AQA · GCSE Maths 8300

AQA GCSE Maths: Ratio, proportion and rates of change — Practice Questions & Answers

Q: Simplify the ratio $12:18$ to its lowest terms.

$2:3$. Divide both parts by the highest common factor, which is $6$, giving $2:3$.

Q: Share $60$ pounds between two people in the ratio $1:2$. How much does the person with the larger share receive?

$40$ pounds. There are $1+2=3$ parts, so one part is $60\div 3=20$ pounds. The larger share is $2$ parts, $2\times 20=40$ pounds.

Q: In a class the ratio of boys to girls is $3:5$. What fraction of the class are boys?

$\frac{3}{8}$. Total parts $=3+5=8$, and boys are $3$ of those parts, so the fraction is $\frac{3}{8}$.

Q: A car travels $150$ km in $3$ hours at a constant speed. What is its speed?

$50$ km/h. Speed $=$ distance $\div$ time $=150\div 3=50$ km/h.

Q: Increase $80$ by $10\%$.

$88$. $10\%$ of $80$ is $8$, so the new amount is $80+8=88$.

Q: A map has a scale of $1:50000$. Two towns are $4$ cm apart on the map. What is the real distance?

$2$ km. Real distance $=4\times 50000=200000$ cm $=2000$ m $=2$ km.

Q: $5$ pens cost $2$ pounds. At the same rate, how much do $20$ pens cost?

$8$ pounds. $20$ pens is $4$ times as many as $5$ pens, so the cost is $4\times 2=8$ pounds.

Q: Decrease $200$ by $25\%$.

$150$. $25\%$ of $200$ is $50$, so $200-50=150$.

Q: Which of these is a measure of density?

kg/m$^{3}$. Density is mass per unit volume, so its units are mass divided by volume, for example kg/m$^{3}$.

Q: Divide $150$ pounds in the ratio $2:3:5$. What is the largest share?

$75$ pounds. Total parts $=2+3+5=10$, so one part is $150\div 10=15$ pounds. The largest share is $5\times 15=75$ pounds.

A complete guide to ratio and proportion for AQA GCSE Maths (8300): simplifying and sharing in ratios, converting ratios to fractions and percentages, scale drawings and maps, direct and inverse proportion with their equations, best-buy comparisons, percentage change including growth, decay, compound interest and depreciation, compound measures such as speed, density, pressure and rates of flow, unit conversion, and gradient as a rate of change.

502 practice questions available for this topic — here are 10 with full answers and explanations.

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Practice questions with answers

1 Multiple choice · Easy

Simplify the ratio $12:18$ to its lowest terms.

$2:3$
$3:2$
$4:6$
$6:9$

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2 Multiple choice · Easy

Share $60$ pounds between two people in the ratio $1:2$. How much does the person with the larger share receive?

$40$ pounds
$20$ pounds
$30$ pounds
$45$ pounds

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3 Multiple choice · Easy

In a class the ratio of boys to girls is $3:5$. What fraction of the class are boys?

$\frac{3}{8}$
$\frac{3}{5}$
$\frac{5}{8}$
$\frac{5}{3}$

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4 Multiple choice · Easy

A car travels $150$ km in $3$ hours at a constant speed. What is its speed?

$50$ km/h
$45$ km/h
$450$ km/h
$0.02$ km/h

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5 Multiple choice · Easy

Increase $80$ by $10\%$.

$88$
$90$
$72$
$8$

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6 Multiple choice · Easy

A map has a scale of $1:50000$. Two towns are $4$ cm apart on the map. What is the real distance?

$2$ km
$20$ km
$0.2$ km
$200$ km

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7 Multiple choice · Easy

$5$ pens cost $2$ pounds. At the same rate, how much do $20$ pens cost?

$8$ pounds
$10$ pounds
$4$ pounds
$40$ pounds

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8 Multiple choice · Easy

Decrease $200$ by $25\%$.

$150$
$50$
$175$
$250$

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9 Multiple choice · Easy

Which of these is a measure of density?

kg/m$^{3}$
m/s
N/m$^{2}$
km/h

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10 Multiple choice · Medium

Divide $150$ pounds in the ratio $2:3:5$. What is the largest share?

$75$ pounds
$50$ pounds
$45$ pounds
$30$ pounds

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Key terms in Ratio, proportion and rates of change

Ratio: A way of comparing two or more quantities, written with a colon, such as $3:2$.

Simplifying ratio: Writing a ratio in its simplest form by dividing all parts by their highest common factor, so $6:8$ becomes $3:4$.

Equivalent ratio: A ratio that represents the same comparison as another, such as $1:2$ and $3:6$.

Unit ratio: A ratio written so one part equals one, such as $1:n$, useful for comparison.

Dividing in a ratio: Sharing a quantity into parts that match a given ratio, such as splitting $20$ in the ratio $3:1$.

Part to part ratio: A ratio comparing one part of a whole with another part, such as boys to girls.

Part to whole ratio: A comparison of one part to the total, which can be written as a fraction of the whole.

Proportion: A statement that two ratios or fractions are equal, or the relationship between a part and a whole.

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AQA GCSE Maths: Ratio, proportion and rates of change — Practice Questions & Answers

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Key terms in Ratio, proportion and rates of change

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