A-Level Maths steps up sharply from GCSE in both depth and the expectation of clear, logical working. The way through is volume and variety: solve a steady stream of problems across pure, mechanics and statistics, and study clean solutions to internalise the methods examiners reward. Maths Daily Helper generates unlimited fresh A-Level-style problems across all three strands, each with a full worked solution, so you always have something new to attempt and a model answer to check against.
Content covered
- Pure mathematics: algebra and functions, coordinate geometry, sequences, trigonometry, exponentials and logarithms, differentiation, integration, numerical methods, vectors.
- Mechanics: kinematics, forces and Newton's laws, moments, projectiles.
- Statistics: data presentation, probability, statistical distributions, hypothesis testing.
Try a few A-Level-style problems
Attempt each one on paper first, then reveal the working.
Differentiate y = 3x⁴ − 2x + 7 with respect to x.
1. Differentiate term by term using the power rule d/dx(xⁿ) = n·xⁿ⁻¹.
2. d/dx(3x⁴) = 12x³; d/dx(−2x) = −2; d/dx(7) = 0.
Answer: dy/dx = 12x³ − 2.
Find ∫ (6x² + 4) dx.
1. Integrate term by term: ∫ 6x² dx = 2x³, and ∫ 4 dx = 4x.
2. Add the constant of integration.
Answer: 2x³ + 4x + C.
Solve 2ˣ = 10, giving x to 3 significant figures.
1. Take logs of both sides: x·log 2 = log 10 = 1.
2. So x = 1 / log 2 = 1 / 0.30103.
3. = 3.3219…
Answer: x ≈ 3.32.
Find the gradient of the line joining (1, 2) and (4, 11).
1. Gradient = (y₂ − y₁)/(x₂ − x₁) = (11 − 2)/(4 − 1).
2. = 9/3.
Answer: 3.
A body starts from rest and accelerates at 4 m/s² for 6 s. Find its final velocity.
1. Use v = u + at, with u = 0, a = 4, t = 6.
2. v = 0 + 4 × 6 = 24.
Answer: 24 m/s.
A force of 20 N acts on a mass of 5 kg. Find the acceleration.
1. Newton's second law: F = ma, so a = F/m.
2. a = 20 / 5 = 4.
Answer: 4 m/s².
Find the mean of the data set: 4, 8, 10, 6, 12.
1. Sum the values: 4 + 8 + 10 + 6 + 12 = 40.
2. Divide by how many there are: 40 ÷ 5 = 8.
Answer: 8.
Solve cos x = 0 for x in [0°, 360°).
1. cos x = 0 where the cosine graph crosses zero.
2. In [0°, 360°) that happens at x = 90° and x = 270°.
Answer: x = 90° or 270°.
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Open Maths Daily Helper →How to build A-Level Maths fluency
The jump from GCSE is real, so consistency matters more than ever. Fifteen to twenty problems a day, spread across the strands you are studying, keeps every method fresh across the two-year course. Use hints before full solutions so you train the habit of finding the next step yourself, then reserve worked solutions for checking and for the problems that genuinely defeat you. Closer to exams, generate timed papers so pace and rigorous working become automatic.