BECE 2015 Mathematics Past Questions and Answers
The BECE 2015 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. List the members of the set Q = {Prime factors of 30}
- A. {2,3,5}
- B. {2,6,10}
- C. {3,5,15}
- D. {3,6,15}
Answer: A. {2,3,5}
A prime number is a number that has only two factors: 1 and the number itself.
Finding prime factors
1. Keep on dividing with prime number until you get 1
2. Multiply each of the prime numbers used in the division
Finding prime factors of 30
$\begin{matrix}2 & 30 \\ 3 & 15 \\ 5 & 5 \\ & 1\end{matrix}$
Prime factors of 30 = 2 x 3 x 5
Set of prime factors of 30 = {2,3,5}
A prime number is a number that has only two factors: 1 and the number itself.
Finding prime factors
1. Keep on dividing with prime number until you get 1
2. Multiply each of the prime numbers used in the division
Finding prime factors of 30
$\begin{matrix}2 & 30 \\ 3 & 15 \\ 5 & 5 \\ & 1\end{matrix}$
Prime factors of 30 = 2 x 3 x 5
Set of prime factors of 30 = {2,3,5}
2. Given that set P = {m,n,o,p}, find the number of subsets of P.
- A. 4
- B. 8
- C. 10
- D. 16
Answer: D. 16
Number of subsets = 2$^{n}$
Where n = number of elements of the set
The set P has 4 elements.
n = 4
Number of subsets = 2$^{4}$ = 2 x 2 x 2 x 2 = 16
Number of subsets = 2$^{n}$
Where n = number of elements of the set
The set P has 4 elements.
n = 4
Number of subsets = 2$^{4}$ = 2 x 2 x 2 x 2 = 16
3. If M = {Multiples of 4 between 10 and 25} and N = {even numbers between 11 and 23}, find M∪N.
- A. {12,16,20}
- B. {14,18,22}
- C. {12,14,16,18,22}
- D. {12,14,16,18,20,22,24}
Answer: D. {12,14,16,18,20,22,24}
M = {Multiples of 4 between 10 and 25}
M = {12,16,20,24}
N = {even numbers between 11 and 23}
N = {12,14,16,18,20,22}
Union (∪) is the list of each of the elements once in both sets.
M∪N = {12,14,16,18,20,22,24}
M = {Multiples of 4 between 10 and 25}
M = {12,16,20,24}
N = {even numbers between 11 and 23}
N = {12,14,16,18,20,22}
Union (∪) is the list of each of the elements once in both sets.
M∪N = {12,14,16,18,20,22,24}
4. What is the place value of 7 in 24.376?
- A. Unit
- B. Ten
- C. Tenth
- D. Hundredth
Answer: D. Hundredth
5. Find the Highest Common Factor of 24, 42 and 72
- A. 4
- B. 6
- C. 7
- D. 12
Answer: B. 6
Prime factors of 24
$\begin{matrix}2 & 24 \\ 2 & 12 \\ 2 & 6 \\ 3 & 3 \\ & 1\end{matrix}$
Prime factors = 2 x 2 x 2 x 3 = 2$^{3}$ x 3
Prime factors of 42
$\begin{matrix}2 & 42 \\ 3 & 21 \\ 7 & 7 \\ & 1\end{matrix}$
Prime factors = 2 x 3 x 7
Prime factors of 72
$\begin{matrix}2 & 72 \\ 2 & 36 \\ 2 & 18 \\ 3 & 9 \\ 3 & 3 \\ & 1\end{matrix}$
Prime factors = 2 x 2 x 2 x 3 x 3 = 2$^{3}$ x 3$^{2}$
Common prime factors are 2 and 3
The H.C.F is the product of each of the common prime factors in their lowest power = 2 x 3 = 6
Prime factors of 24
$\begin{matrix}2 & 24 \\ 2 & 12 \\ 2 & 6 \\ 3 & 3 \\ & 1\end{matrix}$
Prime factors = 2 x 2 x 2 x 3 = 2$^{3}$ x 3
Prime factors of 42
$\begin{matrix}2 & 42 \\ 3 & 21 \\ 7 & 7 \\ & 1\end{matrix}$
Prime factors = 2 x 3 x 7
Prime factors of 72
$\begin{matrix}2 & 72 \\ 2 & 36 \\ 2 & 18 \\ 3 & 9 \\ 3 & 3 \\ & 1\end{matrix}$
Prime factors = 2 x 2 x 2 x 3 x 3 = 2$^{3}$ x 3$^{2}$
Common prime factors are 2 and 3
The H.C.F is the product of each of the common prime factors in their lowest power = 2 x 3 = 6
6. Express 120$_{5}$ as a number in base 10.
- A. 25
- B. 27
- C. 32
- D. 35
Answer and explanation: practise this paper on ePrep.
7. If p x q x r = 1197, and p = 19, q = 3, find r.
- A. 21
- B. 49
- C. 57
- D. 61
Answer and explanation: practise this paper on ePrep.
8. How many integers are within the interval -5 < x < 7?
- A. 10
- B. 11
- C. 12
- D. 13
Answer and explanation: practise this paper on ePrep.
9. Divide 1.612 by 0.4.
- A. 4.3
- B. 4.03
- C. 0.403
- D. 0.43
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10. Arrange the following fractions in ascending order:$\frac{5}{8}$, $\frac{11}{20}$, $\frac{7}{10}$.
- A. $\frac{5}{8}$, $\frac{11}{20}$, $\frac{7}{10}$
- B. $\frac{7}{10}$, $\frac{5}{8}$, $\frac{11}{20}$
- C. $\frac{11}{20}$, $\frac{5}{8}$, $\frac{7}{10}$
- D. $\frac{5}{8}$, $\frac{7}{10}$, $\frac{11}{20}$
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