EmSAT Mathematics 3 — Questions and Answers
Question 1: If f(x) = 3x² − 2x + 1, what is f(−2)?
- 9
- 17 (Correct answer)
- 13
- −3
Correct answer: 17
f(−2) = 3(4) − 2(−2) + 1 = 12 + 4 + 1 = 17.
Question 2: The equation of a circle with centre (3, −1) and radius 5 is:
- (x−3)² + (y+1)² = 25 (Correct answer)
- (x+3)² + (y−1)² = 25
- (x−3)² + (y+1)² = 5
- (x+3)² + (y+1)² = 25
Correct answer: (x−3)² + (y+1)² = 25
Standard form is (x−h)² + (y−k)² = r², giving (x−3)² + (y+1)² = 25.
Question 3: What is the sum of the infinite geometric series 8 + 4 + 2 + 1 + …?
- 12
- 16 (Correct answer)
- 24
- 32
Correct answer: 16
S = a/(1−r) = 8/(1−0.5) = 8/0.5 = 16.
Question 4: If log₂(x) = 5, what is x?
- 10
- 25
- 32 (Correct answer)
- 64
Correct answer: 32
log₂(x) = 5 means x = 2⁵ = 32.
Question 5: A triangle has vertices A(0,0), B(6,0), and C(3,4). What is its area?
- 8
- 10
- 12 (Correct answer)
- 24
Correct answer: 12
Area = ½ × base × height = ½ × 6 × 4 = 12 square units.
Question 6: Which of the following is equivalent to sin²θ + cos²θ?
- 0
- 2
- 1 (Correct answer)
- tan²θ
Correct answer: 1
The Pythagorean identity states sin²θ + cos²θ = 1 for all θ.
Question 7: The polynomial p(x) = x³ − 6x² + 11x − 6 has (x−1) as a factor. Which of the following is also a factor?
- (x−2) (Correct answer)
- (x+2)
- (x+3)
- (x−4)
Correct answer: (x−2)
Factoring fully gives (x−1)(x−2)(x−3), so (x−2) is a factor.
EmSAT Mathematics 3
If f(x) = 3x² − 2x + 1, what is f(−2)?