Bluebook SAT Test Digital SAT Math Practice 8 — Questions and Answers
Question 1: What is the solution to the system of equations: x + y = 10 and x − y = 4?
- x = 7, y = 3 (Correct answer)
- x = 6, y = 4
- x = 5, y = 5
- x = 8, y = 2
Correct answer: x = 7, y = 3
Adding the equations: 2x = 14, x = 7; substituting back gives y = 3.
Question 2: An experiment selects a card from a deck of 52. What is the probability of drawing a king or a queen?
- 2/13 (Correct answer)
- 1/13
- 1/26
- 4/13
Correct answer: 2/13
There are 4 kings and 4 queens = 8 favorable cards; P = 8/52 = 2/13.
Question 3: The equation y = 2x² − 4x + 1 represents a parabola. What is the x-coordinate of the vertex?
- 1 (Correct answer)
- 2
- −1
- 4
Correct answer: 1
The vertex x-coordinate is −b/(2a) = −(−4)/(2·2) = 4/4 = 1.
Question 4: A scale on a map is 1 inch = 50 miles. Two cities are 3.5 inches apart on the map. What is the actual distance?
- 175 miles (Correct answer)
- 150 miles
- 200 miles
- 125 miles
Correct answer: 175 miles
3.5 × 50 = 175 miles.
Question 5: For what value of k does the equation 3x + k = 3(x + 5) have no solution?
- Any value of k except 15 (Correct answer)
- k = 15
- k = 0
- There is always a solution.
Correct answer: Any value of k except 15
Expanding the right side: 3x + k = 3x + 15; subtracting 3x gives k = 15 as a contradiction for any k ≠ 15, making k ≠ 15 yield no solution.
Question 6: A right circular cone has a radius of 4 and a height of 6. What is its volume?
- 32π (Correct answer)
- 48π
- 16π
- 64π
Correct answer: 32π
V = (1/3)πr²h = (1/3)π(16)(6) = 32π.
Question 7: In a two-way frequency table, 80 students chose between Math or Science and between morning or afternoon classes. If 30 chose Math-morning, 20 chose Math-afternoon, and 15 chose Science-morning, how many chose Science-afternoon?
- 15 (Correct answer)
- 20
- 10
- 25
Correct answer: 15
Total = 80; Math total = 50; Science total = 30; Science-afternoon = 30 − 15 = 15.
Bluebook SAT Test Digital SAT Math Practice 8
What is the solution to the system of equations: x + y = 10 and x − y = 4?