SmartPrep

SAT — Scholastic Assessment Test (Digital SAT)

SAT Math — Geometry and Trigonometry, Set 1

Take the SAT Math — Geometry and Trigonometry, Set 1: 20 multiple-choice questions (30 minutes) with instant scoring and a full answer review. Covers 20…

What this test covers

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

  1. Q1. In the figure, the legs of the right triangle are 6 and 8. What is the length of the hypotenuse?

    Right triangle with a horizontal leg of length 8, a vertical leg of length 6, an unknown hypotenuse, and angle theta between the leg of length 8 and the hypotenuse.
    • A. 12
    • B. √28
    • C. 10 ✓
    • D. 14

    Answer: C. 10

    Explanation: √(6² + 8²) = √100 = 10.

  2. Q2. In the figure, what is sin θ?

    Right triangle with a horizontal leg of length 8, a vertical leg of length 6, an unknown hypotenuse, and angle theta between the leg of length 8 and the hypotenuse.
    • A. 4/3
    • B. 3/5 ✓
    • C. 4/5
    • D. 3/4

    Answer: B. 3/5

    Explanation: sin θ = opposite/hypotenuse = 6/10 = 3/5.

  3. Q3. In the same triangle, what is tan θ?

    Right triangle with a horizontal leg of length 8, a vertical leg of length 6, an unknown hypotenuse, and angle theta between the leg of length 8 and the hypotenuse.
    • A. 3/4 ✓
    • B. 4/5
    • C. 3/5
    • D. 4/3

    Answer: A. 3/4

    Explanation: tan θ = opposite/adjacent = 6/8 = 3/4.

  4. Q4. What is the area of the right triangle with legs 6 and 8?

    • A. 48
    • B. 30
    • C. 24 ✓
    • D. 14

    Answer: C. 24

    Explanation: Area = ½ × 6 × 8 = 24.

  5. Q5. In the figure, the circle has radius 9 and the shaded sector has a central angle of 60°. What is the arc length of the sector?

    Circle with centre O and radius 9, with a shaded sector whose central angle is 60 degrees.
    • A. 9π
    • B. 13.5π
    • C. 6π
    • D. 3π ✓

    Answer: D. 3π

    Explanation: Arc = (60/360) × 2π × 9 = 3π.

The other 15 questions

Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.

  1. Q6. In the same figure, what is the area of the shaded sector?

    Circle with centre O and radius 9, with a shaded sector whose central angle is 60 degrees.
    • A. 27π
    • B. 81π
    • C. 3π
    • D. 13.5π

  2. Q7. What are the centre and radius of the circle (x − 2)² + (y + 3)² = 16?

    • A. Centre (2, −3), radius 16
    • B. Centre (2, 3), radius 4
    • C. Centre (2, −3), radius 4
    • D. Centre (−2, 3), radius 4

  3. Q8. What is the sum of the interior angles of a heptagon (7 sides)?

    • A. 1260°
    • B. 720°
    • C. 900°
    • D. 1080°

  4. Q9. Two similar triangles have a scale factor of 3. What is the ratio of their areas?

    • A. 6 : 1
    • B. 3 : 1
    • C. 27 : 1
    • D. 9 : 1

  5. Q10. What is the volume of a cylinder with radius 3 and height 10?

    • A. 30π
    • B. 90π
    • C. 60π
    • D. 9π

  6. Q11. What is the volume of a sphere with radius 3?

    • A. 36π
    • B. 12π
    • C. 108π
    • D. 27π

  7. Q12. Two angles on a straight line measure x and 2x. What is x?

    • A. 60°
    • B. 90°
    • C. 120°
    • D. 45°

  8. Q13. An isosceles triangle has a vertex angle of 40°. What is each base angle?

    • A. 40°
    • B. 70°
    • C. 140°
    • D. 50°

  9. Q14. In a 30°-60°-90° triangle, the shorter leg is 5. What is the hypotenuse?

    • A. 5√3
    • B. 7.5
    • C. 5√2
    • D. 10

  10. Q15. In a 45°-45°-90° triangle, each leg is 7. What is the hypotenuse?

    • A. 14
    • B. 49
    • C. 7√2
    • D. 7√3

  11. Q16. If sin x° = cos 30° and x is acute, what is x?

    • A. 90
    • B. 60
    • C. 45
    • D. 30

  12. Q17. What is 180° in radians?

    • A. π
    • B. π/2
    • C. 2π
    • D. 180π

  13. Q18. What is the distance between (1, 2) and (4, 6)?

    • A. 5
    • B. 25
    • C. 7
    • D. √7

  14. Q19. What is the midpoint of (−2, 4) and (6, 0)?

    • A. (−4, 2)
    • B. (2, 2)
    • C. (4, 4)
    • D. (2, 4)

  15. Q20. What is the surface area of a cube with edge length 4?

    • A. 64
    • B. 16
    • C. 48
    • D. 96