GCSE Maths Foundation: Algebra practice questions
Ten free GCSE Maths Foundation tier questions on simplifying, expanding, factorising, equations, sequences, rearranging and inequalities, each with a worked solution. Suitable for AQA, Edexcel and OCR.
Original questions written by Studoli tutors in the style of the GCSE exam. They are not official past questions.
Timed mode
10 questions in 15 minutes, one question at a time. Your answers are marked when you submit or when the time runs out.
Topic: Simplifying
1. Simplify 3a + 5b − a + 2b.
Solution
B. 2a + 7b
- Collect the a terms: 3a − a = 2a.
- Collect the b terms: 5b + 2b = 7b.
Topic: Expanding
2. Expand 4(x − 3).
Solution
A. 4x − 12
- Multiply each term in the bracket by 4.
- 4 × x = 4x and 4 × −3 = −12.
Topic: Equations
3. Solve 3x + 5 = 20.
Solution
D. x = 5
- Subtract 5 from both sides: 3x = 15.
- Divide by 3: x = 5.
Topic: Factorising
4. Factorise fully 6x + 9.
Solution
C. 3(2x + 3)
- The highest common factor of 6x and 9 is 3.
- 6x + 9 = 3(2x + 3). Check by expanding.
Topic: Substitution
5. Work out 2p + q² when p = 4 and q = −3.
Solution
B. 17
- 2p = 2 × 4 = 8.
- q² = (−3)² = 9, because a negative squared is positive.
- 8 + 9 = 17.
Topic: Sequences
6. Find the nth term of the sequence 5, 8, 11, 14, ...
Solution
A. 3n + 2
- The terms go up by 3, so the nth term starts 3n.
- When n = 1, 3n = 3, and the first term is 5, so add 2: 3n + 2.
Topic: Rearranging
7. Make t the subject of v = u + at.
Solution
D. t = (v − u)/a
- Subtract u from both sides: v − u = at.
- Divide by a: t = (v − u)/a.
Topic: Equations
8. Solve 2(x + 4) = 18.
Solution
C. x = 5
- Divide both sides by 2: x + 4 = 9.
- Subtract 4: x = 5.
Topic: Inequalities
9. Solve 4x − 1 < 11.
Solution
B. x < 3
- Add 1 to both sides: 4x < 12.
- Divide by 4: x < 3.
Topic: Straight-line graphs
10. What is the gradient of the line y = 4x − 7?
Solution
A. 4
- In y = mx + c, m is the gradient.
- Here m = 4.
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