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Free SAT Math Additional Topics Geometry and Trigonometry Practice Test Flashcards

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

Read the first 20 Free SAT Math Additional Topics Geometry and Trigonometry Practice Test flashcards as text

  1. What is the area of a circle with radius 5?

    Answer: 25π

    Area = πr² = π(5)² = 25π.

  2. In a right triangle, the two legs have lengths 3 and 4. What is the hypotenuse?

    Answer: 5

    By the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25. So c = 5.

  3. What is the circumference of a circle with diameter 10?

    Answer: 10π

    Circumference = πd = π(10) = 10π.

  4. A rectangle has length 8 and width 5. What is its perimeter?

    Answer: 26

    Perimeter = 2(l + w) = 2(8 + 5) = 2(13) = 26.

  5. In a right triangle, if sin(θ) = 3/5, what is cos(θ)?

    Answer: 4/5

    Using the Pythagorean identity: sin²θ + cos²θ = 1. (3/5)² + cos²θ = 1 → 9/25 + cos²θ = 1 → cos²θ = 16/25 → cosθ = 4/5.

  6. What is the volume of a rectangular prism with length 4, width 3, and height 5?

    Answer: 60

    Volume = l × w × h = 4 × 3 × 5 = 60.

  7. The sum of interior angles in a pentagon (5 sides) is:

    Answer: 540°

    Sum of interior angles = (n - 2) × 180°. For n = 5: (5 - 2) × 180° = 3 × 180° = 540°.

  8. A right triangle has hypotenuse 13 and one leg of 5. What is the other leg?

    Answer: 12

    By Pythagorean theorem: 5² + b² = 13² → 25 + b² = 169 → b² = 144 → b = 12.

  9. In a right triangle, if tan(θ) = 1, what is θ?

    Answer: 45°

    tan(45°) = 1. When the opposite and adjacent sides are equal, the angle is 45°.

  10. What is the area of a triangle with base 10 and height 6?

    Answer: 30

    Area = (1/2) × base × height = (1/2) × 10 × 6 = 30.

  11. Two angles of a triangle measure 55° and 75°. What is the third angle?

    Answer: 50°

    The sum of angles in a triangle is 180°. Third angle = 180° - 55° - 75° = 50°.

  12. What is the distance between the points (1, 2) and (4, 6)?

    Answer: 5

    Distance = √((4-1)² + (6-2)²) = √(9 + 16) = √25 = 5.

  13. A sphere has radius 3. What is its volume? (V = (4/3)πr³)

    Answer: 36π

    V = (4/3)π(3)³ = (4/3)π(27) = 36π.

  14. In a right triangle with hypotenuse 1 and angle θ = 30°, what is the length of the side opposite to θ?

    Answer: 1/2

    sin(30°) = opposite/hypotenuse = opposite/1 = 1/2. The opposite side is 1/2.

  15. The midpoint of segment with endpoints (2, 4) and (8, 10) is:

    Answer: (5, 7)

    Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) = ((2+8)/2, (4+10)/2) = (5, 7).

  16. A cylinder has radius 4 and height 7. What is its volume? (V = πr²h)

    Answer: 112π

    V = π(4²)(7) = π(16)(7) = 112π.

  17. Parallel lines are cut by a transversal. Which pair of angles are always equal?

    Answer: Alternate interior angles

    When parallel lines are cut by a transversal, alternate interior angles are equal (congruent).

  18. A 45-45-90 triangle has legs of length 6. What is the hypotenuse?

    Answer: 6√2

    In a 45-45-90 triangle, the hypotenuse = leg × √2 = 6√2.

  19. What is the area of a trapezoid with parallel sides 8 and 12, and height 5?

    Answer: 50

    Area = (1/2)(b₁ + b₂)(h) = (1/2)(8 + 12)(5) = (1/2)(20)(5) = 50.

  20. A 30-60-90 triangle has a shorter leg of 5. What is the length of the longer leg?

    Answer: 5√3

    In a 30-60-90 triangle, the longer leg = shorter leg × √3 = 5√3.