GSCE EdExcel Maths

What is the formula for the area of a rectangle?

Area = length × width

How do you calculate the perimeter of a rectangle?

Perimeter = 2 × (length + width)

What is the formula for the area of a triangle?

Area = ½ × base × height

How do you calculate the area of a trapezium?

Area = ½ × (a + b) × h

What is the formula for the circumference of a circle?

Circumference = πd or Circumference = 2πr

What is the formula for the area of a circle?

Area = πr²

What is Pythagoras' Theorem?

a² + b² = c²

What are SOH CAH TOA used for?

SOH: Sin(θ) = Opposite/Hypotenuse

CAH: Cos(θ) = Adjacent/Hypotenuse

TOA: Tan(θ) = Opposite/Adjacent (used for right-angled triangles)

What is the sine rule?

a/sinA = b/sinB = c/sinC (used for non-right-angled triangles)

What is the cosine rule (to find a side)?

a² = b² + c² - 2bc cosA (used for non-right-angled triangles)

What is the cosine rule (to find an angle)?

cosA = (b² + c² - a²) / 2bc (used for non-right-angled triangles)

What is the formula for the area of a non-right-angled triangle?

Area = ½ab sinC

How do you calculate the volume of a cuboid?

Volume = length × width × height

What is the formula for the volume of a prism?

Volume = area of cross-section × length

What is the formula for the volume of a cylinder?

Volume = πr²h

What is the formula for the surface area of a cylinder?

Surface Area = 2πr² + 2πrh

What is the formula for the volume of a cone?

Volume = ⅓πr²h

What is the formula for the volume of a sphere?

Volume = ⁴⁄₃πr³

How do you calculate the surface area of a sphere?

Surface Area = 4πr²

How do you find the mean of a set of data?

Sum of all values ÷ Number of values

How do you find the median of a set of data?

Order the data and find the middle value. If two

What is the mode of a set of data?

The value that appears most frequently.

What is the range of a set of data?

Highest value – Lowest value

What is the interquartile range (IQR)?

IQR = Upper Quartile (Q3) - Lower Quartile (Q1)

How do you calculate relative frequency?

Frequency of an event ÷ Total number of trials

What is the formula for percentage increase?

((New Value - Original Value) / Original Value) × 100%

What is the formula for percentage decrease?

((Original Value - New Value) / Original Value) × 100%

How do you calculate simple interest?

Interest = Principal × Rate × Time

What is the formula for compound interest (total amount)?

A = P(1 + r/100)^n

What is the formula for the nth term of an arithmetic sequence?

an = a1 + (n-1)d

What is the formula for the nth term of a geometric sequence?

an = a1 × r^(n-1)

What are prime numbers?

Numbers greater than 1 that have exactly two factors: 1 and themselves.

What are factors of a number?

Numbers that divide exactly into another number.

What are multiples of a number?

Numbers that are in the times table of that number.

How do you find the Lowest Common Multiple (LCM)?

Find the smallest multiple common to two or more numbers.

How do you find the Highest Common Factor (HCF)?

Find the largest factor common to two or more numbers.

What is a reciprocal?

1 divided by the number (e.g.

What is standard form (scientific notation)?

A way of writing very large or very small numbers using powers of 10 (e.g.

How do you simplify algebraic expressions?

Combine like terms.

How do you expand brackets?

Multiply each term inside the bracket by the term outside.

How do you factorise an expression?

Put it into brackets by finding common factors.

What is the equation of a straight line?

y = mx + c

How do you find the gradient of a line from two points (x1

y1) and (x2

What are parallel lines?

Lines that have the same gradient and never intersect.

What are perpendicular lines?

Lines that intersect at 90 degrees. The product of their gradients is -1.

How do you solve linear equations?

Use inverse operations to isolate the variable.

How do you solve simultaneous equations by elimination?

Multiply equations so that one variable has the same coefficient

How do you solve simultaneous equations by substitution?

Rearrange one equation to make a variable the subject

How do you solve quadratic equations by factorising?

Set the equation to zero

What is the quadratic formula?

x = [-b ± √(b² - 4ac)] / 2a (used to solve ax² + bx + c = 0)

What is the formula for speed

distance

Distance = Speed × Time

Time = Distance / Speed

What is a bearing?

A direction measured clockwise from North

What is direct proportion?

When two quantities increase or decrease at the same rate (y = kx)

What is inverse proportion?

When one quantity increases as the other decreases proportionally (y = k/x)

What is a probability?

The likelihood of an event occurring

What is the sum of probabilities of all possible outcomes?

1

What are mutually exclusive events?

Events that cannot happen at the same time.

What is the 'OR' rule for mutually exclusive events?

P(A or B) = P(A) + P(B)

What are independent events?

Events where the outcome of one does not affect the outcome of the other.

What is the 'AND' rule for independent events?

P(A and B) = P(A) × P(B)

How do you interpret a scatter graph with positive correlation?

As one variable increases

How do you interpret a scatter graph with negative correlation?

As one variable increases

How do you interpret a scatter graph with no correlation?

There is no obvious linear relationship between the variables.

What is a line of best fit?

A line drawn on a scatter graph to show the general trend of the data.

What is interpolation?

Estimating a value within the range of the observed data.

What is extrapolation?

Estimating a value outside the range of the observed data.

What are inequalities?

Mathematical statements comparing two expressions using <

How do you solve inequalities?

Similar to solving equations

How do you represent inequalities on a number line?

Open circle for < or >

What is a Venn diagram used for?

To show relationships between sets of data.

What is a frequency tree (or tree diagram) used for?

To show the probabilities or frequencies of a sequence of events.

How do you calculate density

mass

Mass = Density × Volume

Volume = Mass / Density

What is pressure

force

Force = Pressure × Area

Area = Force / Pressure

What is a conversion graph used for?

To convert between two different units or quantities.

What is compound measure?

A measure that combines two or more different units (e.g.

How do you describe a transformation of a shape?

State the type of transformation (translation

What is a translation?

Moving a shape without rotating

What is a rotation?

Turning a shape around a fixed point (centre of rotation) by a certain angle.

What is a reflection?

Flipping a shape across a line (mirror line).

What is an enlargement?

Resizing a shape by a scale factor from a centre of enlargement.

What is the meaning of congruence?

Two shapes are congruent if they are exactly the same size and shape.

What is the meaning of similarity?

Two shapes are similar if one is an enlargement of the other (same shape

How do you calculate area scale factor for similar shapes?

(Linear scale factor)²

How do you calculate volume scale factor for similar shapes?

(Linear scale factor)³

What is standard index form?

A number written as A × 10ⁿ

How do you calculate the lowest common multiple (LCM) using prime factors?

Find the prime factorisation of each number

How do you calculate the highest common factor (HCF) using prime factors?

Find the prime factorisation of each number

What is a terminating decimal?

A decimal that has a finite number of digits after the decimal point.

What is a recurring decimal?

A decimal that has a pattern of digits that repeat indefinitely.

How do you convert a recurring decimal to a fraction?

Set the decimal equal to x

What are algebraic fractions?

Fractions that contain algebraic expressions in the numerator

How do you add or subtract algebraic fractions?

Find a common denominator