GCSE Maths Specification

AQA 8300

Section R: Ratio, proportion and rates of change

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#R1

change freely between related standard units (eg time, length, area, volume/capacity, mass) and compound units (eg speed, rates of pay, prices) in numerical contexts

compound units (eg density, pressure)

in numerical and algebraic contexts

#R2

use scale factors, scale diagrams and maps

Notes: including geometrical problems.

#R3

express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1

#R4

use ratio notation, including reduction to simplest form

#R5

divide a given quantity into two parts in a given part : part or part : whole ratio

express the division of a quantity into two parts as a ratio

apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

Notes: including better value or best-buy problems.

#R6

express a multiplicative relationship between two quantities as a ratio or a fraction

#R7

understand and use proportion as equality of ratios

#R8

relate ratios to fractions and to linear functions

Notes: see also N11, R14

#R9

define percentage as ‘number of parts per hundred’

interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively

express one quantity as a percentage of another

compare two quantities using percentages

work with percentages greater than 100%

solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics

Notes: see also N2, N12

#R10

solve problems involving direct and inverse proportion, including graphical and algebraic representations

#R11

use compound units such as speed, rates of pay, unit pricing

use compound units such as density and pressure

Notes: including making comparisons.

#R12

compare lengths, areas and volumes using ratio notation

scale factors

make links to similarity (including trigonometric ratios)

Notes: see also G19, G20

#R13

understand that \(X\) is inversely proportional to \(Y\) is equivalent to \(X\) is proportional to \(\dfrac{1}{Y}\)

interpret equations that describe direct and inverse proportion

construct and interpret equations that describe direct and inverse proportion

#R14

interpret the gradient of a straight-line graph as a rate of change

recognise and interpret graphs that illustrate direct and inverse proportion

Notes: see also A15, R8

#R15

interpret the gradient at a point on a curve as the instantaneous rate of change

apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts


Notes: see also A15

#R16

set up, solve and interpret the answers in growth and decay problems, including compound interest

and work with general iterative processes