MPT Geometry 3

Question 1

In a 30-60-90 triangle, the shortest leg has length 5. What is the length of the hypotenuse?

Accepted Answer

10

Answer

In a 30-60-90 triangle, the hypotenuse is twice the length of the shortest leg, so it is 2 × 5 = 10.

Question 2

In a 45-45-90 triangle, one leg has length 7. What is the length of the hypotenuse?

Accepted Answer

7√2

Answer

In a 45-45-90 triangle, the hypotenuse = leg × √2 = 7√2.

Question 3

What is the surface area of a cube with side length 4?

Accepted Answer

96

Answer

A cube has 6 faces, each with area 4² = 16, so surface area = 6 × 16 = 96.

Question 4

A sector of a circle has a central angle of 90° and radius 8. What is the arc length? (Use π ≈ 3.14)

Accepted Answer

12.56

Answer

Arc length = (θ/360°) × 2πr = (90/360) × 2 × 3.14 × 8 = (1/4) × 50.24 = 12.56.

Question 5

Two parallel lines are cut by a transversal. One pair of alternate interior angles measures (3x + 10)° and (5x − 20)°. What is x?

Accepted Answer

15

Answer

Alternate interior angles are equal: 3x + 10 = 5x − 20, so 30 = 2x, giving x = 15.

(MPT) UCF Math Placement Test Practice Test