BECE 2011 Mathematics Past Questions and Answers
The BECE 2011 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. Which of the following is the set of prime factors of 12?
- A. {2, 3}
- B. {1, 2, 3}
- C. {1, 2, 4, 6}
- D. {2, 3, 4, 6}
Answer: A. {2, 3}
Prime numbers are numbers which has only two factors, thus only two numbers can divide without a remainder (1 and itself).
Note: 1 is not a prime number because 1 can only be divided by one number, 1 itself.
Prime numbers are numbers which has only two factors, thus only two numbers can divide without a remainder (1 and itself).
Note: 1 is not a prime number because 1 can only be divided by one number, 1 itself.
2. Expand 3*a*(a – 4*b*)
- A. 3*a* – 12*ab*
- B. 3*a*$^{2}$ – 12*ab*
- C. 3*a*$^{2}$ – 12*b*
- D. 3*a*$^{2}$ – 12*a*
Answer: B. 3*a*$^{2}$ – 12*ab*
Expansion simply means multiply each of the terms outside the bracket by each of the terms inside the bracket.
3*a*(a – 4*b*) = 3*a* x a - 3*a* x 4*b*
3*a*(a – 4*b*) = 3*a*$^{2}$ - 12*ab*
Note: Every number is raised to the power 1 but it is not written.
Law of multiplication of indices
a$^{m}$ x a$^{n}$ = a$^{m + m}$
a x a = a$^{1}$ x a$^{1}$
a x a = a$^{1+1}$
a x a = a$^{2}$
3 x 4 = 12
Expansion simply means multiply each of the terms outside the bracket by each of the terms inside the bracket.
3*a*(a – 4*b*) = 3*a* x a - 3*a* x 4*b*
3*a*(a – 4*b*) = 3*a*$^{2}$ - 12*ab*
Note: Every number is raised to the power 1 but it is not written.
Law of multiplication of indices
a$^{m}$ x a$^{n}$ = a$^{m + m}$
a x a = a$^{1}$ x a$^{1}$
a x a = a$^{1+1}$
a x a = a$^{2}$
3 x 4 = 12
3. Express 5 as a percentage of 4.
- A. 125%
- B. 120%
- C. 25%
- D. 20%
Answer: A. 125%
Expressing one number as a % of another number
You calculate one number as a percentage of another by dividing the numbers and multiplying by 100.
The percentage = $\frac{The number}{The other number}$ x 100%
$\frac{5}{4}$ x 100% = 5 x 25%
$\frac{5}{4}$ x 100% = 125%
Expressing one number as a % of another number
You calculate one number as a percentage of another by dividing the numbers and multiplying by 100.
The percentage = $\frac{The number}{The other number}$ x 100%
$\frac{5}{4}$ x 100% = 5 x 25%
$\frac{5}{4}$ x 100% = 125%
4. Express 2700 as a product of prime numbers.
- A. 2$^{2}$ × 3$^{2}$ × 5$^{2}$
- B. 2 × 3$^{3}$ × 5$^{2}$
- C. 2$^{2}$ × 3$^{3}$ × 5$^{2}$
- D. 2 × 3$^{2}$ × 5$^{3}$
Answer: C. 2$^{2}$ × 3$^{3}$ × 5$^{2}$
Expressing a number as a product of prime numbers
1. Divide the number with the smallest prime factor until it cannot be divided any further
2. Move to the next prime factor. Keep on dividing until it cannot be divided any further.
3. Repeat step 2 until you get 1 as a remainder.
4. Write down the product (multiplication) of each of the prime factors in the division.
5. Simplify the indices using the multiplication law of indices.
Prime products of 2700
$\begin{matrix} & 2700 \\ 2 & 1350 \\ 2 & 675 \\ 3 & 225 \\ 3 & 75 \\ 3 & 25 \\ 5 & 5 \\ 5 & 1\end{matrix}$
Count each of the prime numbers to get their exponents/power.
2700 = 2$^{2}$ x 3$^{3}$ x 5$^{2}$
Expressing a number as a product of prime numbers
1. Divide the number with the smallest prime factor until it cannot be divided any further
2. Move to the next prime factor. Keep on dividing until it cannot be divided any further.
3. Repeat step 2 until you get 1 as a remainder.
4. Write down the product (multiplication) of each of the prime factors in the division.
5. Simplify the indices using the multiplication law of indices.
Prime products of 2700
$\begin{matrix} & 2700 \\ 2 & 1350 \\ 2 & 675 \\ 3 & 225 \\ 3 & 75 \\ 3 & 25 \\ 5 & 5 \\ 5 & 1\end{matrix}$
Count each of the prime numbers to get their exponents/power.
2700 = 2$^{2}$ x 3$^{3}$ x 5$^{2}$
5. The ratio of mangoes to oranges in a basket is 3:2. If there are 36 mangoes, how many oranges are in the basket?
- A. 90
- B. 60
- C. 24
- D. 12
Answer: C. 24
The sum of the ratios correspond to the total items. Each ratio correspond to its number of items.
Ratio of mangoes = 3
Ratio of oranges = 2
If ratio 3 (mangoes) = 36
then ratio 2 (oranges) = $\frac{2 x 36}{3}$ = 24 oranges
Note: 3 divides itself one and 36, 12 times.
The sum of the ratios correspond to the total items. Each ratio correspond to its number of items.
Ratio of mangoes = 3
Ratio of oranges = 2
If ratio 3 (mangoes) = 36
then ratio 2 (oranges) = $\frac{2 x 36}{3}$ = 24 oranges
Note: 3 divides itself one and 36, 12 times.
6. Express 0.125 as a fraction in its lowest form.
- A. $\frac{1}{8}$
- B. $\frac{1}{9}$
- C. $\frac{1}{12}$
- D. $\frac{1}{16}$
Answer and explanation: practise this paper on ePrep.
7. Convert 222$_{five}$ to a number in base ten.
- A. 30
- B. 52
- C. 60
- D. 62
Answer and explanation: practise this paper on ePrep.
8. If A = {18, 19, 20} and B = {15, 16, 17}, find A∩B.
- A. {15, 16, 17, 18, 19, 20}
- B. {15, 16, 18, 19}
- C. {18, 19}
- D. {}
Answer and explanation: practise this paper on ePrep.
9. Simplify 3$^{9}$ ÷ 3$^{3}$
- A. 3$^{27}$
- B. 3$^{12}$
- C. 3$^{6}$
- D. 3$^{3}$
Answer and explanation: practise this paper on ePrep.
10. An article which costs GH¢ 25.00 was sold for GH¢ 35.00. Find the percentage profit made.
- A. 10%
- B. 28%
- C. 40%
- D. 70%
Answer and explanation: practise this paper on ePrep.
Answer all 46 questions of the BECE 2011 Mathematics paper
Timed papers like the real exam, instant marking, worked explanations, topic tests and mock exams. Theory answers marked by real teachers. 3 weeks free.
Practise free on ePrep