These are the solutions for BECE 2024 Mathematics Paper 1. The questions without the solutions may be found at BECE 2024 Maths Paper 1.
1. Two brands of air conditioners S and T cost GH₵ 3,000.00 and GH₵ 4,000.00 respectively. A company budgeted GH₵ 20,000.00 to buy air conditioners. If the company bought 5 units of brand S instead of brand T, how much did it save?
A. GH₵ 1,000.00
B. GH₵ 5,000.00
C. GH₵ 20,000.00
D. GH₵ 15,000.00
Answer: B
Solution
Method 1
By buying 5 units of brand S, the company spent 5 × GH₵ 3,000.00 = GH₵ 15,000.00.
If it had bought 5 units of brand T, it would have spent 5 × GH₵ 4,000.00 = GH₵ 20,000.00.
Hence, by buying brand S instead of brand T, the company saved GH₵ (20,000.00 – 15,000.00) = GH₵ 5,000.00
Method 2
Since the company bought 5 units of brand S instead of brand T, we can find the amount it saved by calculating how much it saved on each unit it bought and multiplying by the number of units bought.
On each unit of air conditioner, the company spent GH₵ 3,000.00 instead of GH₵ 4,000.00. That means the company saved GH₵ 1,000.00 on each unit it bought. Hence, the total savings for 5 units was 5 × GH₵ 1,000.00 = GH₵ 5,000.00.
2. Zalia and Amina shared an amount of money in the ratio 2:5. If Amina had GH₵ 150.00 more than Zalia, how much did they share?
A. GH₵ 100.00
B. GH₵ 250.00
C. GH₵ 450.00
D. GH₵ 350.00
Answer: D
Solution
Let the total amount of money Zalia and Amina shared be T.
If they shared it in the ratio 2:5, Zalia got \( \displaystyle \frac{2}{7}T \) while Amina got \( \displaystyle \frac{5}{7}T \).
Since Amina had GH₵ 150.00 more than Zalia, we have
$$ \frac{5}{7}T- \frac{2}{7}T = 150 $$
Solving for T gives
$$ \begin{align} \frac{5}{7}T- \frac{2}{7}T &= 150 \\ \frac{3}{7} T &= 150 \\ T &= 150 \times \frac{7}{3} \\ T &= 350 \end{align} $$
Hence, the total amount they shared was GH₵ 350.00.
3. Which of the following is an example of quantitative data?
A. Colour
B. Gender
C. Marital status
D. Length
Answer: D
Solution
Quantitative data relates to measurements, scales and the like, while categorical data relates to what kind or type a thing is.
Among the options given, length is the only entity that relates to measurement. Hence, it is the only example of quantitative data in the list.
In the diagram, P and Q are two sets and U is the universal set. Us the information to answer questions 4 and 5.
4. Find \( P \cap Q \).
A. {c, d, e}
B. {a, b}
C. {a, b, c, d, e}
D. {f, g, h}
Answer: A
Solution
The intersection of P and Q is the set of elements that are in both P and Q. In the Venn diagram, we see that Q is a subset of P. Hence, every element in Q is also in P, making Q the intersection of the two sets.
5. How many members are in set Q?
A. 2
B. 3
C. 8
D. 5
Answer: B
Solution
The members in set Q are those in the circle representing set Q. These are c, d, and e. Hence, there are three members in that set.
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