ic Formula Sheet Arithmetic Operations ac + bc = c(a + b) ( a b ) c = a bc a b + c d = ad + bc
TICAL FORMULAE Algebra 1 (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) 4 (a + b)3
ic Formula Sheet Arithmetic Operations ac + bc = c(a + b) ( a b ) c = a bc a b + c d = ad + bc
3 = a3 - b3 - 3ab(a - b) 5 (a + b + c)2 = a2 + b2 + c2 +2ab+2bc +2ca 6 (
4 GED® Mathematical Reasoning test contains a formula sheet, which y = ax2 + bx + c
GCSE (9-1) Maths: edexcel need-to-know formulae www edexcel com/ gcsemathsformulae
GCSE (9-1) Maths: need-to-know The formula for pressure does not need to be learnt, and
ution de cette équation s'appelle une racine du trinôme ax2 + bx + c Exemple : L'équation 3x2 −
ametric form : x cos α + y sin α = a 4 Pair of Tangents from a Point: SS1 = T² 5 Length of a Tangent
ecting Like Terms 7 Solving Equations 8 Rearranging Formulas 9 Measurement Units 10
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Algebraic Formula Sheet
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)
x 2+ 2xy+y2= (x+y)2
x 22xy+y2= (xy)2
x 3+ 3x2y+ 3xy2+y3= (x+y)3
x 33x2y+ 3xy2y3= (xy)3x
3+y3= (x+y)x2xy+y2
x 3y3= (xy)x2+xy+y2
x 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
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MATHEMATICAL FORMULAE Algebra 1 (a + b)2 = a2 + 2ab +