What does the Ratio, proportion and rates of change content cover?

It covers ratio and scale (simplifying ratios, sharing in a ratio, maps and scale drawings), direct and inverse proportion using the unitary method and proportion equations, percentage change and interest including multipliers, reverse percentages and compound interest, compound measures such as speed, density and pressure, and growth, decay and rates of change from graphs. It applies number skills to real-world contexts.

How do you share an amount in a ratio?

Add the parts of the ratio to find the total number of shares, divide the amount by that total to find the value of one share, then multiply by each part of the ratio. For example, sharing thirty-six pounds in the ratio two to one gives three shares of twelve pounds, so the parts are twenty-four pounds and twelve pounds. Always check the parts add back to the original total.

What is the difference between simple and compound interest?

Simple interest pays the same amount each year, calculated on the original sum, so it grows in a straight line. Compound interest pays interest on the growing balance, calculated with a repeated multiplier, so it grows faster over time. For compound interest, multiply the starting amount by one plus the rate as a decimal, raised to the power of the number of years.

How do you do a reverse percentage?

A reverse percentage finds the original amount before a change. Because the percentage was applied to the original, you divide the new amount by the multiplier rather than subtracting the percentage of the new value. If a price after a twenty percent reduction is sixty-eight pounds, divide by zero point eight to get the original price of eighty-five pounds.

What does the gradient of a graph tell you?

The gradient is a rate of change. On a distance-time graph the gradient is the speed; on a speed-time graph the gradient is the acceleration, and the area under the line is the distance travelled. For a curved graph, the gradient at a point is estimated by drawing a tangent and finding its gradient. Reading the axes tells you what the rate represents.

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Edexcel GCSE Mathematics Ratio, proportion and rates of change: a complete overview

A deep-dive Edexcel GCSE Mathematics guide to Ratio, proportion and rates of change. Covers ratio and scale, direct and inverse proportion, percentage change and interest, compound measures, and growth, decay and rates of change, with the methods and exam patterns Edexcel repeats across both tiers.

Generated by Claude Opus 4.815 min read1MA1 RUpdated 2026-06-02

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What this content demands
Ratio and scale
Direct and inverse proportion
Percentage change and interest
Compound measures
Growth, decay and rates of change
Check your knowledge

What this content demands

Ratio, proportion and rates of change is where number skills meet the real world: money, mixtures, maps, speed, density and growth. Edexcel examines it heavily because it underpins everyday reasoning, and many questions are multi-step word problems that reward clear method and careful units.

This guide walks through the five areas and ties together the matching dot-point pages, each of which has its own practice questions.

Ratio and scale

Simplify ratios by dividing all parts by their highest common factor, after converting to the same units. Share a quantity by adding the parts, finding one part, then scaling up. A ratio $a : b$ gives fractions $\dfrac{a}{a+b}$ and $\dfrac{b}{a+b}$ of the whole. Combine ratios by matching the shared quantity. Map scales such as $1 : 25000$ convert between map and real distances by multiplying or dividing, with care over unit conversion.

Direct and inverse proportion

In direct proportion $y = kx$ : more means proportionally more, and the graph is a line through the origin. In inverse proportion $y = \dfrac{k}{x}$ : more means proportionally less, and the graph is a reciprocal curve. The unitary method (find one unit, then scale) handles most problems, while Higher tier forms proportion equations with a constant $k$ , including squares and roots.

Percentage change and interest

Use multipliers: $+15\%$ is $\times 1.15$ , $-15\%$ is $\times 0.85$ . Percentage change divides the change by the original. A reverse percentage divides by the multiplier. Compound interest uses a repeated multiplier $\left(1 + \tfrac{r}{100}\right)^n$ , growing faster than simple interest, and depreciation uses a multiplier below $1$ .

Compound measures

Speed $= \dfrac{\text{distance}}{\text{time}}$ , density $= \dfrac{\text{mass}}{\text{volume}}$ , pressure $= \dfrac{\text{force}}{\text{area}}$ , each rearrangeable with a formula triangle. The frequent pitfall is units: write minutes as a fraction of an hour, and convert both parts when changing a compound unit such as m/s to km/h.

Growth, decay and rates of change

Repeated growth or decay uses a multiplier raised to a power. The gradient of a graph is a rate of change (speed on distance-time, acceleration on speed-time), and the area under a speed-time graph is distance. For curves, estimate the gradient with a tangent and the area with strips.

Check your knowledge

A mix of ratio, proportion and percentage questions. Attempt them under timed conditions, then check against the solutions.

Share $£900$ in the ratio $4 : 5$ . (3 marks)
$7$ pens cost $£2.45$ . Work out the cost of $11$ pens. (2 marks)
Increase $£240$ by $12\%$ . (2 marks)
A price falls by $20\%$ to $£96$ . Find the original price. (3 marks)
£1500 is invested at $2\%$ compound interest for $3$ years. Find its value. (3 marks)
A car travels $90\,\text{km}$ in $1$ hour $30$ minutes. Find its average speed. (2 marks)
An object has mass $500\,\text{g}$ and volume $20\,\text{cm}^3$ . Find its density. (2 marks)
$y$ is inversely proportional to $x$ ; when $x = 3$ , $y = 8$ . Find $y$ when $x = 6$ . (3 marks)

Solutions

Step 1: Q1 - sharing in a ratio

Add the parts of the ratio to find the total number of shares, find the value of one share by dividing the total amount, then multiply each part:

$4 + 5 = 9$ parts; one part $= 900 \div 9 = \text{\pounds}100$ ; shares are $\text{\pounds}400$ and $\text{\pounds}500$ .

Step 2: Q2 - unitary method for proportion

Find the cost of one item (the unitary value), then scale up to the required quantity:

One pen $= 2.45 \div 7 = \text{\pounds}0.35$ ; $11$ pens $= 0.35 \times 11 = \text{\pounds}3.85$ .

Step 3: Q3 - percentage increase with a multiplier

An increase of $12\%$ corresponds to a multiplier of $1.12$ (keeping the original $100\%$ and adding $12\%$ ). Multiply the original amount directly:

240 \times 1.12 = \text{\pounds}268.80

Step 4: Q4 - reverse percentage

A reduction of $20\%$ gives a multiplier of $0.8$ , so the new price equals $0.8 \times \text{original}$ . Reverse this by dividing:

\text{original} = 96 \div 0.8 = \text{\pounds}120

Step 5: Q5 - compound interest

Compound interest uses a repeated multiplier: multiply the principal by $(1 + r)^n$ where $r$ is the rate as a decimal and $n$ is the number of years:

1500 \times 1.02^3 = \text{\pounds}1591.81

Step 6: Q6 - average speed

Speed is distance divided by time, but the time must be in hours. Convert $1$ hour $30$ minutes to $1.5$ hours first:

90 \div 1.5 = 60\,\text{km/h}

Step 7: Q7 - density

Density is mass divided by volume. Substitute the given values, keeping consistent units:

500 \div 20 = 25\,\text{g/cm}^3

Step 8: Q8 - inverse proportion

In inverse proportion $y = \frac{k}{x}$ , so $k = xy$ . Find the constant using the given pair, then use it to find $y$ for the new $x$ :

$k = 3 \times 8 = 24$ , so $y = 24 \div 6 = 4$ .

Sources & how we know this

Pearson Edexcel GCSE (9-1) Mathematics (1MA1) specification — Pearson Edexcel (2015)