Diese Aufgaben gibt es in ihrer Originalsprache.
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.
Originale Aufgaben von Studoli-Lehrkräften im Stil der Prüfung GCSE. Es sind keine offiziellen Prüfungsaufgaben.
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.
Thema: Simplifying
1. Simplify 3a + 5b − a + 2b.
Lösung
B. 2a + 7b
- Collect the a terms: 3a − a = 2a.
- Collect the b terms: 5b + 2b = 7b.
Thema: Expanding
2. Expand 4(x − 3).
Lösung
A. 4x − 12
- Multiply each term in the bracket by 4.
- 4 × x = 4x and 4 × −3 = −12.
Thema: Equations
3. Solve 3x + 5 = 20.
Lösung
D. x = 5
- Subtract 5 from both sides: 3x = 15.
- Divide by 3: x = 5.
Thema: Factorising
4. Factorise fully 6x + 9.
Lösung
C. 3(2x + 3)
- The highest common factor of 6x and 9 is 3.
- 6x + 9 = 3(2x + 3). Check by expanding.
Thema: Substitution
5. Work out 2p + q² when p = 4 and q = −3.
Lösung
B. 17
- 2p = 2 × 4 = 8.
- q² = (−3)² = 9, because a negative squared is positive.
- 8 + 9 = 17.
Thema: Sequences
6. Find the nth term of the sequence 5, 8, 11, 14, ...
Lösung
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.
Thema: Rearranging
7. Make t the subject of v = u + at.
Lösung
D. t = (v − u)/a
- Subtract u from both sides: v − u = at.
- Divide by a: t = (v − u)/a.
Thema: Equations
8. Solve 2(x + 4) = 18.
Lösung
C. x = 5
- Divide both sides by 2: x + 4 = 9.
- Subtract 4: x = 5.
Thema: Inequalities
9. Solve 4x − 1 < 11.
Lösung
B. x < 3
- Add 1 to both sides: 4x < 12.
- Divide by 4: x < 3.
Thema: Straight-line graphs
10. What is the gradient of the line y = 4x − 7?
Lösung
A. 4
- In y = mx + c, m is the gradient.
- Here m = 4.