NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers

Question 1

In the Cartesian plane, a circle has its center at C(3, -2) and passes through the point P(7, 1). Which of the following is the correct equation for this circle?

Accepted Answer

(x - 3)² + (y + 2)² = 25

Answer

(x + 3)² + (y - 2)² = 25

Answer

(x - 7)² + (y - 1)² = 5

Answer

(x - 3)² + (y + 2)² = 5

Question 2

A surveyor stands 100 meters from the base of a tall cliff. The angle of elevation to the top of the cliff is 30°. A flagpole is situated on top of the cliff. The angle of elevation to the top of the flagpole is 35°. What is the approximate height of the flagpole?

Accepted Answer

12.2 m

Answer

25.4 m

Answer

70.0 m

Answer

57.7 m

Question 3

Which of the following statements is always true for any non-special triangle ABC with corresponding side lengths a, b, and c?

Accepted Answer

sin(A)/a = sin(B)/b = sin(C)/c

Answer

a² = b² + c²

Answer

a = b * sin(A)

Answer

cos(C) = (a² + b² + c²)/2ab

Question 4

If sin(θ) = -4/5 and θ is in the third quadrant, what is the value of cos(θ)?

Accepted Answer

-3/5

Answer

3/5

Answer

4/5

Answer

-4/5

Question 5

A rectangle ABCD has vertices A(1, 2), B(5, 2), and C(5, 8). What are the coordinates of the vertex D?

Accepted Answer

(1, 8)

Answer

(1, 5)

Answer

(2, 8)

Answer

(5, 5)

Question 6

The function f(x) = 2sin(3x) has its graph drawn. What is the period of this function?

Accepted Answer

2π/3

Answer

2π

Answer

3π/2

Answer

3