SAT — Scholastic Assessment Test (Digital SAT)

SAT Math — Geometry and Trigonometry, Set 2

Take the SAT Math — Geometry and Trigonometry, Set 2: 20 multiple-choice questions (30 minutes) with instant scoring and a full answer review. Covers 20…

What this test covers

• 20 SAT Math

Sample questions with answers

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

1. Q1. A rectangle has area 48 and length 8. What is its perimeter?

   • A. 28 ✓
   • B. 96
   • C. 14
   • D. 56

   Answer: A. 28

   Explanation: Width = 48 ÷ 8 = 6, so perimeter = 2(8 + 6) = 28.

2. Q2. Two angles of a triangle are 50° and 65°. What is the third angle?

   • A. 115°
   • B. 65° ✓
   • C. 55°
   • D. 75°

   Answer: B. 65°

   Explanation: 180° − 50° − 65° = 65°.

3. Q3. A right triangle has hypotenuse 13 and one leg 5. How long is the other leg?

   • A. 8
   • B. √194
   • C. 18
   • D. 12 ✓

   Answer: D. 12

   Explanation: √(13² − 5²) = √144 = 12.

4. Q4. In a right triangle with sides 5, 12 and 13, angle θ is opposite the side of length 5. What is cos θ?

   • A. 12/13 ✓
   • B. 13/12
   • C. 5/13
   • D. 5/12

   Answer: A. 12/13

   Explanation: cos θ = adjacent/hypotenuse = 12/13.

5. Q5. A circle has circumference 10π. What is its area?

   • A. 10π
   • B. 100π
   • C. 5π
   • D. 25π ✓

   Answer: D. 25π

   Explanation: 2πr = 10π gives r = 5, so the area is 25π.

The other 15 questions

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6. Q6. A circle has area 49π. What is its diameter?

   • A. 7
   • B. 24.5
   • C. 14
   • D. 49

7. Q7. Which equation describes the circle with centre (−1, 4) and radius 3?

   • A. (x − 1)² + (y + 4)² = 9
   • B. (x − 1)² + (y − 4)² = 9
   • C. (x + 1)² + (y − 4)² = 3
   • D. (x + 1)² + (y − 4)² = 9

8. Q8. What is the length of an arc with central angle 90° in a circle of radius 8?

   • A. 8π
   • B. 4π
   • C. 2π
   • D. 16π

9. Q9. What is the volume of a rectangular box measuring 3 by 4 by 5?

   • A. 12
   • B. 94
   • C. 60
   • D. 47

10. Q10. What is the volume of a cone with radius 6 and height 5?

    • A. 180π
    • B. 30π
    • C. 60π
    • D. 90π

11. Q11. Two similar triangles have corresponding sides 4 and 6. If a side of the smaller triangle is 10, how long is the matching side of the larger one?

    • A. 12
    • B. 20
    • C. 6.7
    • D. 15

12. Q12. A triangle has interior angles of 40° and 75°. What is the exterior angle at the third vertex?

    • A. 115°
    • B. 105°
    • C. 140°
    • D. 65°

13. Q13. Two parallel lines are cut by a transversal, making an angle of 72°. What is the alternate interior angle?

    • A. 18°
    • B. 144°
    • C. 72°
    • D. 108°

14. Q14. What is the value of tan 45°?

    • A. 1
    • B. 0
    • C. √2/2
    • D. √3

15. Q15. How many degrees are in 3π/2 radians?

    • A. 180
    • B. 540
    • C. 270
    • D. 135

16. Q16. If sin θ = 0.6 and θ is acute, what is cos θ?

    • A. 0.4
    • B. 0.8
    • C. 0.6
    • D. 1.6

17. Q17. What is the distance between (−3, −1) and (3, 7)?

    • A. 14
    • B. 10
    • C. 8
    • D. 100

18. Q18. The point (4, k) lies on the circle x² + y² = 25, and k > 0. What is k?

    • A. 3
    • B. 21
    • C. 5
    • D. 4

19. Q19. A square has a diagonal of 10. What is its area?

    • A. 100
    • B. 50
    • C. 25
    • D. 40

20. Q20. What is the surface area of a sphere with radius 5?

    • A. 25π
    • B. 20π
    • C. 500π/3
    • D. 100π