SAT Geometry & Trigonometry 2 — Questions and Answers
Question 1: What is the slope of a line perpendicular to y = 2x + 3?
- 2
- −2
- 1/2
- −1/2 (Correct answer)
Correct answer: −1/2
Perpendicular lines have slopes that are negative reciprocals; the negative reciprocal of 2 is −1/2.
Question 2: What is the area of a triangle with base 8 and height 5?
- 13
- 20 (Correct answer)
- 40
- 80
Correct answer: 20
Area = (1/2) × base × height = (1/2)(8)(5) = 20.
Question 3: In right triangle ABC, angle C = 90° and angle A = 30°. If BC (the shorter leg) = 4, what is the length of hypotenuse AB?
- 2
- 4√3
- 8 (Correct answer)
- 4√2
Correct answer: 8
In a 30-60-90 triangle the hypotenuse is twice the shorter leg, so AB = 2 × 4 = 8.
Question 4: What is the circumference of a circle with diameter 10?
- 5π
- 10π (Correct answer)
- 20π
- 100π
Correct answer: 10π
Circumference = πd = π(10) = 10π.
Question 5: A rectangle has a perimeter of 30 and a width of 6. What is its area?
- 36
- 54 (Correct answer)
- 72
- 108
Correct answer: 54
2(l + w) = 30 → l + w = 15 → l = 9; Area = 9 × 6 = 54.
Question 6: What is the value of tan(45°)?
- 0
- 1/2
- 1 (Correct answer)
- √2
Correct answer: 1
tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.
Question 7: A central angle of 60° intercepts an arc of a circle with radius 6. What is the arc length?
- 2π (Correct answer)
- 6π
- 12π
- π
Correct answer: 2π
Arc length = (60/360) × 2π(6) = (1/6)(12π) = 2π.
SAT Geometry & Trigonometry 2
What is the slope of a line perpendicular to y = 2x + 3?