BECE 2026 Mathematics Past Questions and Answers

Paper 1: Objectives

1. A trader sold an article for $\text{GH}¢126.00$ marking a profit of 20%.
   Find the cost price of the item.
   1. A. $\text{GH}¢100.80$
   2. B. $\text{GH}¢151.20$
   3. C. $\text{GH}¢105.00$
   4. D. $\text{GH}¢100.50$
   Answer: C

   Cost price = Selling price ÷ (1 + profit%) = 126 ÷ 1.20 = $\text{GH}¢105.00$
2. Ivy and Abbey share an amount of $\text{GH}¢30.00$ in the ratio 3 : 2 respectively. Find Abbey's share.
   1. A. $\text{GH}¢18.00$
   2. B. $\text{GH}¢12.00$
   3. C. $\text{GH}¢10.00$
   4. D. $\text{GH}¢15.00$
   Answer: B

   Total parts = 3 + 2 = 5. Abbey's share = (2/5) × 30 = $\text{GH}¢12.00$
3. Given the sequence $-9,-5,m,3,7,11$, find the value of $m$.
   1. A. $1$
   2. B. $-2$
   3. C. $-3$
   4. D. $-1$
   Answer: D

   The common difference is $-5-(-9)=4$. So $m=-5+4=-1$.
4. A class of 42 learners shared some oranges and each received 11.
   If 22 learners shared the same number of oranges equally, how many will each get?
   1. A. 22
   2. B. 15
   3. C. 21
   4. D. 20
   Answer: C

   Total oranges = 42 × 11 = 462. Each of 22 learners gets 462 ÷ 22 = 21.
5. Kofi had 150 birds.
   He sold 26 of them and kept the rest equally in 4 cages.
   How many birds were kept in each cage?
   1. A. 36
   2. B. 35
   3. C. 30
   4. D. 31
   Answer: D

   Remaining birds = 150 − 26 = 124. Birds per cage = 124 ÷ 4 = 31.
6. Arrange the following: $\frac{3}{4},0.8,\frac{5}{8},0.65$ in descending order.
   1. A. $0.65,\frac{5}{8},\frac{3}{4},0.8$
   2. B. $\frac{3}{4},\frac{5}{8},0.8,0.65$
   3. C. $\frac{5}{8},0.8,\frac{3}{4},0.65$
   4. D. $0.8,\frac{3}{4},0.65,\frac{5}{8}$
   Answer: D

   Converting all to decimals: 3/4 = 0.75, 0.8, 5/8 = 0.625, 0.65. Descending order: 0.8, 0.75, 0.65, 0.625 → $0.8,\frac{3}{4},0.65,\frac{5}{8}$
7. Find the volume of a cube with side 5 m.
   1. A. $10{\text{ m}}^3$
   2. B. $125{\text{ m}}^3$
   3. C. $75{\text{ m}}^3$
   4. D. $25{\text{ m}}^3$
   Answer: B

   Volume of a cube = side³ = 5³ = 125 m³
8. Make $y$ the subject of the relation $p=\frac{r-4y}{3}$.
   1. A. $y=\frac{1}{4}(r+3p)$
   2. B. $y=\frac{1}{4}(r+p)$
   3. C. $y=\frac{1}{4}(r-3p)$
   4. D. $y=\frac{1}{4}(3p-r)$
   Answer: C

   Multiply both sides by 3: $3p=r-4y$. Rearranging: $4y=r-3p$, so $y=\frac{1}{4}(r-3p)$.
9. In a test, $\frac{2}{3}$ of the learners passed.
   If the number of learners who failed was 69, how many passed?
   1. A. 23
   2. B. 207
   3. C. 138
   4. D. 46
   Answer: C

   If 2/3 passed, then 1/3 failed. So 1/3 of total = 69, meaning total = 207. Passed = 2/3 × 207 = 138.
10. Write 0.000437 in standard form.
    1. A. $4.37\times 10^{-3}$
    2. B. $4.37\times 10^3$
    3. C. $4.37\times 10^4$
    4. D. $4.37\times 10^{-4}$
    Answer: D

    0.000437 = 4.37 × 10⁻⁴ (move decimal 4 places to the right).

Answers and solutions for questions 11 to 40 are free in the BECE Past Questions app, with timed practice and offline study.

On an iPhone? Download on the App Store

On Android? Get it on Google Play

11. Find the circumference of a circle whose area is $100\pi {\text{ cm}}^2$.
    1. A. $10\pi \text{ cm}$
    2. B. $5\pi \text{ cm}$
    3. C. $15\pi \text{ cm}$
    4. D. $20\pi \text{ cm}$
12. A number is chosen at random from the set $P=\{1,2,3,4,5,\dots 10\}$.
    What is the probability that the number is greater than 3?
    1. A. $\frac{7}{10}$
    2. B. $\frac{4}{5}$
    3. C. $\frac{3}{10}$
    4. D. $\frac{1}{5}$
13. Antwi has 20 mangoes and 20% are rotten.
    How many of them are not rotten?
    1. A. 8
    2. B. 4
    3. C. 16
    4. D. 12
14. Simplify: $\sqrt{75}-\sqrt{18}-\sqrt{3}+\sqrt{2}$.
    1. A. $4\sqrt{3}-2\sqrt{2}$
    2. B. $3\sqrt{3}+2\sqrt{2}$
    3. C. $3\sqrt{3}-2\sqrt{2}$
    4. D. $4\sqrt{3}+2\sqrt{2}$
15. If $a=\left(\begin{array}{c}3\\ 1\end{array}\right)$ and $b=\left(\begin{array}{c}-2\\ 1\end{array}\right)$, evaluate $6b+2a$.
    1. A. $\left(\begin{array}{c}6\\ 8\end{array}\right)$
    2. B. $\left(\begin{array}{c}1\\ 3\end{array}\right)$
    3. C. $\left(\begin{array}{c}-6\\ 8\end{array}\right)$
    4. D. $\left(\begin{array}{c}-1\\ 3\end{array}\right)$
16. Which of the following is not a composite number?
    1. A. 39
    2. B. 24
    3. C. 65
    4. D. 41
17. Factorize: $3a^{2}b-9a{b}^2$.
    1. A. $3ab(b-3a)$
    2. B. $3ab(a-3b)$
    3. C. $ab(3b-a)$
    4. D. $ab(3a-b)$
18. A boy spends $\frac{1}{4}$ of his pocket money on books and $\frac{1}{3}$ on pens.
    What fraction remains?
    1. A. $\frac{5}{6}$
    2. B. $\frac{1}{6}$
    3. C. $\frac{7}{12}$
    4. D. $\frac{5}{12}$
19. Change 25% to a fraction in its lowest form.
    1. A. $\frac{1}{2}$
    2. B. $\frac{5}{6}$
    3. C. $\frac{1}{8}$
    4. D. $\frac{1}{4}$
20. Evaluate: $p^2(q-1)$ when $p=2$ and $q=\frac{3}{4}$.
    1. A. $-1$
    2. B. $1$
    3. C. $2$
    4. D. $-2$
21. A cyclist travelling at 20 km/h covered a distance in 35 minutes.
    What time will it take to cover the same distance travelling at 28 km/h?
    1. A. 48 minutes
    2. B. 16 minutes
    3. C. 25 minutes
    4. D. 49 minutes
22. Mary receives a commission of 15% on articles sold in a week.
    If her commission was $\text{GH}¢60.00$, how much sales did she make?
    1. A. $\text{GH}¢40.00$
    2. B. $\text{GH}¢900.00$
    3. C. $\text{GH}¢400.00$
    4. D. $\text{GH}¢90.00$
23. Find the value of $y$ in the diagram.
    
    1. A. $34°$
    2. B. $28°$
    3. C. $30°$
    4. D. $60°$
24. The product of three numbers is 90.
    If two of the numbers are 6 and 3, find the third number.
    1. A. 9
    2. B. 18
    3. C. 15
    4. D. 5
25. What is the rule for the mapping?
    
    1. A. $x\to x+2$
    2. B. $x\to 3x$
    3. C. $x\to 4-x$
    4. D. $x\to 2x+1$
26. Simplify: $x-5(3-2x)-12x+7$.
    1. A. $x+8$
    2. B. $-21x+8$
    3. C. $-x-8$
    4. D. $-21x-8$
27. Given that $\mu =\{1,2,3,\dots 10\}$ and $M=\{2,3,5,7\}$, where $M$ is a subset of $\mu$.
    List the members in $\mu$ that are not in $M$.
    1. A. {2, 4, 6, 8, 10}
    2. B. {1, 4, 6, 8, 9, 10}
    3. C. {2, 4, 6, 8}
    4. D. {1, 4, 6}
28. Find the median mark.
    
    1. A. 1
    2. B. 2
    3. C. 4
    4. D. 3
29. Find the probability that a learner selected at random scored 2.
    
    1. A. $\frac{7}{22}$
    2. B. $\frac{4}{22}$
    3. C. $\frac{2}{22}$
    4. D. $\frac{1}{22}$
30. If $(x+2):(x-2)=1:2$,
    find the value of $x$.
    1. A. $-3$
    2. B. $-2$
    3. C. $-6$
    4. D. $-35$
31. Kofi paid an interest of $\text{GH}¢30.00$ on a loan he took for 4 years.
    If the rate was 3% per annum simple interest, find the amount borrowed.
    1. A. $\text{GH}¢250.00$
    2. B. $\text{GH}¢280.00$
    3. C. $\text{GH}¢360.00$
    4. D. $\text{GH}¢90.00$
32. Solve: $7-2x>15-4x$.
    1. A. $x<4$
    2. B. $x>-4$
    3. C. $x<-4$
    4. D. $x>4$
33. Theresa was asked to select at random a letter from the word HAPPY.
    What is the probability that she selects the letter P?
    1. A. $\frac{2}{5}$
    2. B. $\frac{3}{5}$
    3. C. $\frac{1}{2}$
    4. D. $\frac{1}{5}$
34. Mr Mensah left his house at 9:45 am and reached his village at 4:15 pm.
    Find the time spent.
    1. A. 6 hours 30 minutes
    2. B. 7 hours
    3. C. 8 hours
    4. D. 5 hours 30 minutes
35. Two sets which have the same number of members are . . . sets
    1. A. union
    2. B. equivalent
    3. C. equal
    4. D. intersecting
36. A square of area 144 cm² has the same perimeter as an equilateral triangle.
    Find the length of a side of the triangle.
    1. A. 14 cm
    2. B. 16 cm
    3. C. 10 cm
    4. D. 18 cm
37. If $2^{2m}=8$, find the value of $m$.
    1. A. 1.5
    2. B. 2.0
    3. C. 1.0
    4. D. 0.5
38. If $\frac{3}{4}x=2+\frac{1}{4}$,
    find the value of $x$.
    1. A. 3
    2. B. 5
    3. C. 1
    4. D. 4
39. The marks obtained by 11 learners in a test are:
    2, 5, 5, 6, 7, 7, 8, 8, 8, 9, 10.
    What is the modal mark?
    1. A. 9
    2. B. 7
    3. C. 2
    4. D. 8
40. Find the image of the point $(2,-3)$ under the transformation $\left(\begin{array}{c}x\\ y\end{array}\right)\to \left(\begin{array}{c}x\\ y-2\end{array}\right)$.
    1. A. $(2,-1)$
    2. B. $(2,5)$
    3. C. $(2,-5)$
    4. D. $(2,1)$

Paper 2: Theory

1. Given that $K=\{1,2,3,\dots 11\}$:
   (i) List the prime numbers in $K$.
   (ii) Find the probability that a number selected at random from the set $K$ is not a prime number.
2. Factorize completely: $(x+y)(2m-n)-m(x+y)$.
3. A typist charges GH¢ 68.00 for the first 8 sheets typed, and GH¢ 11.00 for each additional sheet. Calculate the amount earned if the typist typed a total of 35 sheets.
4. The image of $P(2,5)$ when translated by the vector $r$ is $(-3,8)$.
   Find:
   (i) $r$.
   (ii) The image $Q^{\prime }$ of $Q(-4,-6)$ when translated by $r$.
5. Joyce and Richard contributed GH¢ 10,000.00 and GH¢ 5,000.00 respectively to start a business. They agreed that Richard will be paid one-third of the profit as a manager and the rest of the profit will be shared in the ratio of their contributions.
   If the profit of GH¢ 9,000.00 was made, how much did:
   (i) Joyce receive?
   (ii) Richard receive in total?
6. Asana was engaged to collect cashew-fruits on a farm and was paid a wage of GH¢ 25.00 a day. If the daily wage increased by 10% and she worked for 30 days, how much will she be paid?
7. The diagram shows the floor of a room with its dimensions (an L-shaped floor with outer dimensions 8 m × 5 m and a rectangular notch of 5 m × 3 m cut from one corner).
   Find the:
   (i) Perimeter.
   (ii) Area.
   (iii) Cost of carpeting the floor if a carpet costs GH¢ 20.00 per square metre.
   
8. In a school, the monthly incomes of three workers, Aku, Brako and Dagadu, are GH¢ 5,000.00, GH¢ 6,500.00 and GH¢ 4,200.00 respectively.
   (i) Calculate the yearly income of each worker.
   (ii) Find the yearly income difference between Aku and Dagadu.
   (iii) Find the total yearly income of all three workers.
9. A painter places a ladder against a building at the window. The angle the foot of the ladder makes with the horizontal ground is 60°. The distance from the foot of the ladder to the base of the building is 5 m.
   (i) Illustrate the information in a diagram.
   (ii) Find, correct to one decimal place, the:
   (α) Length of the ladder.
   (β) Distance between the window and the foot of the building.
   [Take tan 60° = 1.732 and cos 60° = 1/2]
10. Simplify $\frac{\sqrt{72}}{\sqrt{18}-\sqrt{12}}$, leave the answer in the form $a+b\sqrt{c}$, where $a$, $b$ and $c$ are integers.
11. Solve: $\frac{1}{2}(2x+1)\ge \frac{1}{3}x+1\frac{9}{10}$.
12. An athlete runs four times round a circular track of radius 70 m.
    Find, in metres, the total distance covered by the athlete.
    [Take $\pi =\frac{22}{7}$]
13. The data shows the shoe sizes of learners in a school.
    (a) Construct a frequency distribution table for the data.
    (b) If the school supplies shoes to the learners:
    (i) Which size should be purchased in large quantities?
    (ii) Give a reason for the answer in (b)(i).
    (iii) Which size should be purchased in fewer quantities?
    (iv) Give a reason for the answer in (b)(iii).
    (c) Find, correct to the nearest whole number, the mean shoe size.
    

Worked solutions to the theory questions are free in the app.

On an iPhone? Download on the App Store

On Android? Get it on Google Play