EmSAT Mathematics 4 — Questions and Answers
Question 1: What is the value of ∫₀² (3x² − 2x) dx?
- 2
- 4 (Correct answer)
- 6
- 8
Correct answer: 4
∫(3x²−2x)dx = x³−x², evaluated from 0 to 2 gives (8−4)−0 = 4.
Question 2: If matrix A = [[2, 1],[3, 4]], what is det(A)?
- 5 (Correct answer)
- 11
- 8
- −5
Correct answer: 5
det(A) = (2)(4) − (1)(3) = 8 − 3 = 5.
Question 3: How many ways can 4 students be chosen from a group of 10?
- 210 (Correct answer)
- 5040
- 10000
- 40
Correct answer: 210
C(10,4) = 10!/(4!6!) = 210.
Question 4: The line y = 2x + 3 is parallel to which of the following lines?
- y = −2x + 3
- y = 2x − 7 (Correct answer)
- y = ½x + 3
- 2y = x + 6
Correct answer: y = 2x − 7
Parallel lines have identical slopes; y = 2x − 7 has slope 2, matching the original.
Question 5: A probability distribution table shows P(X=1)=0.2, P(X=2)=0.5, P(X=3)=0.3. What is E(X)?
- 1.8
- 2.0
- 2.1 (Correct answer)
- 2.5
Correct answer: 2.1
E(X) = 1(0.2) + 2(0.5) + 3(0.3) = 0.2 + 1.0 + 0.9 = 2.1.
Question 6: Simplify: (2x³y²)³
- 6x⁶y⁵
- 8x⁹y⁶ (Correct answer)
- 6x⁹y⁶
- 8x⁶y⁵
Correct answer: 8x⁹y⁶
(2x³y²)³ = 2³·x⁹·y⁶ = 8x⁹y⁶.
Question 7: Solve: 2sin(x) = √3 for 0° ≤ x ≤ 360°.
- x = 60° only
- x = 60° and 300°
- x = 60° and 120° (Correct answer)
- x = 30° and 150°
Correct answer: x = 60° and 120°
sin(x) = √3/2, which gives x = 60° and x = 180°−60° = 120° in [0°,360°].
EmSAT Mathematics 4
What is the value of ∫₀² (3x² − 2x) dx?