Skip to main content

GCSE Higher · grades 4–9 · 20% of marks

GCSE Higher — Ratio, proportion and rates of change

On GCSE Higher, ratio, proportion and rates of change is worth 20% of the marks — enough that a weak patch here shows up in the final grade. 16 statements make up ratio, proportion and rates of change here. Each has its own page with the specification wording, the common mistakes, and questions. The list includes converting between standard and compound units, scale factors, scale diagrams and maps, one quantity as a fraction of another, ratio notation and simplest form, dividing in a ratio and multiplicative relationships as ratios or fractions. The Higher-only part of this area is instantaneous rate of change: gradients of curves. The assessment objectives split 40% AO1 against 60% AO2 and AO3 combined, which is why so many questions ask you to explain or to justify rather than simply to calculate. Most of this area is natural Paper 1 material, so practise it without a calculator before you practise it with one.

  • R1 — Converting between standard and compound units
  • R2 — Scale factors, scale diagrams and maps
  • R3 — One quantity as a fraction of another
  • R4 — Ratio notation and simplest form
  • R5 — Dividing in a ratio
  • R6 — Multiplicative relationships as ratios or fractions
  • R7 — Proportion as equality of ratios
  • R8 — Ratios, fractions and linear functions
  • R9 — Percentages and percentage change
  • R10 — Direct and inverse proportion
  • …and 6 more ratio, proportion and rates of change statements at this tier

Practise

GCSE Higher · Ratio, proportion and rates of changeQuestion 1 of 20 · 0 correct
Practice mode· no pressure · hints available

Ratio, proportion and rates of change

R6

Intermediate

A baker uses 450 g of flour and 300 g of butter in a batch of pastry. Write the mass of butter as a fraction of the total mass of flour and butter, in its simplest form.

💡 Hints:
Printable worksheetNon-calculator sheetSample Paper 1Sample Paper 2

The 16 DfE statements in ratio, proportion and rates of change at Higher

R1Converting between standard and compound unitseither paper
30 questions
R2Scale factors, scale diagrams and mapseither paper
30 questions
R3One quantity as a fraction of anothernon-calculator
30 questions
R4Ratio notation and simplest formnon-calculator
30 questions
R5Dividing in a rationon-calculator
30 questions
R6Multiplicative relationships as ratios or fractionsnon-calculator
30 questions
R7Proportion as equality of ratiosnon-calculator
31 questions
R8Ratios, fractions and linear functionsnon-calculator
30 questions
R9Percentages and percentage changeeither paper
30 questions
R10Direct and inverse proportioneither paper
30 questions
R11Compound units: speed, density, pressureeither paper
30 questions
R12Ratio in similar shapes: lengths, areas and volumeseither paper
30 questions
R13Equations of direct and inverse proportionpart Highereither paper
Higher-only part: "construct and"30 questions
R14Gradient as a rate of changeeither paper
30 questions
R15Instantaneous rate of change: gradients of curvesHigher onlyeither paper
30 questions
R16Growth and decay, compound interestpart Highercalculator
Higher-only part: "and work with general iterative processes"30 questions

Related

Ratio, proportion and rates of change at Foundation25% of Higher marksNumberHigher · 15% of marksAlgebraHigher · 30% of marksStatisticsHigher · 7.5% of marks

Questions people ask

How much of the GCSE Higher paper is ratio, proportion and rates of change?

20% of the total marks, and the three papers each carry an equal share of the qualification, so it is spread across all of them rather than concentrated in one.

How many topics are there in ratio, proportion and rates of change at GCSE Higher?

16 DfE content statements, coded R1 to R16 within this area. Every question in the bank is tagged to one of them.

Which ratio, proportion and rates of change topics are Higher only?

Instantaneous rate of change: gradients of curves (R15). A further 2 statements have a Higher-only part inside otherwise shared content.

Can I use a calculator for ratio, proportion and rates of change questions?

Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 16 statements in this area, 6 are naturally non-calculator and 1 naturally calculator, with the rest workable either way — so practise both.

What kind of marks does ratio, proportion and rates of change carry?

The GCSE Higher split is 40% AO1 (use and apply standard techniques), 30% AO2 (reason, interpret and communicate) and 30% AO3 (solve problems in and out of context). Questions in this area are set across all three.

Are these past paper questions?

No. Every question at /gcse-higher is original, written to the DfE content statements and checked before it is published. We do not host past papers or mark schemes.

We keep your progress and preferences in your browser only (local storage), and use analytics cookies to improve the site. Read the privacy notice.

More information