Edexcel International GCSE Mathematics A · 4MA1
Maths questions with worked solutions
Use these original teaching questions to practise a method before attempting an exam paper. Each linked lesson contains a worked solution and a second question to try independently. They are Maiths teaching examples, not reproduced Pearson exam questions or official mark schemes.
Choose a question by skill
Quadratic equations: Solve x² − 2x − 15 = 0 without a calculator.
Simultaneous equations: Solve 3x + y = 14 and x + y = 6.
The quadratic formula: How many real roots does x² + 2x + 5 = 0 have?
Linear inequalities: List the integer solutions of 1 ≤ 2x − 1 < 7.
Arithmetic sequences: Does 100 occur in this sequence?
Rearranging formulae: Make r the subject of A = πr² for a radius r ≥ 0.
Percentage change: A value of 200 increases by 10% then decreases by 20%. Find the final value.
Reverse percentages: A population is 1260 after a 5% increase. Find the starting population.
Ratio: Simplify 45 minutes : 2 hours.
Standard form: Write 0.000072 in standard form.
Upper and lower bounds: A distance is 20 m to the nearest metre. State its error interval.
Right-angled trigonometry: Opposite = 6 and adjacent = 8. Find the angle to one decimal place.
Pythagoras’ theorem: Find the diagonal of a rectangle with sides 6 cm and 8 cm.
Vectors: If u = (3, −2) and v = (−1, 4), find 2u + v.
Transformations: Reflect (4, −2) in the line y = x.
Similarity: Similar triangles have areas 18 and 50. Find their corresponding length ratio.
Circle theorems: A radius meets a tangent at T. What angle do they form?
Straight-line graphs: Find the gradient of a line perpendicular to y = 2x + 1.
Differentiation: Find the tangent gradient to y = 2x³ − x at x = 2.
Histograms: A bar from 30 to 45 has density 2.4. Find its frequency.
Mean, median and mode: Four values have mean 7. A fifth value of 12 is added. Find the new mean.
Probability trees: Find the probability of one counter of each colour in either order.
Detailed question solutions
How to use the answers
Write a complete attempt before revealing the answer section. When your result differs, locate the first incorrect line rather than copying the entire solution. Then cover both attempts and reconstruct the calculation. A correct final number is useful evidence, but your explanation should also show why the method applies.
Choosing difficulty
Begin with a worked example when the method is unfamiliar. Move to the independent question after you can explain each step. Combine topics in a full paper only when you can choose the method without a heading giving it away. These are learning stages, not official exam grades or predicted marks.
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