O Level Mathematics: Coordinate Geometry Practice Questions (Cambridge 4024)

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs — Cambridge International holds copyright in its own papers. Use these alongside the official past papers available from your board.

Most questions practise a skill tested in the June 2025 papers. Questions marked (no calculator) are Paper 1 style; the rest allow a calculator, as in Paper 2. After each answer there is a tip and the real question to try next.

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Questions

1. (no calculator) Rearrange 4y + 3x = 12 to make y the subject, and state the gradient of the line. [2]

2. (no calculator) Line P is perpendicular to the line 4y + 3x = 12 and passes through (3, 2). Find the equation of line P. [3]

3. (no calculator) A is (−2, 5) and B is (6, −1). Find the midpoint of AB and the length of AB. [3]

4. (no calculator) Find the equation of the line through (1, 4) and (5, 12). [3]

5. (no calculator) Show that the lines y = 3x − 2 and 6x − 2y = 7 are parallel. [2]

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Answers

1. 4y = 12 − 3x, so y = 3 − ¾x [1]. Gradient = −¾ [1].

Tip: the gradient is the coefficient of x once y is the subject.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 17.

2. Gradient of P = 4/3, the negative reciprocal of −3/4 [1]. y − 2 = 4/3(x − 3) [1], so y = 4/3 x − 2 [1].

Tip: for a perpendicular gradient, flip the fraction and change the sign.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 17.

3. Midpoint = ((−2 + 6)/2, (5 − 1)/2) = (2, 2) [1]. Length = √(8² + 6²) [1] = 10 units [1].

Tip: subtract coordinates carefully when one of them is negative.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 14.

4. Gradient = (12 − 4) ÷ (5 − 1) = 2 [1]. y − 4 = 2(x − 1) [1], so y = 2x + 2 [1].

Tip: check your equation with the second point.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 17.

5. 6x − 2y = 7 gives y = 3x − 3.5 [1]. Both lines have gradient 3, so they are parallel [1].

Tip: parallel lines have equal gradients; say so in your conclusion.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 17.

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Where marks are usually lost

• Using the reciprocal without changing the sign for a perpendicular gradient.
• Making a sign error when subtracting negative coordinates.
• Leaving y not as the subject when asked.