Practice Test Geeks(NBT) National Benchmark Test Practice Test
← All NBT Flashcard Decks

NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers 3 Flashcards

6 cards from real NBT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers 3 flashcards as text

  1. Calculate the exact value of tan(45°):

    Answer: 1

    tan(45°) = sin(45°) / cos(45°) = (1/√2) / (1/√2) = 1.

  2. A ladder 10 m long leans against a wall, making an angle of 60° with the ground. How high up the wall does the ladder reach?

    Answer: 5√3 m

    Height = 10 × sin(60°) = 10 × (√3/2) = 5√3 m.

  3. The exterior angle of a regular polygon is 36°. How many sides does the polygon have?

    Answer: 10

    The sum of exterior angles of any polygon = 360°. Number of sides = 360° ÷ 36° = 10 sides.

  4. In the unit circle, what are the coordinates of the point at 270°?

    Answer: (0, -1)

    At 270°, the point is directly at the bottom of the unit circle: (cos 270°, sin 270°) = (0, -1).

  5. A right triangle has legs of length a and b, and hypotenuse c. Which identity correctly expresses the cosine of the angle opposite the leg of length a?

    Answer: cos θ = b/c

    cos θ = adjacent/hypotenuse. The side adjacent to angle θ (which is opposite leg a) is leg b. So cos θ = b/c.

  6. The volume of a cone is given by V = (1/3)πr²h. A cone has radius 6 cm and height 9 cm. What is its volume? (Use π ≈ 3.14)

    Answer: 339.12 cm³

    V = (1/3) × 3.14 × 6² × 9 = (1/3) × 3.14 × 36 × 9 = (1/3) × 1017.36 = 339.12 cm³.