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17th Jun, 2025 9:30 AM

BECE

BECE 2025 - MATHEMATICS [PAPER II]

1. (a)

Given that $P = \{ \text{multiples of 3} \}$ and $Q = \{ \text{positive even numbers} \}$ are subsets of $\mu = \{ x : 1 \leq x \leq 20, \text{where } x \text{ is a counting number} \}$.

(i) List all the elements in $P \cap Q$.

(ii) If $y = 3k - \frac{2}{x}$,

(i) Make $y$ the subject of the relation.

(ii) Using the result in (b)(i), find the value of $y$ when $x = -1$ and $k = 2$.

2. (a)

Evaluate $\frac{4000 \times 0.35}{0.05}$, leaving the answer in standard form.

(b) Mr Boakye gets 10% commission on type 

$P$ houses he sells and 15% on type $Q$ house. He sells 3 type $P$ houses at GH¢ 700,000.00 each and 4 type $Q$ at GH¢ 1,400,000.00 each. Calculate the total commissions he makes.

3. (a)

Given that $a = \left( \frac{2}{3} \right)$, $b = \left( \frac{3}{-3} \right)$ and $c = \left( \frac{7}{3} \right)$, find:

(i) The value of $x$, if $2a + b = c$.

(ii) $d = c - 3a$.

(iii) $|d|$.

(b) A Polytank contains 4500 litres of water and $\frac{1}{3}$ of the water is used for cleaning.

(i) Find the volume of water used for cleaning.

(ii) What percentage of water is left in the tank?

4. (a)

A woman borrowed GH¢ 5,300.00 to pay for her child's university fees. If she borrowed at a rate of 8% simple interest per annum for 9 months, find the interest paid.

(b) A father shared his piece of land to his three children. The first child had $\frac{1}{4}$ of the land and the second had 5 acres more than the first. If the third child had 20 acres, find how many acres of land:

(i) The father shared.

(ii) The first child received.

(iii) The second child received.

5. (a)

The pie chart shows the weight (in kg) of items Mrs. Mensah bought for her household.

NOT DRAWN TO SCALE

(i) What angle represents fish?

(ii) If she bought a total of 20 kg of items,

(a) What is the weight of flour bought?

(b) Express, correct to one decimal place, the weight of sugar as a percentage of the weight of rice.

(b) In a class of 30 students, five wear glasses. If a student is selected at random from the class, what is the probability that the student does not wear glasses?

(c) Adamu was travelling a distance of 40 km from Kadungu to Datanu. Sixty minutes after starting the journey, he made a stop at Cooltown, 10 km from Kadungu to rest for 30 minutes. He then continued the journey from Cooltown and reached Datanu 60 minutes later.

(i) Using a scale of 2 cm to 20 minutes on the horizontal axis and 2 cm to 5 km on the vertical axis, draw a distance-time graph for Adamu's journey.

(ii) Use the graph to determine:

(i) Distance from Cooltown to Datanu.

(ii) Total time (in minutes) taken by Adamu to make the whole journey including the rest time.

(iii) Average speed of Adamu from Cooltown to Datanu.

(iii) If Adamu did not rest but travelled to Datanu within the time, what was his average speed?

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