FTCE Mathematics 3

Question 1

A teacher asks students to evaluate log₂(64). What is the correct answer?

Accepted Answer

6

Answer

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?

Accepted Answer

5, 12, 13

Answer

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?

Accepted Answer

83

Answer

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)?

Accepted Answer

0.12

Answer

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°?

Accepted Answer

5π cm²

Answer

Area of sector = (θ/360°)×πr² = (72/360)×π(5²) = 0.2×25π = 5π cm².

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