Maths AQA GCSE Higher

area of a circle

surface area of a sphere

surface area of a cone

πr x slanted length x πr^2

volume of cone

volume of a sphere

area of trapezium

1/2(a+b) x height

circumference of a circle

π x d

volume of a cuboid

l x w x h

volume of a cylinder

volume of a pyramid

1/3 x area of base x h

distance

speed x time

density

mass/volume

pressure

force/area

Pythagoras' Theorem

a^2 + b^2 = c^2

Quadratic equation

when ax^2 + bx + c = 0

Sine rule

a/sinA = b/sinB = c/sinC

Cosine rule

Area of a triangle

1/2 x a x b x sinC

area of a sector

angle/360 x area of full circle

segment area

sector area - area of triangle

x angles

equal

corresponding angles

equal

alternate angles

equal

co-interior angles

add to 180

total of exterior angles

360

1 exterior angle

360/number of sides

sum of interior angles

(sides - 2) x 180

sin/cos/tan 45, lengths=

sin/cos/tan 30 or 60, lengths=

a^m x b^n

ab^m+n

a^m / b^n

a/b^m-n

a^0

1

a^1

a

(a^m)^n

a^mxn

(a/m)^n

a^n/m^n

a^-m

1/a^m

a^1/m

^m√a

a^m/n

(^n√a)^m

3D Pythagoras' theorem

a^2 + b^2 + c^2 = d^2

when to use cosine rule

2 sides and an angle enclosed by them all 3 sides no angle

when to use sine rule

2 angles any side 2 sides and an angle thats not enclosed by them

inverse functions

replace x's with y's and make everything equal to x make y the subject replace the y with f^-1(x)

y=f(x)+a

translation in the y-axis (move up or down by the amount of a eg. +2 = move up 2)

y=f(x+a)

translation in the x-axis (but if it says +2 move down 2 ITS OPPOSITE!!)

y=f(xa)

stretch in the x direction (leaving the y values unchanged) by a factor of 1/a

y=f(x/a)

stretch in the x direction (leaving the y values unchanged) by a factor of a

y=-f(x)

reflection in the x-axis

y=f(-x)

reflection in the y-axis

∉

not a member of a set

∈

member of a set

ξ

universal set (all the numbers in the Q)

∪

union (combination of all members of each set in question)

∩

intersect (all numbers that are members of exclusively both sets in question)

'

Everything NOT in the set

√a x √b

√a x b

√a / √b

√a/b

√a + √b

DO NOTHING

a/ √b

a/√b x √b/√b = a√b/b

'exact value' meaning

surd form

when to use quadratic formula

if it wont factorise if the question mentions decimal places or significant figures

dividing fractions

KEEP TIMES SWITCH- KTS

common denominator is also....

something both denominators divide into

fibonacci sequence

adding together the 2 previous terms

how to know if 2 lines are perpendicular

if gradient is m perpendicular will be -(1/m)

cubic graph

reciprocal graph (positive)

exponential graph

gradient

vertical/horizontal or ycoord/xcoord

estimated gradient of a curve

tangent to curve (meets curve at point your trying to find) then calculate gradient

compound interest

amount x percentage^years

how to know if 2 lines are parallel

gradients are the same

quadratic graph

how to find equation for a tangent to a circle

find gradient (ycoord/xcoord) use gradient to find perpendicular -(1/m) put coords into y=mx+c to find c where m is -(1/m)

circle equation

x^2+y^2 = r^2

2 consecutive numbers

n, n+1

2 consecutive odd numbers

2n+1, 2n+3

2 consecutive even numbers

2n, 2n+2

sin 0

0

sin 30

0.5

sin 45

1 / √2

sin 60

√3 / 2

sin 90

1

cos 0

1

cos 30

√3 / 2

cos 45

1 / √2

cos 60

0.5

cos 90

0

tan 0

0

tan 30

1 / √3

tan 45

1

tan 60

√3

tan 90

DOES NOT EXIST

x^2 > a^2

x > a x < -a

x^2 < a^2

-a < x < a

how to solve a simultaneous equation by plotting a line and circle graph

the coordinates where the line meets the circle are the solutions

2:3 =

2/3

y is proportional to x

y is inversely proportional to x

y is proportional to x squared

exponential graph

percentage change=

(new value/original) x100