- No data uploaded
- Instant results
A-Level Maths Algebra Questions
Practise algebra (mathematics) for the A-Level Mathematics: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Algebra practice
-
Q1.Find the sum of the first 26 terms of the AP 9, 18, 27, …
Show answer & explanation
Answer: C — 3159
Sₙ = n/2 × [2a + (n − 1)d] = 26/2 × [18 + 225] = 3,159.
-
Q2.Solve: x² − 3x − 18 = 0
Show answer & explanation
Answer: B — -3, 6
Find two roots with sum 3 and product -18: -3 and 6. So x² − 3x − 18 = (x + 3)(x − 6) = 0.
-
Q3.Find the sum of the first 12 terms of the AP 10, 16, 22, …
Show answer & explanation
Answer: D — 516
Sₙ = n/2 × [2a + (n − 1)d] = 12/2 × [20 + 66] = 516.
-
Q4.Solve: x² + 10x + 24 = 0
Show answer & explanation
Answer: C — -6, -4
Find two roots with sum -10 and product 24: -4 and -6. So x² + 10x + 24 = (x + 4)(x + 6) = 0.
-
Q5.Find log 100 (base 10).
Show answer & explanation
Answer: C — 2
log_10(100) asks “10 to what power gives 100?” → 10^2 = 100, so the answer is 2.
-
Q6.Solve: 3x + 5y = 64 and 4x + 5y = 67
Show answer & explanation
Answer: B — x = 3, y = 11
Elimination/substitution gives x = 3, y = 11. Check: 3(3) + 5(11) = 64 ✓ and 4(3) + 5(11) = 67 ✓.
-
Q7.Solve: 2x + 3y = 4 and 4x + y = 28
Show answer & explanation
Answer: C — x = 8, y = -4
Elimination/substitution gives x = 8, y = -4. Check: 2(8) + 3(-4) = 4 ✓ and 4(8) + 1(-4) = 28 ✓.
-
Q8.Solve: x² + 12x + 27 = 0
Show answer & explanation
Answer: D — -9, -3
Find two roots with sum -12 and product 27: -9 and -3. So x² + 12x + 27 = (x + 9)(x + 3) = 0.
-
Q9.Solve: x + 3y = 40 and x + 4y = 50
Show answer & explanation
Answer: C — x = 10, y = 10
Elimination/substitution gives x = 10, y = 10. Check: 1(10) + 3(10) = 40 ✓ and 1(10) + 4(10) = 50 ✓.
-
Q10.Solve: 5x + 2y = 23 and 3x + 5y = 10
Show answer & explanation
Answer: C — x = 5, y = -1
Elimination/substitution gives x = 5, y = -1. Check: 5(5) + 2(-1) = 23 ✓ and 3(5) + 5(-1) = 10 ✓.
How to approach algebra questions
Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution. For simultaneous equations, elimination is usually faster than substitution under time pressure.
About A-Level Maths
A-Level Mathematics — conducted by AQA, Pearson Edexcel, OCR and other boards. Pure maths, statistics and mechanics for university entrance in the UK.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
A-Level Maths practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |