BECE Mathematics Past Questions 2023

Find the volume of a cylinder with height 5 cm and base radius 7 cm. [Take π = 22/7]

A square has a side of 2 cm with a circle inscribed in it. Find the area of the region inside the square but outside the circle. [Take π = 22/7]

Convert 12.03 metres to centimetres.

What is the three-figure bearing of S25°E?

A quadrilateral with exactly one pair of opposite sides parallel is called a

Solve: 3(x − 2) − x/3 + 6 > 0.

Write 0.01723 in standard form.

What is the value of 3x² + 2x − 7 when x = −3?

The mapping x → y gives pairs (1, 4), (2, 2), (3, 0), (4, −2), (5, −4). Find the rule.

Find the gradient of line PQ that passes through P(−5, −3) and Q(−4, −7).

If n(E) = 15, n(F) = 20 and n(E ∩ F) = 6, find n(E ∪ F).

Given that m = b/2 − t, make t the subject.

Tony shared 2/3 of his plot equally among his three sons. What fraction of the plot did each son receive?

A square has a side of 2 cm with a circle inscribed in it. Find the area of the circle. [Take π = 22/7]

Araba and Ama share 20 oranges and Ama receives 12. Find the ratio of Araba's share to Ama's share.

Which of the following is an even prime number?

Find the translation vector that maps the point (2, 6) onto (5, 4).

Find the image of the point S(−2, 2) when reflected in the y-axis.

Expand: (x − 2)(x + 4).

A bag contains 20 oranges, 6 of which are bad. If one orange is picked at random, what is the probability that it is good?

If 2n − 5 = n/2, find n.

Find the simple interest on GH₵ 350.00 for 4 years at 5% per annum.

Madam Esi used ¼ and ⅔ of her x acres of land to cultivate mangoes and oranges respectively. (a) Express, in terms of x, the acres used for: (i) mangoes; (ii) oranges. (b) If Madam Esi used 20 more acres for oranges than mangoes, find the value of x. (c) How many acres were used to cultivate mangoes? (d) Calculate, correct to the nearest whole number, the percentage of land NOT used.

Given that 1 km = 5/8 mile, what is 240 miles in kilometres?

John walks for 22½ minutes and runs for 7½ minutes. What percentage of the total time does he spend walking?

Kobby is 5 years older than his brother. If Kobby is 13 years old, how old is his brother?

Arrange in ascending order: 9/5, 1.88 and 15/8.

Simplify: (x − 1)² − 1.

Simplify: (1½ − 5/6) × 9/10.

Factorise: 2pq + 6p − 6q − 18.

One man takes 12 hours to complete a piece of work. How long will 6 men, working at the same rate, take to complete the same work?

A book was sold for GH₵ 48.00 at a profit of 20%. Find the cost price.

A mixture of cement and sand weighs 35 kg. The ratio of cement to sand is 2:5. How many kilograms of cement are in the mixture?

Which of the following is NOT an integer?

Simplify: 5⁷ × 5⁻⁴ ÷ 5³.

If q = (−2, 3) and r = (3, −2), find q − r.

(a)(i) Express 8 × 32 × 4 × 2 in the form 2ᵐ. (a)(ii) Using your answer in (a)(i), state the value of m. (b)(i) Factorize the expression πn²k − ¼πn²Q. (b)(ii) Using your answer in (b)(i), find the value when π = 22/7, n = 2, k = 19 and Q = 20. (c) Gifty and Justina shared GH₵418.00. If Gifty had 20% more than Justina, how much did Justina receive?

(a) Simplify: 15(4 − 6) × 49 ÷ 7 (b) Expand and simplify: b(12a − 3) − (a − b)(3 + b) (c) Akosua walked for 3 hours at 1½ km/h from her village to Paamu to take a bus to Quamu. The bus travelling at 15½ km/h takes 2 hours to travel from Paamu to Quamu. (i) What is the distance from Akosua's village to Quamu? (ii) How long would it take a man riding a bicycle at 5 km/h to travel the same distance?

Given the sets A = {multiples of 3 less than 12}, B = {integers between 4 and 8} and C = {4, 5, 7}, find: (a)(i) A∩B (a)(ii) (A∪B)∩C (a)(iii) (A∩B)∪C (b) Simplify: 1¾ − 2⅚ − 1 9/10 + 4⅞