BECE 2005 Mathematics Past Questions and Answers
The BECE 2005 Mathematics paper has 40 objective and 6 theory questions. Here are sample objective questions with the correct answers and explanations. Sit the full paper with the real time limit on ePrep.
Sample questions with answers
1. 
In the diagram above, A and B are two intersecting sets. How many members are in the set B?
In the diagram above, A and B are two intersecting sets. How many members are in the set B?
- A. 2
- B. 3
- C. 5
- D. 7
Answer: C. 5
B = {b, d, i, o, u}
B has 5 members.
B = {b, d, i, o, u}
B has 5 members.
2. Which of the following is not a factor of 18?
- A. 3
- B. 4
- C. 6
- D. 9
Answer: B. 4
A factor of a number is a number which can divide the number without a remainder.
3 divides 18, 6 times
6 divides 18, 3 times
9 divides 18, 2 times
4 divides 18, 4 times (4 x 4 = 16) with a remainder of 2.
A factor of a number is a number which can divide the number without a remainder.
3 divides 18, 6 times
6 divides 18, 3 times
9 divides 18, 2 times
4 divides 18, 4 times (4 x 4 = 16) with a remainder of 2.
3. Multiply 0.014 by 0.2
- A. 0.00028
- B. 0.0028
- C. 0.028
- D. 0.28
Answer: B. 0.0028
Change the decimals to whole number x 10$^{-n}$.
Where n is the number of times you have to move the decimal point to the right to obtain a whole number.
0.014 = 0.⌒0⌒1⌒4. = 14 x 10$^{-3}$
0.2 = 0.⌒2. = 2 x 10$^{-1}$
0.014 x 0.2 = 14 x 10$^{-3}$ x 2 x 10$^{-1}$
0.014 x 0.2 = 14 x 2 x 10$^{-3}$ x 10$^{-1}$
Apply the law of multiplication of indices for the base 10
Law of multiplication of indices
a$^{m}$ x a$^{n}$ = a$^{m + m}$
0.014 x 0.2 = 28 x 10$^{-3 + -1}$ = 28 x 10$^{-4}$
Change the whole number x 10$^{-n}$ back to decimal by moving the decimal point n times to the left.
Every whole number has a decimal point at the end which is not written.
28 = 28.0
In 28 x 10$^{-4}$, you are to move the decimal point 4 times to the left.
28 x 10$^{-4}$ = 0.⌒0⌒0⌒2⌒8.0 = 0.0028
Change the decimals to whole number x 10$^{-n}$.
Where n is the number of times you have to move the decimal point to the right to obtain a whole number.
0.014 = 0.⌒0⌒1⌒4. = 14 x 10$^{-3}$
0.2 = 0.⌒2. = 2 x 10$^{-1}$
0.014 x 0.2 = 14 x 10$^{-3}$ x 2 x 10$^{-1}$
0.014 x 0.2 = 14 x 2 x 10$^{-3}$ x 10$^{-1}$
Apply the law of multiplication of indices for the base 10
Law of multiplication of indices
a$^{m}$ x a$^{n}$ = a$^{m + m}$
0.014 x 0.2 = 28 x 10$^{-3 + -1}$ = 28 x 10$^{-4}$
Change the whole number x 10$^{-n}$ back to decimal by moving the decimal point n times to the left.
Every whole number has a decimal point at the end which is not written.
28 = 28.0
In 28 x 10$^{-4}$, you are to move the decimal point 4 times to the left.
28 x 10$^{-4}$ = 0.⌒0⌒0⌒2⌒8.0 = 0.0028
4. Given that A = {b, c, i} and B = {a, e, f, i}, find A ∩ B.
- A. {a, b, c, e, f, i}
- B. {f, i}
- C. {a}
- D. {i}
Answer: D. {i}
Intersection (∩) are elements that can be found in both sets
The element(s) that can be found in both the sets A and B is/are {i}
Intersection (∩) are elements that can be found in both sets
The element(s) that can be found in both the sets A and B is/are {i}
5. If a = 64 and b = 2$^{2}$, find $\frac{a}{b}$.
- A. 32
- B. 16
- C. $\frac{1}{16}$
- D. $\frac{1}{32}$
Answer: B. 16
Method I
2$^{2}$ = 2 x 2 = 4
a = 64 and b = 4
$\frac{a}{b}$ = $\frac{64}{4}$ = 16
Method II
Using indices.
64 = 2 x 2 x 2 x 2 x 2 x 2 = 2$^{6}$
a = 2$^{6}$
$\frac{a}{b}$ = $\frac{{2}^{6}}{{2}^{2}}$
Apply the law of division of indices.
Law of division of indices
$\frac{{a}^{m}}{{a}^{n}}$ = a$^{m - n}$
$\frac{a}{b}$ = $\frac{{2}^{6}}{{2}^{2}}$ = 2$^{6 - 2}$ = 2$^{4}$
2$^{4}$ = 2 x 2 x 2 x 2 = 16
$\frac{a}{b}$ = 16
Method I
2$^{2}$ = 2 x 2 = 4
a = 64 and b = 4
$\frac{a}{b}$ = $\frac{64}{4}$ = 16
Method II
Using indices.
64 = 2 x 2 x 2 x 2 x 2 x 2 = 2$^{6}$
a = 2$^{6}$
$\frac{a}{b}$ = $\frac{{2}^{6}}{{2}^{2}}$
Apply the law of division of indices.
Law of division of indices
$\frac{{a}^{m}}{{a}^{n}}$ = a$^{m - n}$
$\frac{a}{b}$ = $\frac{{2}^{6}}{{2}^{2}}$ = 2$^{6 - 2}$ = 2$^{4}$
2$^{4}$ = 2 x 2 x 2 x 2 = 16
$\frac{a}{b}$ = 16
6. Arrange the following numbers from the highest to the lowest: $\frac{2}{3}$, -7, 0.
- A. -7, 0, $\frac{2}{3}$
- B. -7, $\frac{2}{3}$, 0
- C. 0, $\frac{2}{3}$, -7
- D. $\frac{2}{3}$, 0, -7
Answer and explanation: practise this paper on ePrep.
7. Simplify 2$^{2}$ × 3$^{2}$ × 2$^{3}$ × 3$^{4}$.
- A. 2$^{2}$ × 3$^{6}$
- B. 2$^{4}$ × 3$^{7}$
- C. 2$^{5}$ × 3$^{6}$
- D. 2$^{6}$ × 3$^{8}$
Answer and explanation: practise this paper on ePrep.
8. In an examination 40% of the students failed. The number of students that passed was 180. How many students failed?
- A. 120
- B. 270
- C. 300
- D. 450
Answer and explanation: practise this paper on ePrep.
9. Evaluate $\frac{1}{3}$[(5 – 1) – (2 – 7)]
- A. -3
- B. -1
- C. 1
- D. 3
Answer and explanation: practise this paper on ePrep.
10. If 6*n* + 4 = 16, find the value of n.
- A. 2
- B. 3
- C. 5
- D. 6
Answer and explanation: practise this paper on ePrep.
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