Introduction to algebra: past paper questions

Where the questions come from

• Question 2May/June 2026, paper 11Structured2 marks

  Bella is $b$ years old. Alan is 5 years older than Bella. Write an expression, in terms of $b$, for how old Alan is.

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• Question 8Oct/Nov 2025, paper 11Structured2 marksHas a diagram

  $p=3q-2r$ Work out the value of $q$ when $p=50$ and $r=5$.

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• Question 2Oct/Nov 2023, paper 12Structured2 marks

  Asha works in a café. Her wage is calculated using the formula $\text{wage}=\text{hourly rate}\times \text{number of hours}+\text{bonus}$. Her hourly rate is $11.52 . One week Asha works 25 hours and receives a bonus of $5.40 .

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• Question 4May/June 2026, paper 13Structured2 marks

  A car hire company uses this formula to work out the hire cost, in dollars.

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• Question 11Oct/Nov 2025, paper 13Structured5 marks

  Sam buys 3 apples at 40 cents each. He also buys 5 peaches.

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• Question 15Oct/Nov 2024, paper 12Structured2 marks

  In a league, teams gain 4 points for each win, 2 points for each draw and bonus points.

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• Question 9Oct/Nov 2023, paper 12Structured2 marks

  $v=u+at$ Find the value of $v$ when $u=30$, $a=-2$ and $t=7$.

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• Question 10May/June 2026, paper 13Structured2 marks

  $K=2x+\sqrt{y}$ Find the value of $K$ when $x=5$ and $y=169$.

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• Question 11Oct/Nov 2025, paper 32Structured2 marks

  Y = 3t^2 + 2m Find the value of Y when t = 6 and m = -3.

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• Question 17Oct/Nov 2024, paper 13Structured4 marks

  Ed has $n$ books. Sam has 3 times as many books as Ed Jane has 2 books fewer than Sam. The total number of books is 54.

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• Question 20May/June 2026, paper 31Structured5 marks

  $P=5x+4y$ Find the value of $x$ when $P=18$ and $y=-3$.

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• Question 4Oct/Nov 2024, paper 33Structured10 marks

  $$n=15r+20c$$ Find the value of $r$ when $n=180$ and $c=3$.

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• Question 14May/June 2026, paper 32Structured7 marks

  There are 60 counters in a jar. Kan adds $C$ counters into the jar. Mo adds $2C+7$ counters into the jar.

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• Question 7May/June 2025, paper 11Structured2 marks

  A ticket costs $18.

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• Question 6May/June 2024, paper 33Structured14 marks

  In a sport, teams are given points using the formula $$\text{number of points}=\text{number of wins}\times 4+\text{number of draws}\times 2+\text{bonus points}\mathrm{.}$$ One team has 15 wins, 7 draws and 6 bonus points. Calculate the total number of points for this team.

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• Question 8May/June 2025, paper 31Structured4 marks

  $T=3(5P-8)+4$ Find the value of $T$ when $P=12$.

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• Question 5May/June 2023, paper 33Structured14 marksHas a diagram

  The grid shows the first three diagrams in a sequence. Each diagram is made using sticks. On the grid, draw Diagram 4.

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• Question 14May/June 2025, paper 32Structured4 marks

  $P=6a+5b$ Find the value of $b$ when $P=25$ and $a=3$.

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• Question 15May/June 2025, paper 33Structured7 marks

  The table gives information about the costs of hiring bikes.

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