FTCE Mathematics 3 — Questions and Answers
Question 1: A teacher asks students to evaluate log₂(64). What is the correct answer?
- 4
- 5
- 6 (Correct answer)
- 8
Correct answer: 6
log₂(64) asks for the power to which 2 must be raised to get 64; since 2⁶=64, the answer is 6.
Question 2: Which set of side lengths forms a valid triangle?
- 2, 3, 6
- 5, 12, 13 (Correct answer)
- 1, 1, 3
- 4, 4, 9
Correct answer: 5, 12, 13
By the triangle inequality, the sum of any two sides must exceed the third; 5+12=17>13, 5+13=18>12, and 12+13=25>5.
Question 3: An arithmetic sequence begins 7, 11, 15, 19, … What is the 20th term?
- 79
- 83 (Correct answer)
- 83
- 87
Correct answer: 83
Using aₙ = a₁ + (n−1)d = 7 + (19)(4) = 7 + 76 = 83.
Question 4: If P(A) = 0.4 and P(B) = 0.3, and A and B are independent events, what is P(A and B)?
- 0.70
- 0.12 (Correct answer)
- 0.10
- 0.58
Correct answer: 0.12
For independent events, P(A and B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.
Question 5: A circle has a diameter of 10 cm. What is the area of a sector with a central angle of 72°?
- 5π cm² (Correct answer)
- 10π cm²
- 25π cm²
- 2.5π cm²
Correct answer: 5π cm²
Area of sector = (θ/360°)×πr² = (72/360)×π(5²) = 0.2×25π = 5π cm².
Question 6: Which of the following is equivalent to (x² - 9)/(x - 3) for x ≠ 3?
- x - 3
- x + 3 (Correct answer)
- x² + 3
- x² - 3
Correct answer: x + 3
Factoring the numerator: (x-3)(x+3)/(x-3) = x+3 when x≠3.
Question 7: A student records the heights (in inches) of classmates: 60, 62, 63, 65, 65, 67, 70. What is the median?
- 63
- 64.57
- 65 (Correct answer)
- 67
Correct answer: 65
With 7 values ordered from least to greatest, the median is the 4th value, which is 65.
FTCE Mathematics 3
A teacher asks students to evaluate log₂(64).
What is the correct answer?