=1TopicVideo/NotesTopicVideo/NotesIntroduction to the Pythagorean theorem: part 1https://youtu.be/AA6RfgP-AHUIntroduction to the Pythagorean theorem: part 2https://youtu.be/AEIzy1kNRqoPythagorean theorem word problem: fishing boathttps://youtu.be/JVrkLIcA2qwExample: Pythagorean theoremhttps://youtu.be/O64YFlX1_aIPythagorean theorem word problem: carpethttps://youtu.be/T0IOrRETWhIIntroduction to the trigonometric ratioshttps://youtu.be/Jsiy4TxgIMETrigonometric ratios in right triangleshttps://youtu.be/G-T_6hCdMQcHypotenuse, opposite, and adjacenthttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/a/opposite-adjacent-hypotenuse?modal=1Trigonometric ratios in right triangleshttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/a/finding-trig-ratios-in-right-triangles?modal=1Solving for a side in right triangles with trigonometryhttps://youtu.be/l5VbdqRjTXcSolving for a side in right triangles with trigonometryhttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-a-side/a/unknown-side-in-right-triangle-w-trig?modal=1Introduction to inverse trig functionshttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-an-angle/a/inverse-trig-functions-intro?modal=1Right triangle: word problemhttps://youtu.be/aHzd-u35LuAAngles of elevation and depressionhttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/a/angles-of-elevation-and-depression?modal=1
Right triangle trigonometry: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/a/right-triangle-trigonometry-review?modal=1Triangle similarity & the trigonometric ratioshttps://youtu.be/QuZMXVJNLCoSine & cosine of complementary angleshttps://youtu.be/BLQNL_UGONgUsing complementary angleshttps://youtu.be/yiH6GoscimYTrig word problem: complementary angleshttps://youtu.be/Z5EnuVJawmYSolving for a side with the law of sineshttps://youtu.be/VjmFKle7xIwSolving for an angle with the law of sineshttps://youtu.be/IJySBMtFlnQProof of the law of sineshttps://youtu.be/APNkWrD-U1kSolving for a side with the law of cosineshttps://youtu.be/ZElOxG7_m3cSolving for an angle with the law of cosineshttps://youtu.be/Ei54NnQ0FKsProof of the law of cosineshttps://youtu.be/pGaDcOMdw48Laws of sines and cosines: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solving-general-triangles/a/laws-of-sines-and-cosines-review?modal=1Introduction to radianshttps://youtu.be/EnwWxMZVBegRadians & degreeshttps://youtu.be/z8vj8tUCkxYDegrees to radianshttps://youtu.be/O3jvUZ8wvZsRadians to degreeshttps://youtu.be/z0-1gBy1ykEhttps://youtu.be/sjUhr0HkLUghttps://youtu.be/08zHioOVTd4https://youtu.be/FK6-tZ5D7xMFeatures of sinusoidal functionshttps://youtu.be/s4cLM0l1gd4Amplitude & period of sinusoidal functions from equationhttps://youtu.be/SBqnRja4CW4Amplitude & period of sinusoidal functions from equationhttps://youtu.be/SBqnRja4CW4Midline, amplitude, and period: reviewhttps://www.khanacademy.org/math/trigonometry/trig-function-graphs/period-of-sinusoids/a/midline-amplitude-and-period-review?modal=1Transforming sinusoidal graphs: vertical stretch & horizontal reflectionhttps://youtu.be/0zCcFSO8ouETopicVideo/NotesGraph of y=tanx
Intersection points of and y=sinxy=cosx
Graph of y=sinx
Transforming sinusoidal graphs: vertical & horizontal stretcheshttps://youtu.be/uBVhtGL9y88Sinusoidal function from graphhttps://youtu.be/yHo0CcDVHskTrig word problem: modelling daily temperaturehttps://youtu.be/RX0DY9eRp8gTrig word problem: modeling annual temperaturehttps://youtu.be/mVlCXkht6hgTrig word problem: length of day (phase shift)https://youtu.be/MJBjGnR6vlkhttps://youtu.be/JGU74wbZMLghttps://youtu.be/Idxeo49szW0https://youtu.be/eTDaJ4ebK28Restricting domains of functions to make them invertiblehttps://youtu.be/tCV9VyIIaw0Domain & range of inverse tangent functionhttps://youtu.be/QGfdhqbilY8Using inverse trig functions with a calculatorhttps://youtu.be/MABWdzmZFIQInverse trigonometric functions: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:inverse-trig/a/inverse-trigonometric-functions-review?modal=1https://youtu.be/NC7iWEQ9Kughttps://youtu.be/SdHwokUU8xITrig word problem: solving for temperaturehttps://youtu.be/2pwnr_soZEUTrigonometric equations: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:sinus-models/a/trigonometric-equations-review?modal=1Sine & cosine identities: symmetryhttps://youtu.be/tzQ7arA917ETangent identities: symmetryhttps://youtu.be/k_wJsio68D4Sine & cosine identities: periodicityhttps://youtu.be/h-TPSylHrvETangent identities: periodicityhttps://youtu.be/C3HFAyigqoYReview of trig angle addition identitieshttps://youtu.be/a70-dYvDJZYUsing the cosine angle addition identityhttps://youtu.be/h0SNEO25vIwUsing the cosine double-angle identityhttps://youtu.be/D_smr0GBPvAProof of the sine angle addition identityhttps://youtu.be/R0EQg9vgbQwProof of the cosine angle addition identityhttps://youtu.be/0VBQnR2h8XMTopicVideo/NotesIntroduction to arctanx
Solving and cos!=1cos!=!1
Introduction to arcsinx
Solving sinusoidal equations of the form sinx=d
Introduction to arccosx
Analytic Geometry and Circles
Finding trig values using angle addition identitieshttps://youtu.be/2RbKfRfzD-MUsing trig angle addition identities: finding side lengthshttps://youtu.be/sI789G6FBb4Using trig angle addition identities: manipulating expressionshttps://youtu.be/yV4Xa8XtmrcUsing trigonometric identitieshttps://youtu.be/4OEeVLo5V1oTrig identity referencehttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:using-trig-id/a/trig-identity-reference?modal=1TopicVideo/NotesTopicVideo/NotesDistance formulahttps://youtu.be/nyZuite17PcDistance formula: noteshttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/a/distance-formula?modal=1Midpoint formulahttps://youtu.be/Ez_-RwV9WVoMidpoint formula: noteshttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/a/midpoint-formula?modal=1Distance formula: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/a/distance-formula-review?modal=1Midpoint formula: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/a/midpoint-formula-review?modal=1Dividing line segments: graphicalhttps://youtu.be/0rlNHYHhrWsDividing line segmentshttps://youtu.be/lEGS5ECgFxEIntroduction to parallel & perpendicular lineshttps://youtu.be/V0xounKGEXsParallel & perpendicular lines from graphhttps://youtu.be/6riBTnlI4fwExample 1: parallel lines from equationhttps://youtu.be/T-aCweuimisExample 2: parallel lines from equationhttps://youtu.be/lOWXZFP8VucExample 3: parallel lines from equationhttps://youtu.be/y5yNi08cr6IPerpendicular lines from equationhttps://youtu.be/0671cRNjeKI
Complex Numbers
Example 1: writing equations of perpendicular lineshttps://youtu.be/TsEhZRT16LUExample 2: writing equations of perpendicular lineshttps://youtu.be/8m8hFcFJ-JMProof: parallel lines have the same slopehttps://youtu.be/9ZYoIliBXYEProof: perpendicular lines have opposite reciprocal slopeshttps://youtu.be/HyThzLRuqXoCircles glossaryhttps://youtu.be/U2W7HPyC0cMhttps://youtu.be/jyLRpr2P0MQIntroduction to arc measurehttps://youtu.be/_H4jllna_ecFinding arc measureshttps://youtu.be/GOA9XWEo7QIFinding arc measures with equationshttps://youtu.be/bsDu8VQKwxAArc length from subtended anglehttps://youtu.be/tVcasOt55LcSubtended angle from arc lengthhttps://youtu.be/1BH2TNzAAikArc length as fraction of circumferencehttps://youtu.be/XFI7GK4Nv-sArc length from subtended angle: radianshttps://youtu.be/dtQyiDMoub4Area of a sectorhttps://youtu.be/u8JFdwmBvvQInscribed angleshttps://youtu.be/aNi1-zeEps8Graphing circles from featureshttps://youtu.be/LDjMDIuTWtMFeatures of a circle from its graphhttps://youtu.be/SLyM_-sQwMMFeatures of a circle from its standard equationhttps://youtu.be/JvDpYlyKkNUGraphing a circle from its standard equationhttps://youtu.be/thDrJvWNI8MWriting standard equation of a circlehttps://youtu.be/iX5UgArMyiIFeatures of a circle from its expanded equationhttps://youtu.be/XyDMsotfJhECircle equation: reviewhttps://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-circle-expanded-equation/a/circle-equation-review?modal=1TopicVideo/NotesRadius, diameter, circumference & "
TopicVideo/NotesIntroduction to the imaginary numbershttps://youtu.be/ysVcAYo7UPIPowers of the imaginary unithttps://youtu.be/QiwfF83NWNASimplifying roots of negative numbershttps://youtu.be/s03qez-6JMAhttps://youtu.be/rYG1D5lUE4IIntroduction to complex numbershttps://youtu.be/SP-YJe7VldoClassifying complex numbershttps://youtu.be/A_ESfuN1PkgPlotting numbers on the complex planehttps://youtu.be/kGzXIbauGQkThe complex planehttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-plane/a/the-complex-plane?modal=1Adding complex numbershttps://youtu.be/SfbjqVyQljkSubtracting complex numbershttps://youtu.be/tvXRaZbIjO8Distance & midpoint of complex numbershttps://youtu.be/Efoeqb6tC88Multiplying complex numbershttps://youtu.be/cWn6g8Qqvs4Complex number operations: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul/a/complex-number-operations-review?modal=1Introduction to complex number conjugateshttps://youtu.be/BZxZ_eEuJBMComplex number conjugateshttps://youtu.be/dbxJ6LD0344Dividing complex numbershttps://youtu.be/Z8j5RDOibV4Dividing complex numbers: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-div/a/dividing-complex-numbers-review?modal=1Complex numbers & sum of squares factorizationhttps://youtu.be/8TPofjGXDR4Factoring sum of squareshttps://youtu.be/C3QPTCwpIZoAbsolute value of complex numbershttps://youtu.be/yvzyC4VBpUUAbsolute value & angle of complex numbershttps://youtu.be/FwuPXchH2rAComplex number absolute value & angle: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-abs-angle/a/complex-number-absolute-value-and-angle-review?modal=1Polar & rectangular forms of complex numbershttps://youtu.be/8RasCV_LgggTopicVideo/Notes as the principal root of -1i
Vectors
Complex number forms: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-polar/a/complex-number-forms-review?modal=1Dividing complex numbers: polar & exponential formhttps://youtu.be/xOa-l_tXgWAVisualizing complex number multiplicationhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/a/visualizing-complex-multiplication?modal=1Powers of complex numbershttps://youtu.be/dl_9NC_J6yohttps://youtu.be/N0Y8ia57C24Visualizing complex number powershttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/a/visualizing-complex-powers?modal=1Complex number polar form: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/a/complex-number-polar-form-review?modal=1Solving quadratic equations: complex rootshttps://youtu.be/dnjK4DPqh0kTopicVideo/NotesComplex number equations: x
3 =1TopicVideo/NotesIntroduction to vectors and scalarshttps://youtu.be/ihNZlp7iUHERecognizing vectorshttps://youtu.be/n8Ic2Oj-zvARecognizing vectors practicehttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vectors-intro/a/recognizing-vectors?modal=1Equivalent vectorshttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vectors-intro/v/equivalent-vectors-examples?modal=1Example 1: components of vectorshttps://youtu.be/BmDph4uNfPIExample 2: components of vectorshttps://youtu.be/v7ZZ1ctT1k0Vector magnitude from graphhttps://youtu.be/-U53eHKCLcgVector magnitude from componentshttps://youtu.be/qMZnsj4ZO9g
Vector magnitude from initial & terminal pointshttps://youtu.be/jfaSZhNFEOEScalar multiplication of vectorshttps://youtu.be/JuTvjQgpUMQAnalyzing scalar multiplicationhttps://youtu.be/kLLsJXc1E1EAdding & subtracting vectorshttps://youtu.be/VgqsM-XdBD0Graphically adding & subtracting vectorshttps://youtu.be/BsBH8nAv5l4Graphically subtracting vectorshttps://youtu.be/coDfeoi2zcQAdding vectors algebraically & graphicallyhttps://youtu.be/8QihetGj3pgCombined vector operationshttps://youtu.be/TdhbEonaHrcVector operations: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vec-ops/a/vector-operations-review?modal=1Introduction to unit vectorshttps://youtu.be/9ylUcCOTH8YExample: finding unit vector with given directionhttps://youtu.be/jCkhbKFZgLkExample: finding unit vector with given directionhttps://youtu.be/jCkhbKFZgLkExample: scaling unit vectorshttps://youtu.be/OFBI_rNDZE0Direction of vectors from components: 1st & 2nd quadrantshttps://youtu.be/A3OuFLHum6wDirection of vectors from components: 3rd & 4th quadrantshttps://youtu.be/EX0Ha42WQ24Vector forms: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:magnitude-direction/a/vector-forms-review?modal=1Vector components from magnitude & directionhttps://youtu.be/MkFbisCyjFcVector components from magnitude & direction: advancedhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:component-form/a/vector-component-form-no-direction-angle?modal=1Vector magnitude and direction: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:component-form/a/vector-magnitude-and-direction-review?modal=1Adding vectors in magnitude & direction form: part 1https://youtu.be/6Kw2nIwWYL0TopicVideo/Notes
Coins Sections
Adding vectors in magnitude & direction form: part 2https://youtu.be/SjY5UytlTTsVector addition & magnitudehttps://youtu.be/0t8W4JFpP2MVectors word problem: pushing a boxhttps://youtu.be/9A8wM1UMLyoVectors word problem: tug of warhttps://youtu.be/KNklNvGof8oVectors word problem: hikinghttps://youtu.be/cf1-CwrDwrATopicVideo/NotesTopicVideo/NotesIntroduction to conic sectionshttps://youtu.be/0A7RR0oy2hoIntroduction to ellipseshttps://youtu.be/lvAYFUIEpFIEllipse standard equation from graphhttps://youtu.be/_JrQF8RkaioEllipse graph from standard equationhttps://youtu.be/h5dIVNjVjXgEllipse features: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/a/ellipse-features-review?modal=1Ellipse equation: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/a/ellipse-equation-review?modal=1Foci of an ellipse from equationhttps://youtu.be/QR2vxfwiHAUEllipse foci: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-foci/a/ellipse-foci-review?modal=1Introduction to focus & directrixhttps://youtu.be/pe8Dm_FUpdUEquation of a parabola from focus & directrixhttps://youtu.be/okXVhDMuGFgFocus & directrix of a parabola from equationhttps://youtu.be/w56Vuf9tHfAParabola focus & directrix: reviewhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:parab-focus-directrix/a/parabola-focus-directrix-review?modal=1Introduction to hyperbolashttps://youtu.be/pzSyOTkAsY4Example 1: vertices & direction of a hyperbolahttps://youtu.be/oO3nWnJppqg
Example 2: vertices & direction of a hyperbolahttps://youtu.be/hnVFThmLW5QExample: graphing hyperbolashttps://youtu.be/hl58vTCqVIYFoci of a hyperbola from equationhttps://youtu.be/S0Fd2Tg2v7MProof of the hyperbola foci formulahttps://youtu.be/HPRFmu7JsKUEquation of a hyperbola not centered at the originhttps://youtu.be/lGQw-W1PxBERepresenting a line tangent to a hyperbolahttps://youtu.be/c_8QQbVQKU0Common tangent of circle & hyperbola: part 1https://youtu.be/MhLfun2VaskCommon tangent of circle & hyperbola: part 2https://youtu.be/0imeUgSxR10Common tangent of circle & hyperbola: part 3https://youtu.be/RomnHMWSLoECommon tangent of circle & hyperbola: part 4https://youtu.be/eGo8C2JshzsCommon tangent of circle & hyperbola: part 5https://youtu.be/rPoqpQcgNv4Intersection of circle & hyperbolahttps://youtu.be/6g3DPg2HqGwTopicVideo/Notes
- log change of base rule proof