Memorise for IGCSE Maths

Question 1

HCF

Answer 1

Multiply all numbers in the middle of venn diagram

Question 2

LCF

Answer 2

Multiply all the numbers in th whole venn diagram

Question 3

Adding + Subtracting Fractions

Answer 3

Find a common denominator

Question 4

Multiplication of Fractions

Answer 4

Top x Top and Bottom x Bottom

Question 5

Division of Fractions

Answer 5

KFC - Keep, flip, change

Question 6

Sum of all outcomes - Probability

Answer 6

Equals to 1

Question 7

Nth Term - Sequences

Answer 7

difference x n + 0th term

Question 8

Translation - Transformations

Answer 8

By vector (a/b) a = right, -a = left, b = up, -b = down

Question 9

Reflection - Transformations

Answer 9

In line x = a (horizontal) y = b (vertical)

Question 10

Rotation - Transformations

Answer 10

centre, angle, driection (CW or ACW)

Question 11

Enlargement - Transformations

Answer 11

Centre, scale factor

Question 12

Multiplier - Percentages

Answer 12

Increase = 100+x/100, Decrease = 100-x/100

Question 13

% Change - Percentages

Answer 13

Change/Original x 100

Question 14

Reverse % - Percentages

Answer 14

Original = New/Multiplier

Question 15

Inequalities

Answer 15

y<mx+c = shade below the line, y>mx+x = shade above the line

Question 16

Indicies

Answer 16

(a^m)^n = a^mxn
a^-m = 1/a^m
a^1/n = ^n\sqrt{a}
a^m/n = ^n\sqrt{a^m}

Question 17

Measuring Speed, Density + Pressure

Answer 17

Speed = Distance/Time
Density = Mass/Volume
Pressure = Force/Area

Question 18

Angles

Answer 18

Straight line - Adds to 180
Around a point - Adds to 360
Corresponding - Equal
Alternate - Equal
Vertically opposite - Equal
CO-interior - Adds to 180

Question 19

Angles in Polygons

Answer 19

Interior angles = (n-2) x 180
Exterior angles = 360
Interior + Exterior = 180

Question 20

Bearings

Answer 20

Meaured - From North and clockwise
Back bearings - Differ by 180

Question 21

Area

Answer 21

Parallelograms = bxh
Triangle = bxh/2
Trapezium = 1/2(a+b)xh
Circle = Pi x r^2
Circumference = 2 x Pi x r

Question 22

Volume

Answer 22

Prism = Cross-Sectional Area x Height
Surface Area = Sum the areas of all the faces
Cylinder = Pi x r^2 x h
Curved Surface Area = 2 x Pi x r x h
Total Surface Area = 2 x Pi x r x h + 2 x Pi x r^2

Question 23

Straight Lines

Answer 23

y=mx+c where m = gradient and c = y-intercept
Gradient = y2-y1/x2-x1
Length of line = Square root of (x2-1)^2+(y2+y1)^2
Midpoint = (x1+x2/2, y1+y2/2)
Parallel = Same Gradient

Question 24

Probability

Answer 24

And = Multiply
Or = Add
At least 1 = 1-none

Question 25

Circle Theorms

Answer 25

• Angles from same segment are equal
• Angle at centre twice circumference angle
• Opposites in cyclic quadrilateral add to 180
• Tangent and radius 90
• Tangents that meet are equal
• Alternate segment Theorem
• 2 radii make isoscleles triangle

Question 26

Set Theory

Answer 26

AnB - Intersection - Both
AuB - Union - Either
A’ - Not A
Q - Empty
E - Univeral Set
n(A) - Number of elements in A
AcB - A is subset of B

Question 27

Proportion

Answer 27

Directly Proportional - y=kx
Inversely Proportional - y=k/x

Question 28

Histograms

Answer 28

Frequenncy Density = Frequency/Class Width

Question 29

Similar Shapes

Answer 29

Linear Scale factor - k
Area Scale Factor - k^2
Volume Scale Factor - k^3

Question 30

Surds

Answer 30

root a x root b = root axb
root a/b = root a/root b
x/root a = multiply top and bottom by root a
x/root a + b = Multiply top and bottom by root a - b

Question 31

Cones and Spheres

Answer 31

Volume of Cone = 1/3 x Pi x r^2 x h
Curved Surface Area = Pi x r x L
Total Surface Area = Pi x r^2 + Pi x r x L
Volume of Sphere = 4/3 x Pi x r^3
Surface Area = 4x Pir x r^2

Question 32

Sectors

Answer 32

Arc length = O/360 x 2 x Pi x r
Area = O/360 x Pi x r^2

Question 33

3D Pythagoras

Answer 33

Long diagonal of a Cubiod - d = root a^2+b^2+c^2

Question 34

Completing the Square

Answer 34

Minimum point (x+p)^2+q = (-p,q)
Symmetry line - x=-p

Question 35

Perpendicular lines

Answer 35

Perpendicular Gradients - Negative reciprocal, m2 = -1/m1
Alternate Equation of line - y-y1 = m(x-x1)

Question 36

Funcntions

Answer 36

Composite Functions - fg(x) Means do g then f
Inverse Functions - y=f(x) — x=f^-1(y)

Question 37

Differentiation

Answer 37

Differentiating y = ax^n - dy/dx = nax^n-1
Stationary Points - dy/dx = 0

Question 38

Kinematics

Answer 38

Differentiate = Displacement - Velocity - Acceleration

Question 39

Sequences

Answer 39

Notation - a = first term, d = difference, n = position
Summation - Sn = n/2(2a+(n-1)d)
Nth Term - an = a +(n-1)d