Skip to content
Mid-Terms.org

Geometry (Grades 9–10) Midterm — Units 5–6

← Midterm Library / Math / Geometry

Math Grades 9–10 20 multiple choice + 1 written

Free printable Geometry midterm (Grades 9–10): 20 multiple-choice questions plus 1 written response covering Right Triangles & Trigonometry, Circles, Area & Volume. Answer key included — customize it in the Midterm Maker.

Customize in Midterm Maker
Geometry (Grades 9–10) Midterm — Units 5–6
Name: Date: Period:

Directions: Read each question carefully and choose the best answer. Answer the written response in complete sentences.

Covers: Right Triangles & Trigonometry · Circles, Area & Volume

Part 1: Multiple Choice

  1. A right triangle has legs of 9 and 12. How long is the hypotenuse?
    1. A. 15
    2. B. √63
    3. C. 21
    4. D. 225
  2. A right triangle has a 35° angle and a hypotenuse of 20. To the nearest tenth, how long is the side opposite the 35° angle?
    1. A. 11.5
    2. B. 24.4
    3. C. 14.0
    4. D. 16.4
  3. Each leg of a 45°-45°-90° triangle is 7 units long. How long is the hypotenuse?
    1. A. 7√2
    2. B. 49
    3. C. 14
    4. D. 7√3
  4. sin 40° is equal to the cosine of which angle?
    1. A. 90°
    2. B. 40°
    3. C. 140°
    4. D. 50°
  5. From a point on level ground 40 feet from the base of a flagpole, the angle of elevation to the top is 32°. To the nearest tenth of a foot, how tall is the flagpole?
    1. A. 25.0 feet
    2. B. 64.0 feet
    3. C. 21.2 feet
    4. D. 33.9 feet
  6. A right triangle has legs of 7 and 24 and a hypotenuse of 25. Angle θ is opposite the side of length 7. What is cos θ?
    1. A. 7/25
    2. B. 25/24
    3. C. 7/24
    4. D. 24/25
  7. In a 30°-60°-90° triangle, the shorter leg is 5. How long is the longer leg?
    1. A. 10
    2. B. 5√2
    3. C. 15
    4. D. 5√3
  8. A right triangle has legs of 5 and 12. To the nearest tenth of a degree, what is the measure of the angle opposite the side of length 5?
    1. A. 24.6°
    2. B. 65.4°
    3. C. 67.4°
    4. D. 22.6°
  9. A triangle has sides of length 8, 15, and 18. How is it classified by its angles?
    1. A. Acute
    2. B. Obtuse
    3. C. It cannot be a triangle
    4. D. Right
  10. Right triangle ABC has its right angle at C. The side opposite angle A is 8, the side adjacent to angle A is 15, and the hypotenuse is 17. What is sin A?
    1. A. 17/8
    2. B. 8/17
    3. C. 8/15
    4. D. 15/17
  11. A circle has a radius of 6. What is the length of an arc with a central angle of 60°?
    1. A. 12π
    2. B. π
    3. C. 2π
    4. D. 6π
  12. What is the total surface area of a cylinder with radius 3 and height 7?
    1. A. 63π
    2. B. 60π
    3. C. 42π
    4. D. 51π
  13. Which equation describes a circle with center (3, -2) and radius 5?
    1. A. (x + 3)^2 + (y - 2)^2 = 5
    2. B. (x - 3)^2 + (y + 2)^2 = 25
    3. C. (x + 3)^2 + (y - 2)^2 = 25
    4. D. (x - 3)^2 + (y + 2)^2 = 5
  14. What is the area of a regular hexagon with side length 4?
    1. A. 12√3
    2. B. 96
    3. C. 24√3
    4. D. 48√3
  15. A trapezoid has bases of 8 cm and 14 cm and a height of 5 cm. What is its area?
    1. A. 55 square cm
    2. B. 40 square cm
    3. C. 110 square cm
    4. D. 70 square cm
  16. An inscribed angle in a circle intercepts an arc of 110°. What is the measure of the inscribed angle?
    1. A. 220°
    2. B. 110°
    3. C. 70°
    4. D. 55°
  17. A line is tangent to a circle. What is the measure of the angle between the tangent and the radius drawn to the point of tangency?
    1. A. 180°
    2. B. 60°
    3. C. 90°
    4. D. 45°
  18. What is the surface area of a sphere with radius 5?
    1. A. 500π/3
    2. B. 25π
    3. C. 50π
    4. D. 100π
  19. A pyramid has a square base with sides of 6 m and a height of 10 m. What is its volume?
    1. A. 360 cubic meters
    2. B. 240 cubic meters
    3. C. 120 cubic meters
    4. D. 60 cubic meters
  20. A circle has a radius of 10. What is the area of a sector with a central angle of 90°?
    1. A. 100π
    2. B. 25π
    3. C. 5π
    4. D. 50π

Part 2: Written Response

  1. A grain silo is a cylinder with radius 10 ft and height 40 ft, topped by a half sphere (hemisphere) with radius 10 ft. Find the total volume in terms of π and to the nearest cubic foot. Show your work.

More Geometry midterms