Maths iGCSE

Question 1

What’re prime factors?

Answer 1

Example: 12 = 2^2 x 3

Question 2

What’s Least Common Multiple (LCM)?

Answer 2

Smallest common multiple

Question 3

What’s Highest Common Factor (HCF)?

Answer 3

Largest common factor

Question 4

How do you estimate calculations?

Answer 4

Rounding each number, and then calculating it. This will give an approximation (≈)

Question 5

What’re upper & lower bounds?

Answer 5

Upper Bound: Maximum value that a rounded value can be.

Lower Bound: Minimum value that a rounded value can be.

Question 6

Formula for compound growth?

Answer 6

Pₙ = P₀ x (1 + r/100)ⁿ

Question 7

Formula for compound decay?

Answer 7

Pₙ = P₀ x (1 - r/100)ⁿ

Question 8

What’s factorising?

Answer 8

Opposite of expanding brackets. Making brackets

Question 9

What’s an identity?

Answer 9

Are like equations, but always true whatever x is.

Question 10

Equation of a circle?
Radius is r
Centre (a,b)

Answer 10

(x-a)² + (y-b)² = r²

Question 11

How do you reflect in the x-axis?

Answer 11

y = -f(x)

Question 12

How do you reflect in the y-axis?

Answer 12

y = f(-x)

Question 13

What’s intersection symbol?

Answer 13

∩

Question 14

What’s union symbol?

Answer 14

∪

Question 15

What’s the complement of A?

Answer 15

A’

Question 16

What’s the sum of interior angles?

Answer 16

S = (n - 2) x 180º

Question 17

How is exterior angle calculated?

Answer 17

Exterior angle = 360º / n

Question 18

What’s a chord?

Answer 18

Line between 2 points in a circle

Question 19

What do you have to keep in mind about bearing?

Answer 19

Always measured clockwise from North.

Question 20

What’s the sine rule?

Answer 20

(sin A / a) = (sin B / b) = (sin C / c)

Question 21

What’s the cosine rule?

Answer 21

a² = b² + c² - 2bc CosA

Question 22

What’s the area of a triangle (trigonometry)?

Answer 22

Area = 0.5ab sin C

Question 23

Area of a trapezium?

Answer 23

A = 0.5(a + b) x h

Question 24

Sphere surface area?

Answer 24

4πr²

Question 25

Sphere volume?

Answer 25

(4/3)πr³

Question 26

What’s mode?

Answer 26

Most common value

Question 27

What’s median?

Answer 27

Middle value once items in order

Question 28

What’s mean?

Answer 28

total / number of value

Question 29

How to find LCM with prime factors?

Answer 29

Multiply the highest power of each prime factor together.

18 = 2 x 3 x 3
30 = 2 x 3 x 5

LCM = 2 x 3 x 3 x 5

Question 30

How to find HCF with prime factors?

Answer 30

Multiply all prime factors that appear in both numbers.

180 = 2 x 2 x 3 x 3 x 5
84 = 2 x 2 x 3 x 7

HCF = 2 x 2 x 3

Question 31

How do you find common denominators?

Answer 31

LCM of all denominators

Question 32

Is a member of & Is not a member of set notation:

Answer 32

Member of: ∈
Not a member of: ∉

Question 33

Substet symbol set notation

Answer 33

⊂

Question 34

What’s the difference of two squares?

Answer 34

a² + b² = (a + b) (a - b)

Question 35

How do you draw circle for inclusive and non-inclusive? (Inequalities Number lines)

Answer 35

Inclusive: colored in circle ●
Non-Inclusive: open circle ○

Question 36

How do you draw lines for inclusive and non-inclusive? (Graphical Inequalities)

Answer 36

Inclusive: solid line
Non-Inclusive: dotted line

Question 37

Formula for sum of series

Answer 37

Sₙ = (n/2) [2a + (n-1)d]

Question 38

Perpendicular line gradient

Answer 38

m = -(1/m)

Question 39

How do you solve a quadratic graphically?

Answer 39

Points at which it crosses y-axis.

Question 40

What’s a sine wave?

Answer 40

• Repeat every 360º
• Wave that crosses y-axis at x = 0º
• y values between -1 & 1

Question 41

What’s a cos wave?

Answer 41

• Repeat every 360º
• Wave that crosses y-axis at x = 90º
• y values between -1 & 1

Question 42

What’s a tan x graph?

Answer 42

• Repeats every 180º
• y goes from -∞ and ∞
• Never touches x = 90º and repeats

Question 43

How do you translate on the y-axis?

Answer 43

y = f(x) + a

Question 44

How do you translate on the x-axis?

Answer 44

y = f(x - a)

Question 45

How do you stretch in the y-direction?

Answer 45

y = af(x)

Question 46

How do you stretch in the x-direction?

Answer 46

y = f(ax)

Question 47

Formula to differentiate powers of x

Answer 47

nxⁿ⁻¹

Question 48

How do you find stationary points?

Answer 48

1. Differentiate
2. Set dy/dx = 0 and solve for x
3. Substitute x-values into original equation

Question 49

How do you find gradient with differentiation?

Answer 49

1. Differentiate
2. Substitute x-values to find gradient at point

Question 50

What must you give for the translation transformation?

Answer 50

• Vector

Question 51

What must you give for the rotation transformation?

Answer 51

• Angle of rotation
• Direction of rotation
• Centre of rotation

Question 52

What must you give for the reflection transformation?

Answer 52

• Equation of mirror line

Question 53

What must you give for the enlargement transformation?

Answer 53

• Scale factor
• Centre of enlargement

Question 54

Area of trapezium

Answer 54

A = 0.5(a + b) x h

Question 55

How do you write a vector?

Answer 55

• X on top
• Y on bottom

Question 56

Equation of a line

Answer 56

y-y1= m(x-x1)