TOPIC: FRACTIONS
DIRECTION: Choose the correct answers from the lettered options.
1. 3/4 of a class of 32 students study English and 3/8 study mathematics. Every student studies at least one of these subjects. How many students study both subjects?
A. 36
B. 12
C. 4
D. 24
The correct answer is option [C]. Solution: Number of students that study English = 3/4 × 32 = 24 students; Number of students that study mathematics = 3/8 × 32 = 12 students. Add the number of students that offer English and mathematics and subtract from the number of students in the class = 36 – 32 = 4 students offer both subjects.
2. There are 572 students in a mixed school. 5/11 of them are boys. How many girls are in the school?
A. 260
B. 270
C. 312
D. 321
The correct answer is option [C]. Solution: 1 – 5/11 = 6/11 × 572 = 312.
3. 3/4 of a class of 32 students study English and 3/8 study mathematics. Every student studies at least one of these subjects. What fraction of the class studies mathematics but not English?
A. 1/4
B. 5/8
C. 3/8
D. 8/9
The correct answer is option [A]. Solution: Number of student that offer mathematics = 3/8 × 32 = 12 students; Number of students that study mathematics = 12 – 4 = 8. Fraction that study mathematics only = 8/32 = 1/4. Since 3/8 of the class study mathematics 1/4 of students study mathematics not English.
4. Cromwell can hoe a yam plot in 3 hours and Itunuola can hoe it in 4 hours. How long will it take them to hoe the whole plot working together?
A. 11∕5
B. 12∕13
C. 15∕7
D. 22∕5
The correct answer is option [C]. Solution: Since it takes 7/12 to hoe the plot of land working together then 12/7 = 15/7 to hoe the whole plot of land when they work together.
5. Arrange 3/4, 4/5, 2/3, 2/5, 6/7 in ascending order.
A. 2/5, 2/3, 3/4, 4/5, 6/7.
B. 2/3, 3/4, 6/7, 4/5, 2/5.
C. 2/5, 4/5, 6/7, 3/4, 2/3.
D. 6/7, 2/5, 3/4, 4/5, 2/3.
The correct answer is option [A]. Solution: Hint [Convert the given numbers to decimal numbers and arrange accordingly, from the number with the smallest decimal number to the largest decimal number].
6. Cromwell can hoe a yam plot in 3 hours and Itunuola can hoe it in 4 hours. If they work together, what fraction of the plot will they hoe in 1 hour?
A. 7/12
B. 5/6
C. 11/12
D. 17/12
The correct answer is option [A]. Solution: Each working for an hour is 1/3; 1/4. Then the fraction of the plot hoed when both work together is 1/3 + 1/4 = 4 + 3/12 = 7/12.
7. During two years in a school, 7/8 of the students had malaria, 3/4 had catarrh and 5/6 had neither. What fraction of the school had both malaria and catarrh?
A. 11/2
B. 111/24
C. 11/24
D. 1/2
The correct answer is option [B]. Solution: Let the students that had both malaria and catarrh be x; [7/8 – x] + 5/6 + [3/4 – x] + x = 1; 211/24 – x = 1; x = 111/24.
8. What fraction of 5 weeks is 5 days?
A. 7
B. 1
C. 1/6
D. 1/7
The correct answer is option [D].
TOPIC: INDICES AND LOGARITHMS
DIRECTION: Choose the correct answers from the lettered options.
1. Evaluate [0.00385 × 0.00061]/[0.0025 × 0.08] and leave your answer in standard form.
A. 1.347 × 10-3
B. 2.43 × 10-2
C. 1.174 × 10-2
D. 2.18 × 10-3
The correct answer is option [C]. Solution: [0.00385 × 0.00061] / [0.0025 × 0.08] = 0.017425 = 1.174 × 10-2.
2. Evaluate log3 405 – log3 5.
A. 2
B. 3
C. 4
D. 5
The correct answer is option [C]. log3 405 – log3 5 = log3 (405/5) = log3 81 = log3 34 = 4 log3 3
3. Find p in terms of q if log3p + 3log3q = 3.
A. (3 q) 3
B. (3 q) 1/3
C. (q 3)3
D. (q 3)1/3
The correct answer is option [A]. log3p + 3log3q = 3 => log3pq3 = 3 pq3 = 33 . Therefore, p = 33/q3 = [3/q] 3.
4. Given dy/dx = 2×3 + 4×2 – x + 2, what is the value of y?
A. x4/2 + 4×3/3 – x2/2 + x + c
B. 6×2 + 8x – 1
C. x2 – 3x + 2
D. x5/3 + x2 – 2×2/5 + c
The correct answer is option [A]. Solution: dy = [2×3 + 4×2 – x + 2] dx, Integrate the equation ʃdy = ʃ [2×3 + 4×2 – x + 2]dx → y = x4/2 + 4×3/3 – x2/2 + x + c.
5. Simplify log5 (3/5) + 3log5 (15/2) – log5 (81/8).
A. 2
B. 9
C. 7
D. 5
The correct answer is option [A].
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