EmSAT Mathematics 5 — Questions and Answers
Question 1: What is the 10th term of the arithmetic sequence 3, 7, 11, 15, …?
- 35
- 39 (Correct answer)
- 43
- 47
Correct answer: 39
aₙ = a + (n−1)d = 3 + 9×4 = 3 + 36 = 39.
Question 2: Which expression is the derivative of f(x) = x⁴ − 5x² + 3x?
- 4x³ − 10x + 3 (Correct answer)
- 4x³ − 5x + 3
- x³ − 10x + 3
- 4x³ − 10x
Correct answer: 4x³ − 10x + 3
f'(x) = 4x³ − 10x + 3 by applying the power rule to each term.
Question 3: A bag contains 5 red and 3 blue balls. If two balls are drawn without replacement, what is the probability both are red?
- 5/14 (Correct answer)
- 25/64
- 10/56
- 5/28
Correct answer: 5/14
P = (5/8) × (4/7) = 20/56 = 5/14.
Question 4: Which of the following is the inverse function of f(x) = 2x − 4?
- f⁻¹(x) = (x+4)/2 (Correct answer)
- f⁻¹(x) = 2x+4
- f⁻¹(x) = (x−4)/2
- f⁻¹(x) = 4−2x
Correct answer: f⁻¹(x) = (x+4)/2
Swap x and y then solve: x = 2y−4 → y = (x+4)/2.
Question 5: Express 0.000045 in standard form (scientific notation).
- 4.5 × 10⁻⁵ (Correct answer)
- 45 × 10⁻⁶
- 4.5 × 10⁵
- 0.45 × 10⁻⁴
Correct answer: 4.5 × 10⁻⁵
Moving the decimal 5 places right gives 4.5 × 10⁻⁵.
Question 6: Two vectors u = (3, 4) and v = (1, −2). What is u · v (dot product)?
- −5
- 5
- −1 (Correct answer)
- 11
Correct answer: −1
u · v = (3)(1) + (4)(−2) = 3 − 8 = −5.
Question 7: The graph of y = f(x) is translated 3 units right and 2 units down. What is the new equation?
- y = f(x−3) + 2
- y = f(x+3) − 2
- y = f(x−3) − 2 (Correct answer)
- y = f(x+3) + 2
Correct answer: y = f(x−3) − 2
A shift right by 3 replaces x with (x−3), and down by 2 subtracts 2 from the output.
EmSAT Mathematics 5
What is the 10th term of the arithmetic sequence 3, 7, 11, 15, …?