Bluebook SAT Algebra Practice 2 — Questions and Answers
Question 1: The function f is defined by f(x) = 5x - 8. If f(a) = 3a + 6, what is the value of a?
- -1
- 1
- 7 (Correct answer)
- 14
Correct answer: 7
5a - 8 = 3a + 6 gives 2a = 14, so a = 7.
Since f(a) = 5a - 8, set this equal to 3a + 6: 5a - 8 = 3a + 6. Subtract 3a: 2a - 8 = 6. Add 8: 2a = 14, so a = 7. Check: f(7) = 27 and 3(7) + 6 = 27.
Question 2: A line in the xy-plane is perpendicular to the line 2x + 3y = 12 and passes through the point (4, -1). What is the y-intercept of this line?
- -7 (Correct answer)
- 5
- -5
- 7
Correct answer: -7
Perpendicular slope is 3/2; -1 = (3/2)(4) + b gives b = -7.
Rewrite 2x + 3y = 12 as y = (-2/3)x + 4, so its slope is -2/3. A perpendicular line has slope 3/2. Using point (4, -1): -1 = (3/2)(4) + b, so -1 = 6 + b and b = -7.
Question 3: A tank holds 500 liters of water and drains at a constant rate of 12 liters per minute. Which equation gives the volume V, in liters, remaining after t minutes, and after how many minutes is the tank empty?
- V = 500 + 12t; never
- V = 12t - 500; about 41.7 minutes
- V = 500 - 12t; about 41.7 minutes (Correct answer)
- V = 500 - 12t; 12 minutes
Correct answer: V = 500 - 12t; about 41.7 minutes
Volume decreases from 500 by 12 each minute; 500/12 is about 41.7.
The volume starts at 500 and decreases by 12 liters each minute, so V = 500 - 12t. The tank is empty when V = 0: 500 = 12t, so t = 500/12, approximately 41.7 minutes. Choice B has the wrong sign structure and choice D uses the rate as the time.
Question 4: If the system 3x + ky = 7 and 6x - 4y = 14 has infinitely many solutions, what is the value of k?
- 2
- -2 (Correct answer)
- 4
- -4
Correct answer: -2
Multiplying the first equation by 2 must yield the second, so 2k = -4 and k = -2.
For infinitely many solutions, the two equations must represent the same line. Multiply 3x + ky = 7 by 2: 6x + 2ky = 14. Matching with 6x - 4y = 14 gives 2k = -4, so k = -2.
Question 5: What is the solution set of the equation |2x - 5| = 9?
- {7}
- {-2, 7} (Correct answer)
- {-7, 2}
- {2, 7}
Correct answer: {-2, 7}
2x - 5 = 9 gives x = 7; 2x - 5 = -9 gives x = -2.
Set 2x - 5 = 9, so 2x = 14 and x = 7. Set 2x - 5 = -9, so 2x = -4 and x = -2. Both values satisfy the original equation, so the solution set is {-2, 7}.
Question 6: The total cost C, in dollars, of renting a bicycle for h hours is given by C = 6h + 15. Which statement correctly interprets the number 15 in this context?
- The cost per hour of the rental
- The maximum number of hours the bicycle can be rented
- The fixed fee charged regardless of how many hours the bicycle is rented (Correct answer)
- The total cost of renting the bicycle for one hour
Correct answer: The fixed fee charged regardless of how many hours the bicycle is rented
15 is the y-intercept, the cost when h = 0.
In C = 6h + 15, the coefficient 6 is the hourly rate and the constant 15 is the cost when h = 0, meaning a fixed fee that applies before any hours are counted. The one-hour cost would be 6(1) + 15 = 21, not 15.
Bluebook SAT Algebra Practice 2
The function f is defined by f(x) = 5x - 8.
If f(a) = 3a + 6, what is the value of a?