CIVIL SERVICE EXAM REVIEWER - MATH

Solve for x: 3(2x−5)+7=16

• 1

• 2

• 3

• 4

Answer explanation

Solution:
3(2x - 5) + 7 = 16
→ 6x - 15 + 7 = 16
→ 6x - 8 = 16
→ 6x = 24
→ x = 4

Factor the quadratic expression: x² −5x+6

• (x−1)(x−6)

• (x+2)(x+3)

• (x−2)(x−3)

• (x+1)(x−6)

Answer explanation

Solution:
We need two numbers that multiply to 6 and add up to -5:
→ (-2) × (-3) = 6 and (-2) + (-3) = -5
→ (x - 2)(x - 3)

Find the equation of a line passing through the points (1,4) and (3,10).

• y=3x+1

• y=−3x+7

• y= 3/1 x + 3/11

• y=3x−1

In a right-angled triangle, if one acute angle is 30°, what is the measure of the other acute angle?

• 30°

• 45°

• 60°

• 90°

Answer explanation

Solution:
Sum of angles = 180°, right angle = 90°,
→ Other angle = 180° - 90° - 30° = 60°

A circle has a radius of 7 cm. What is its circumference? (Use π≈3.14)

• 21.98 cm

• 43.96 cm

• 153.86 cm

• 14 cm

Answer explanation

Solution:
C = 2πr = 2 × 3.14 × 7 = 43.96 cm

What is the median of the following data set: 2, 5, 8, 3, 9, 1, 6?

• 3

• 5

• 6

• 8

Answer explanation

Solution:
Sorted: 1, 2, 3, 5, 6, 8, 9 → Median = middle = 5

Simplify the trigonometric expression: cosθ / (sin²θ + cos²θ)

• sinθ

• cosθ

• secθ

• tanθ

Answer explanation

Solution:
sin²θ + cos²θ = 1 → expression = cosθ / 1 = cosθ

Find the area of a triangle with a base of 10 cm and a height of 6 cm.

• 60 sq cm

• 30 sq cm

• 16 sq cm

• 8 sq cm

Answer explanation

Solution:
Area = (1/2) × base × height = (1/2)(10)(6) = 30 cm²

What is the value of log₁₀ 1000?

• 1

• 2

• 3

• 4

Answer explanation

Solution:
log₁₀(1000) = log₁₀(10³) = 3

If a dice is rolled, what is the probability of getting an even number?

• 1/6

• 1/2

• 2/1

• 2/3

Answer explanation

Solution:
Even numbers = 2, 4, 6 → 3 out of 6 = 1/2