AFCT Mathematical Aptitude 2 — Questions and Answers

Question 1: What is the value of 3 raised to the 4th power?

12
81 (Correct answer)
64
27

Correct answer: 81

3 to the 4th power means 3 x 3 x 3 x 3 = 81.

Exponentiation means repeated multiplication. 3 to the 4th = 3 x 3 x 3 x 3. Step by step: 3 x 3 = 9, 9 x 3 = 27, 27 x 3 = 81. Common powers of 3: 3, 9, 27, 81, 243.

Question 2: Simplify: 2/3 + 3/4

5/7
17/12 (Correct answer)
5/12
1

Correct answer: 17/12

Common denominator of 12: 2/3 = 8/12 and 3/4 = 9/12. Adding: 8/12 + 9/12 = 17/12.

To add fractions with different denominators, find the LCD. The LCD of 3 and 4 is 12. Convert: 2/3 = 8/12 and 3/4 = 9/12. Add: 8/12 + 9/12 = 17/12 (or 1 and 5/12). Never add numerators and denominators separately.

Question 3: If x + 7 = 15, what is the value of 3x?

8
24 (Correct answer)
45
22

Correct answer: 24

Solving for x: x = 15 - 7 = 8. Therefore 3x = 3 x 8 = 24.

First solve for x by subtracting 7 from both sides: x = 15 - 7 = 8. Then find 3x: 3 x 8 = 24. This tests both basic algebra and the ability to use that result in a follow-up calculation.

Question 4: What is 15% of 240?

30
36 (Correct answer)
24
42

Correct answer: 36

15% of 240 = 0.15 x 240 = 36.

Convert percentage to decimal and multiply: 15% = 0.15, and 0.15 x 240 = 36. Shortcut: 10% of 240 = 24, and 5% of 240 = 12, so 15% = 24 + 12 = 36.

Question 5: What is the area of a triangle with a base of 10 cm and a height of 8 cm?

80 sq cm
40 sq cm (Correct answer)
18 sq cm
36 sq cm

Correct answer: 40 sq cm

Area = 1/2 x base x height = 1/2 x 10 x 8 = 40 sq cm.

Area of a triangle is A = 1/2 x b x h. A = 1/2 x 10 x 8 = 40 sq cm. A triangle is exactly half of a rectangle with the same base and height. The height must be perpendicular to the base.

Question 6: Solve for x: 2x - 5 = 13

4
9 (Correct answer)
6
8

Correct answer: 9

Add 5 to both sides: 2x = 18. Divide by 2: x = 9.

Step 1: Add 5 to both sides: 2x = 18. Step 2: Divide both sides by 2: x = 9. Verify: 2(9) - 5 = 18 - 5 = 13. Always check by substituting back into the original equation.

AFCT Mathematical Aptitude 2

What is the value of 3 raised to the 4th power?

Select your answer