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
Complete the table of values for y = (x + 3)(x - 2). x -4 -3 -2 -1 0 1 2 3 --- ---- ---- ---- ---- --- --- --- --- y 6 -4 -4
Answer this question and get it marked →Beth thinks of a positive number, n. She squares n then subtracts 55. The answer is 9. Work out the value of n.
Answer this question and get it marked →Solve the simultaneous equations. 5x + 2y = 3 3x + 4y = 27
Answer this question and get it marked →May–June 2025, Paper 22
These are the first 4 terms of a sequence. 11 8 5 2 Find the next term of this sequence.
Answer this question and get it marked →The diagram shows the graph of y = 2/x - 1. Write down the coordinates of the point where the graph crosses the x-axis.
Answer this question and get it marked →y is proportional to 1/sqrt(x). When x = 9, y = 2. Find the value of y when x = 36.
Answer this question and get it marked →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…
Answer this question and get it marked →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.
Answer this question and get it marked →May–June 2025, Paper 32
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…
Answer this question and get it marked →P = 6a + 5b Find the value of b when P = 25 and a = 3.
Answer this question and get it marked →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…
Answer this question and get it marked →May–June 2025, Paper 42
y = mx + c Rearrange the formula to make m the subject.
Answer this question and get it marked →Solve the simultaneous equations. You must show all your working. 2w - 3y = 11 3w + y = 11
Answer this question and get it marked →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…
Answer this question and get it marked →f(x) = x + 1 g(x) = 5 - 2x h(x) = 2^x Find f(-3).
Answer this question and get it marked →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 =…
Answer this question and get it marked →Other IGCSE Mathematics topics
- Number (36)
- Geometry (14)
- Mensuration (7)