Algebraic Formula Sheet

Speigel M.R.

BYJUS

The basic maths class 10 formulas are almost the same for all the boards. Download Class 10 Maths Formulas PDF Here: Linear Equations. One Variable ax+b=0 a ...

Differentiation Formulas Integration Formulas

Page 1. Differentiation Formulas d dx k = 0. (1) d dx. [f(x) ± g(x)] = f (x) ± g (x). (2) d dx. [k · f(x)] = k · f (x). (3) d dx. [f(x)g(x)] = f(

Trigonometric Formula Sheet - Definition of the Trig Functions

Even and Odd Formulas sin(−θ) = −sinθ cos(−θ) = cosθ tan(−θ) = −tanθ csc These are all the solutions (including the complex values) of the equation ...

Mensuration and Mensuration Formulas PDF

You will study the mensuration formulas and properties of different geometric shapes and figures in maths in this article. Now let's learn all the important ...

Physical Science: Tables & Formulas

Type of reaction. Generalized formula. Specific Example. Combustion. HC + O2 → H2O + CO2. 2C2H6 + 7O2 → 6H2O + 4CO2. Synthesis. A + B → AB.

Mathcentre

so that the gradient of this line is 1. What about the equation y = 2x? This also represents a straight line and for all the points on the line each y value

INDEX MATHEMATICS FORMULA BOOKLET - GYAAN SUTRA

Fundamental of Mathematics Parametric Equations of a Circle: ... (Note that lateral surfaces of a prism are all rectangle). 15. Volume of a pyramid =.

MATH FORMULAS & FUNDAS

This eBook contains a list of formulas and concepts Arithmetic. Algebra. Geometry. Modern Math ... arranging all the observations from lowest value to.

List MF19

List of formulae and statistical tables. Cambridge International AS & A Level. Mathematics (9709) and Further Mathematics (9231). For use from 2020 in all

Mensuration and Mensuration Formulas PDF

Mensuration is the branch of mathematics which studies the measurement of the Now let's learn all the important mensuration formulas involving 2D and 3D.

Mathematical Formula Handbook.pdf

Speigel M.R.

Formula Sheet 1 Factoring Formulas 2 Exponentiation Rules

Finally the quadratic formula: if a

Trigonometric Formula Sheet - Definition of the Trig Functions

Identities and Formulas Degrees to Radians Formulas ... These are all the solutions (including the complex values) of the equation x4 = 4.

BASIC GEOMETRIC FORMULAS AND PROPERTIES

For further or more advanced geometric formulas and properties consult with a SLAC counselor. r. Square: Perimeter: P = 4s or 2s + 2s. Area: A = s2.

Algebraic Formula Sheet - Middle Georgia State University

Algebraic Formula Sheet Algebraic Formula Sheet Arithmetic Operations ac bc = c(a + b) ! a = bc c ad + bc = bd b b b a = c d d c ab + ac = b + c; a 6 = 0 ! ab = c ac = ! b b c ad bc = d bd + b a b = + c c c ! ad ! = bc Properties of Exponents xnxm = xn+m (xn)m = xnm (xy)n = xnyn n 1 m x m

Arithmetic Operations

ac+bc=c(a+b) ab !c =abc ab +cd =ad+bcbd abcd=badc ab+aca =b+c; a6= 0a bc abc a bc =acb ac cd =adbcbd a+bc =ac +bc ab cd =adbc

Properties of Exponents

x nxm=xn+m (xn)m=xnm (xy)n=xnyn x nm x1m n= x n 1m xy n yx n =ynx nx

0= 1; x6= 0

xy n =xny n 1x n=xn x nx m=xnm x n=1x n

Properties of Radicals

n px=x1n n pxy=npx npy m qn px=mnpx n rx y =npx n py n px n=x;ifnis odd n px n=jxj;ifnis evenProperties of Inequalities

Ifa < bthena+c < b+candac < bc

Ifa < bandc >0 thenac < bcandac

Ifa < bandc <0 thenac > bcandac >bc

Properties of Absolute Value

jxj=( xifx0 xifx <0 jxj 0 jxyj=jxjjyjj xj=jxj xy =jxjjyj jx+yj jxj+jyjTriangle Inequality jxyj jxj jyjReverse Triangle Inequality

Distance Formula

Given two points,PA= (x1;y1) andPB= (x2;y2),

the distance between the two can be found by: d(PA;PB) =p(x2x1)2+ (y2y1)2

Number Classications

Natural Numbers:N=f1, 2, 3, 4, 5, . . .g

Whole Numbers:f0, 1, 2, 3, 4, 5, . . .g

Integers:Z=f... ,-3, -2, -1, 0, 1, 2, 3, .. .g

Rationals:Q=All numbers that can be writ-

ten as a fraction with an integer numerator and a nonzero integer denominator,ab

Irrationals:fAll numbers that cannot be ex-

pressed as the ratio of two integers, for examplep5, p27, andg

Real Numbers:R=fAll numbers that are either a

rational or an irrational numberg 1

Logarithms and Log Properties

Denition

y= logbxis equivalent tox=by

Example

log

216 = 4because24= 16

Special Logarithms

lnx= logexnatural log wheree=2.718281828... logx= log10xcommon logLogarithm Properties log bb= 1 log bbx=x lnex=xlog b1 = 0 b logbx=x e lnx=x log b(xk) =klogbx log b(xy) = logbx+ logby log b xy = log bxlogby

Factoring

xa+xb=x(a+b) x

2y2= (x+y)(xy)

2+ 2xy+y2= (x+y)2

22xy+y2= (xy)2

3+ 3x2y+ 3xy2+y3= (x+y)3

33x2y+ 3xy2y3= (xy)3x

3+y3= (x+y)x2xy+y2

3y3= (xy)x2+xy+y2

2ny2n= (xnyn)(xn+yn)

Ifnis odd then,

x nyn= (xy)xn1+xn2y+:::+yn1 x n+yn= (x+y)xn1xn2y+xn3y2:::yn1

Linear Functions and Formulas

Examples of Linear Functionsxy

y=xlinear functionxy y= 1constant function 2

Constant Function

This graph is a horizontal line passing

through the points (x;c) with slopem= 0 : y=c or f(x) =c

Slope (a.k.a Rate of Change)

The slopemof the line passing through

the points (x1;y1) and (x2;y2) is : m=yx=y2y1x

2x1=riserun

Linear Function/Slope-intercept form

This graph is a line with slopem

andyintercept(0;b) : y=mx+b or f(x) =mx+b

Point-Slope form

The equation of the line passing through

the point (x1;y1) with slopemis : y=m(xx1) +y1

Quadratic Functions and Formulas

Examples of Quadratic Functionsxy

y=x2parabola opening upxy y=x2parabola opening down

Forms of Quadratic Functions

Standard Form

y=ax2+bx+c or f(x) =ax2+bx+c

This graph is a parabola that

opens up ifa >0 or down if a <0 and has a vertex at b2a;f b2a .Vertex Form y=a(xh)2+k or f(x) =a(xh)2+k

This graph is a parabola that

opens up ifa >0 or down if a <0 and has a vertex at (h;k). 3

Quadratics and Solving forx

Quadratic Formula

To solveax2+bx+c= 0,a6= 0,

use : x=bpb

24ac2a.

The Discriminant

The discriminant is the part of the quadratic

equation under the radical,b24ac. We use the discriminant to determine the number of real solutions ofax2+bx+c= 0 as such :

1.Ifb24ac >0, there are two real solutions.

2.Ifb24ac= 0, there is one real solution.

3.Ifb24ac <0, there are no real solutions.Square Root Property

Letkbe a nonnegative number. Then the

solutions to the equation x 2=k are given byx=pk.

Other Useful Formulas

Compound Interest

A=P 1 +rn nt where:

P= principal of P dollars

r= Interest rate (expressed in decimal form) n= number of times compounded per year t= time

Continuously Compounded Interest

A=Pert

where:

P= principal of P dollars

r= Interest rate (expressed in decimal form) t= time

Circle

(xh)2+ (yk)2=r2

This graph is a circle with radiusr

and center (h;k).

Ellipse

(xh)2a

2+(yk)2b

2= 1

This graph is an ellipse with center

(h;k) with verticesaunits right/leftquotesdbs_dbs14.pdfusesText_20

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[PDF] Algebraic Formula Sheet - Middle Georgia State University

Algebraic Formula Sheet

Arithmetic Operations

Properties of Exponents

0= 1; x6= 0

Properties of Radicals

Ifa < bthena+c < b+candac < bc

Ifa < bandc >0 thenac < bcandac

Properties of Absolute Value

Distance Formula

Given two points,PA= (x1;y1) andPB= (x2;y2),

Number Classications

Natural Numbers:N=f1, 2, 3, 4, 5, . . .g

Whole Numbers:f0, 1, 2, 3, 4, 5, . . .g

Integers:Z=f... ,-3, -2, -1, 0, 1, 2, 3, .. .g

Rationals:Q=All numbers that can be writ-

Irrationals:fAll numbers that cannot be ex-

Real Numbers:R=fAll numbers that are either a

Logarithms and Log Properties

Denition

Example

216 = 4because24= 16

Special Logarithms

Factoring

2y2= (x+y)(xy)

2+ 2xy+y2= (x+y)2

22xy+y2= (xy)2

3+ 3x2y+ 3xy2+y3= (x+y)3

33x2y+ 3xy2y3= (xy)3x

3+y3= (x+y)x2xy+y2

3y3= (xy)x2+xy+y2

2ny2n= (xnyn)(xn+yn)

Ifnis odd then,

Linear Functions and Formulas

Examples of Linear Functionsxy

Constant Function

This graph is a horizontal line passing

Slope (a.k.a Rate of Change)

The slopemof the line passing through

2x1=riserun

Linear Function/Slope-intercept form

This graph is a line with slopem

Point-Slope form

The equation of the line passing through

Quadratic Functions and Formulas

Examples of Quadratic Functionsxy

Forms of Quadratic Functions

Standard Form

This graph is a parabola that

This graph is a parabola that

Quadratics and Solving forx

Quadratic Formula

To solveax2+bx+c= 0,a6= 0,

24ac2a.

The Discriminant

The discriminant is the part of the quadratic

1.Ifb24ac >0, there are two real solutions.

2.Ifb24ac= 0, there is one real solution.

3.Ifb24ac <0, there are no real solutions.Square Root Property

Letkbe a nonnegative number. Then the

Other Useful Formulas

Compound Interest

P= principal of P dollars

Continuously Compounded Interest

A=Pert

P= principal of P dollars

Circle

This graph is a circle with radiusr

Ellipse

2+(yk)2b

This graph is an ellipse with center