Rearrange the formula to make m the subject.
k = 4(m − p) [2]
Show model answer
m = k/4 + p (or (k + 4p)/4)
Divide by 4 then add p.
O Level Mathematics: Algebra, questions with answers
Practise 94 real questions on Algebra from 2021 to 2026. See the answer and explanation as soon as you answer.
94real questions
2papers covered
11exam sessions
About Algebra in O Level Mathematics
Algebra is one of the 5 main topics in our O Level Mathematics (Cambridge (CAIE) 4024) question bank, and about 24% of its real questions come from it. Tayyari Karo has 94 real questions on this topic from 2021 to 2026, from Paper 1, Paper 2. By difficulty: 51 medium, 22 hard, 21 easy.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
The mass of a small box is x kg. The mass of a large box is y kg.
(a) The total mass of 4 small boxes and 6 large boxes is 30 kg.
Show that 2x + 3y = 15.
(b) The total mass of 6 small boxes and 1 large box is 13 kg.
Write down an equation in terms of x and y.
(c) Solve the simultaneous equations to find the mass of a small box and the mass of a large box. You must show all your working.
Show model answer
(a) 4x + 6y = 30
Divide every term by 2:
2x + 3y = 15
(b) 6x + y = 13
(c) From (b): y = 13 − 6x
Substitute into (a): 2x + 3(13 − 6x) = 15
2x + 39 − 18x = 15
−16x = 15 − 39 = −24
x = 1.5
y = 13 − 6(1.5) = 13 − 9 = 4
Small box = 1.5 kg
Large box = 4 kg
Form two equations from the word problem, then solve by substitution.
Solve the simultaneous equations. You must show all your working.
2a + 5b = 1.5
3a − 10b = 42.5
Show model answer
Multiply the first equation by 2:
4a + 10b = 3
Add this to the second equation:
4a + 10b + 3a − 10b = 3 + 42.5
7a = 45.5
a = 6.5
Substitute into the first equation:
2(6.5) + 5b = 1.5
13 + 5b = 1.5
5b = −11.5
b = −2.3
a = 6.5, b = −2.3
Scale one equation so a variable's coefficients match, then add or subtract to eliminate it.
a = (5b + 2x)/(x − 3)
Rearrange the formula to make x the subject.
Show model answer
a(x − 3) = 5b + 2x
ax − 3a = 5b + 2x
ax − 2x = 5b + 3a
x(a − 2) = 5b + 3a
x = (5b + 3a)/(a − 2)
Multiply out the denominator first, then collect all the x terms on one side and factorise.
(a) Benjamin's age is t years.
(i) Maryam is 5 years younger than Benjamin. Write an expression for Maryam's age in terms of t.
(ii) Colin's age is twice Benjamin's age. Write an expression for Colin's age in terms of t.
(b) Given that a = 3 and b = −2, evaluate 5a − 2b.
Show model answer
(a)(i) Maryam's age = t − 5
(a)(ii) Colin's age = 2t
(b) 5a − 2b = 5(3) − 2(−2) = 15 + 4 = 19
Translate each sentence directly into an expression; substitute carefully with the negative sign.
f(x) = x/4 + 3 g(x) = 2(x − 1)
(a) Find f(−8).
(b) Find f⁻¹(x).
(c) f(p) = g(p + 5). Find the value of p.
Show model answer
(a) f(−8) = (−8)/4 + 3 = −2 + 3 = 1
(b) Let y = x/4 + 3
y − 3 = x/4
x = 4(y − 3) = 4y − 12
f⁻¹(x) = 4x − 12 (= 4(x − 3))
(c) f(p) = p/4 + 3
g(p + 5) = 2((p+5) − 1) = 2(p + 4) = 2p + 8
p/4 + 3 = 2p + 8
Multiply every term by 4:
p + 12 = 8p + 32
12 − 32 = 8p − p
−20 = 7p
p = −20/7
Substitute into the rule; swap x and y and rearrange to invert; set the two expressions equal and solve for p.
Factorise 3a² + 12a
Show model answer
Highest common factor of 3a² and 12a is 3a.
3a² + 12a = 3a(a + 4)
Take out the highest common factor of the two terms.
Factorise.
(a) 3cx + 2bx − 6cy − 4by
(b) 6x² + 7x − 10
Show model answer
(a) Group in pairs:
3cx + 2bx − 6cy − 4by = x(3c + 2b) − 2y(3c + 2b)
= (3c + 2b)(x − 2y)
(b) Need two numbers multiplying to 6 × (−10) = −60 and summing to 7: these are 12 and −5.
6x² + 12x − 5x − 10
= 6x(x + 2) − 5(x + 2)
= (x + 2)(6x − 5)
Group terms with a common factor for (a); split the middle term for (b) using factors of ac that sum to b.
Sessions with Algebra questions
| Session | Paper 1 | Paper 2 |
|---|---|---|
| May/June 2026 | 4 | 7 |
| May/June 2025 | 5 | 5 |
| Oct/Nov 2025 | 4 | 6 |
| May/June 2024 | 6 | 2 |
| Oct/Nov 2024 | 7 | 2 |
| May/June 2023 | 7 | 1 |
| Oct/Nov 2023 | 4 | 3 |
| May/June 2022 | 5 | 2 |
| Oct/Nov 2022 | 6 | 3 |
| May/June 2021 | 6 | 2 |
| Oct/Nov 2021 | 6 | 1 |
Common questions
What does the Algebra topic cover on this page?
94 real O Level Mathematics (4024) questions on Algebra from 2021 to 2026, from Paper 1, Paper 2. Each one shows the year, session and paper it came from.
Do I get the answers and explanations?
Yes. Every question shows the correct answer and a short explanation the moment you answer.
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