CCEA GCSE Maths flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Standard form

A number written as a × 10^n where 1 ≤ a < 10 and n is an integer; for example, 3.2 × 10^4 = 32,000.

HCF and LCM

For prime factorisations, the HCF uses the lowest power of each common prime and the LCM uses the highest power of every prime that appears.

Percentage multiplier

A single factor used to calculate a percentage change: increase by r% gives multiplier 1 + r/100; decrease by r% gives 1 − r/100.

Compound interest formula

A = P(1 + r/100)^n gives the amount after n years when P is invested at r% compound interest per year.

Rationalising a denominator

Rewrite a fraction so no surd remains in the denominator; multiply numerator and denominator by the surd, for example 3/√2 = 3√2/2.

Upper and lower bounds

For a value rounded to the nearest unit, half a unit below and above gives the bounds; calculations combine the bounds that make the result largest or smallest.

Direct and inverse proportion

Direct proportion has the form y = kx and inverse proportion has y = k/x; k is found by substituting a known pair of values.

Quadratic formula

The solutions of ax² + bx + c = 0 are x = (−b ± √(b² − 4ac)) ÷ 2a, provided a ≠ 0.

Difference of two squares

The identity a² − b² = (a − b)(a + b), used to factorise expressions such as x² − 49 as (x − 7)(x + 7).

Index laws

Rules for powers: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(mn), a^0 = 1 and a^(−n) = 1/a^n.

Gradient of a line

The change in y divided by the change in x between two points: m = (y₂ − y₁)/(x₂ − x₁); it measures steepness and direction.

Perpendicular gradients

Two straight lines are perpendicular exactly when the product of their gradients is −1, so one gradient is the negative reciprocal of the other.

Completing the square

Write x² + bx + c as (x + b/2)² + c − b²/4; the turning point of y = x² + bx + c is at x = −b/2.

Inverse function

A function that reverses another; to find it, replace f(x) with y, swap x and y, then rearrange to make y the subject.

Pythagoras' theorem

In a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides: a² + b² = c².

Sine, cosine and tangent

For a right-angled triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent.

Sine and cosine rules

For any triangle: a/sin A = b/sin B = c/sin C and a² = b² + c² − 2bc cos A.

Sector area and arc length

For angle θ at the centre: arc length = θ/360 × 2πr and sector area = θ/360 × πr².

Similar shape scale factors

If corresponding lengths have scale factor k, areas have scale factor k² and volumes have scale factor k³.

Interior angle sum

An n-sided polygon has interior angles summing to (n − 2) × 180°; its exterior angles always sum to 360°.

Density, speed and pressure

Density = mass ÷ volume, speed = distance ÷ time and pressure = force ÷ area; each formula can be rearranged for the missing quantity.

Estimated mean from grouped data

For grouped data, use each class midpoint as the value: estimated mean = Σ(frequency × midpoint) ÷ Σfrequency.

Mutually exclusive events

Events that cannot happen together; their probabilities add, and the probability of none of them is 1 minus their total probability.

Independent events

Events where one outcome does not affect the other; multiply their probabilities to find the probability that both happen.

Interquartile range

The difference between the upper quartile and lower quartile: IQR = Q3 − Q1; it measures the spread of the middle half of the data.

Frequency density

Frequency density = frequency ÷ class width; on a histogram, the area of each bar represents the frequency of that class.

Stratified sampling

A sample where each group contributes in proportion to its size: group sample = (group size ÷ population size) × total sample size.

Counterexample

A single example that makes a general statement false; one counterexample is enough to disprove a claim, but examples cannot prove a general rule.

Consecutive integer representation

Consecutive integers can be written as n and n + 1; consecutive even integers as 2n and 2n + 2; consecutive odd integers as 2n + 1 and 2n + 3.

Venn diagram probability

For two events A and B, P(A ∪ B) = P(A) + P(B) − P(A ∩ B); the subtraction avoids counting the overlap twice.

Checking by estimation

Round each number to one significant figure, calculate with the rounded values, and compare the estimate with the exact result to judge whether it is reasonable.

Unit consistency in formulas

Before substituting into a formula, convert all measurements to the same unit; if the length factor is L, area and volume factors are L² and L³ (cm to m: L = 100).