BECE 1997 Mathematics Past Questions and Answers
The BECE 1997 Mathematics paper has 40 objective and 5 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. Convert 320$_{five}$ to a base ten numeral.
- A. 25
- B. 77
- C. 85
- D. 86
Answer: C. 85
320$_{five}$ = 3 x 5$^{2}$ + 2 x 5$^{1}$ + 0 x 5$^{0}$
Any number raised to the power 0 is 1.
Any number raised to the power 1 is the same number.
5$^{2}$ = 5 x 5 = 25
320$_{five}$ = 3 x 25 + 2 x 5 + 0 x 1
320$_{five}$ = 75 + 10 + 0
320$_{five}$ = 85
320$_{five}$ = 3 x 5$^{2}$ + 2 x 5$^{1}$ + 0 x 5$^{0}$
Any number raised to the power 0 is 1.
Any number raised to the power 1 is the same number.
5$^{2}$ = 5 x 5 = 25
320$_{five}$ = 3 x 25 + 2 x 5 + 0 x 1
320$_{five}$ = 75 + 10 + 0
320$_{five}$ = 85
2. P = {2, 4, 6, 8} and Q = {even counting numbers less than 12}.
What is the relationship between P and Q?
What is the relationship between P and Q?
- A. P = Q
- B. P ⊂ Q
- C. P < Q
- D. Q ⊂ P
Answer: B. P ⊂ Q
P = {2, 4, 6, 8}
Q = {even counting numbers less than 12}
Q = {2, 4, 6, 8, 10}
All the members of P can be found in Q hence P is a subset (⊂) of Q
P = {2, 4, 6, 8}
Q = {even counting numbers less than 12}
Q = {2, 4, 6, 8, 10}
All the members of P can be found in Q hence P is a subset (⊂) of Q
3. In the diagram below, P is the set of numbers in the circle and Q is the set of numbers in the triangle.
What is P ∩ Q?
What is P ∩ Q?
- A. {1, 2, 4}
- B. {5, 6}
- C. {7}
- D. {1, 2, 4, 5, 6, 7}
Answer: B. {5, 6}
Intersection (∩) is the region both shapes join/intersect.
Intersection (∩) is the region both shapes join/intersect.
4. The product 6287 x 543 = 3,413,841.
What is the value of 628.7 x 5.43?
What is the value of 628.7 x 5.43?
- A. 3,413,841
- B. 342,384.1
- C. 34,138.41
- D. 3,413.841
Answer: D. 3,413.841
Change the decimal 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.
628.7 = 628.⌒7. = 6287 x 10$^{-1}$
5.43 = 5.⌒4⌒3. = 543 x 10$^{-2}$
628.7 x 5.43 = 6287 x 10$^{-1}$ x 543 x 10$^{-2}$
628.7 x 5.43 = 6287 x 543 x 10$^{-1}$ x 10$^{-2}$
But 6287 x 543 = 3413841
628.7 x 5.43 = 3413841 x 10$^{-1}$ x 10$^{-2}$
Law of multiplication of indices
a$^{m}$ x a$^{n}$ = a$^{m + m}$
628.7 x 5.43 = 3413841 x 10$^{-1 + -2}$
628.7 x 5.43 = 3413841 x 10$^{-1 - 2}$
628.7 x 5.43 = 3413841 x 10$^{-3}$
Change the whole number x 10$^{-n}$ to decimal by moving the decimal point n times to the left.
Every whole number has .0 at the end but it is not written.
3,413,841 = 3413841.0
628.7 x 5.43 = 3413.⌒8⌒4⌒1.0 = 3,413.841
Change the decimal 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.
628.7 = 628.⌒7. = 6287 x 10$^{-1}$
5.43 = 5.⌒4⌒3. = 543 x 10$^{-2}$
628.7 x 5.43 = 6287 x 10$^{-1}$ x 543 x 10$^{-2}$
628.7 x 5.43 = 6287 x 543 x 10$^{-1}$ x 10$^{-2}$
But 6287 x 543 = 3413841
628.7 x 5.43 = 3413841 x 10$^{-1}$ x 10$^{-2}$
Law of multiplication of indices
a$^{m}$ x a$^{n}$ = a$^{m + m}$
628.7 x 5.43 = 3413841 x 10$^{-1 + -2}$
628.7 x 5.43 = 3413841 x 10$^{-1 - 2}$
628.7 x 5.43 = 3413841 x 10$^{-3}$
Change the whole number x 10$^{-n}$ to decimal by moving the decimal point n times to the left.
Every whole number has .0 at the end but it is not written.
3,413,841 = 3413841.0
628.7 x 5.43 = 3413.⌒8⌒4⌒1.0 = 3,413.841
5. Express 30 cm as a percentage of 2 m.
- A. 0.5%
- B. 1.5%
- C. 6.7%
- D. 15%
Answer: D. 15%
Percentage = $\frac{Number}{Other Number}$ x 100%
Change the metres to centimetres.
1 m = 100 cm
2 m = 2 x 100 cm = 200 cm
Percentage = $\frac{30 cm}{200 cm}$ x 100% = 15%
Note:
1. the zeros (0) at the end of 200 and 100 cancel each other
2. 2 divides itself 1 time and 30, 15 times
Percentage = $\frac{Number}{Other Number}$ x 100%
Change the metres to centimetres.
1 m = 100 cm
2 m = 2 x 100 cm = 200 cm
Percentage = $\frac{30 cm}{200 cm}$ x 100% = 15%
Note:
1. the zeros (0) at the end of 200 and 100 cancel each other
2. 2 divides itself 1 time and 30, 15 times
6. What solid can be made from this net?
- A. triangle
- B. rectangular pyramid
- C. triangular prism
- D. rectangular prism
- E. triangular pyramid
Answer and explanation: practise this paper on ePrep.
7. Simplify 3(6*b* – 9*a*) + 7(6*a* – 5*b*)
- A. 17*b* + 6*a*
- B. -17*b* + 6*a*
- C. 17*b* + 48*a*
- D. 15*a* – 17*b*
Answer and explanation: practise this paper on ePrep.
8. Arrange the following fractions in descending order $\frac{9}{16}$, $\frac{5}{8}$, 0.62
- A. $\frac{9}{16}$, 0.62, $\frac{5}{8}$
- B. 0.62, $\frac{5}{8}$, $\frac{9}{16}$
- C. $\frac{5}{8}$, $\frac{9}{16}$, 0.62
- D. $\frac{5}{8}$, 0.62, $\frac{9}{16}$
Answer and explanation: practise this paper on ePrep.
9. 18 = 2 x 3$^{2}$; 42 = 2 x 3 x 7; 90 = 2 x 3$^{2}$ x 5
Use the information above to answer the question below.
Find the LCM of 18, 42 and 90.
Use the information above to answer the question below.
Find the LCM of 18, 42 and 90.
- A. 2 × 3$^{2}$
- B. 2 × 3 × 7
- C. 2 × 3$^{2}$ × 5
- D. 2 × 3 × 5 × 7
- E. 2 × 3$^{2}$ × 5 × 7
Answer and explanation: practise this paper on ePrep.
10. 18 = 2 x 3$^{2}$; 42 = 2 x 3 x 7; 90 = 2 x 3$^{2}$ x 5
Use the information above to answer the question below.
What is the HCF of 18, 42 and 90?
Use the information above to answer the question below.
What is the HCF of 18, 42 and 90?
- A. 21
- B. 18
- C. 9
- D. 6
Answer and explanation: practise this paper on ePrep.
Answer all 45 questions of the BECE 1997 Mathematics paper
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