Algebra and graphs — IGCSE Mathematics (0980) questions by topic

Setting up and solving an equation from a bus-ticket pricing scenario, simplifying a power raised to a further power, solving a simple linear equation, and spotting the pattern in a falling number sequence anchor this algebra-and-graphs page's 21 questions, drawn from 2025 papers and worth between 2 and 11 marks. Find, express, calculate, solve and state test both manipulation and clear final statements.

Because algebraic slips often happen in the setting-up stage rather than the final step, submit your full working for instant marking to see exactly where an index law or equation-forming error is being penalised.

May–June 2025, Paper 12

Question 14 · 11 marks

Complete the table of values for y = (x + 3)(x - 2). x -4 -3 -2 -1 0 1 2 3 --- ---- ---- ---- ---- --- --- --- --- y 6 -4 -4

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Question 15 · 2 marks

Beth thinks of a positive number, n. She squares n then subtracts 55. The answer is 9. Work out the value of n.

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Question 23 · 4 marks

Factorise. 9x - 6xy

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Question 24 · 3 marks

Solve the simultaneous equations. 5x + 2y = 3 3x + 4y = 27

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May–June 2025, Paper 22

Question 6 · 5 marks

Solve. 8x + 7 = 39

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Question 7 · 3 marks

These are the first 4 terms of a sequence. 11 8 5 2 Find the next term of this sequence.

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Question 15 · 6 marks

The diagram shows the graph of y = 2/x - 1. Write down the coordinates of the point where the graph crosses the x-axis.

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Question 20 · 4 marks

y is proportional to 1/sqrt(x). When x = 9, y = 2. Find the value of y when x = 36.

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Question 21 · 9 marks

The diagram shows the graph of y = 3x - x^3. The graph crosses the x-axis at A, at O and at B. The turning points of the graph are at P and at Q. Find the x-coordinate of A and…

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Question 24 · 5 marks

The line y = 7x + 3 intersects the curve y = x^2 + 5x - 12 at the points A and B. Find the coordinates of A and B.

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May–June 2025, Paper 32

Question 13 · 5 marks

The sequence begins: 2, e, f, 20, … A linear sequence has a first term of 2 and a fourth term of 20. The term-to-term rule for this sequence is add k. Work out the values of e, f…

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Question 14 · 4 marks

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

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Question 20 · 3 marks

Solve. x + 3 = 3

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Question 21 · 3 marks

Simplify. (w^3)^10

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Question 22 · 7 marks

In this question, all lengths are in centimetres. The diagram shows a right-angled triangle with sides 2x − 5, 2x + 2 and 4x − 9. Write down an expression, in terms of x, for the…

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May–June 2025, Paper 42

Question 7 · 2 marks

y = mx + c Rearrange the formula to make m the subject.

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Question 9 · 3 marks

Solve the simultaneous equations. You must show all your working. 2w - 3y = 11 3w + y = 11

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Question 10 · 3 marks

A group of 12 adults and 9 children travel on a bus. The cost of an adult ticket is $n. The cost of a child ticket is $(n - 10). The total cost of the tickets is $277.50 . Find…

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Question 14 · 2 marks

Factorise. 5x - 10 - ax + 2a

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Question 19 · 6 marks

f(x) = x + 1 g(x) = 5 - 2x h(x) = 2^x Find f(-3).

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Question 24 · 8 marks

Ahmed walks 2 km at a speed of x km/h. He then walks a further 3 km at a speed of (x + 1) km/h. The total time he takes to walk the 5 km is 1 1/4 hours. Show that 5x^2 - 15x - 8 =…

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