Bluebook SAT Algebra Practice Flashcards

The function f is defined by f(x) = 5x - 8. If f(a) = 3a + 6, what is the value of a?

Answer: 7

5a - 8 = 3a + 6 gives 2a = 14, so a = 7.

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?

Answer: -7

Perpendicular slope is 3/2; -1 = (3/2)(4) + b gives b = -7.

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?

Answer: V = 500 - 12t; about 41.7 minutes

Volume decreases from 500 by 12 each minute; 500/12 is about 41.7.

If the system 3x + ky = 7 and 6x - 4y = 14 has infinitely many solutions, what is the value of k?

Answer: -2

Multiplying the first equation by 2 must yield the second, so 2k = -4 and k = -2.

What is the solution set of the equation |2x - 5| = 9?

Answer: {-2, 7}

2x - 5 = 9 gives x = 7; 2x - 5 = -9 gives x = -2.

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?

Answer: The fixed fee charged regardless of how many hours the bicycle is rented

15 is the y-intercept, the cost when h = 0.