Digital SAT Math Practice Flashcards

What is the solution to the system of equations: x + y = 10 and x − y = 4?

Answer: x = 7, y = 3

Adding the equations: 2x = 14, x = 7; substituting back gives y = 3.

An experiment selects a card from a deck of 52. What is the probability of drawing a king or a queen?

Answer: 2/13

There are 4 kings and 4 queens = 8 favorable cards; P = 8/52 = 2/13.

The equation y = 2x² − 4x + 1 represents a parabola. What is the x-coordinate of the vertex?

Answer: 1

The vertex x-coordinate is −b/(2a) = −(−4)/(2·2) = 4/4 = 1.

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?

Answer: 175 miles

3.5 × 50 = 175 miles.

For what value of k does the equation 3x + k = 3(x + 5) have no solution?

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.

A right circular cone has a radius of 4 and a height of 6. What is its volume?

Answer: 32π

V = (1/3)πr²h = (1/3)π(16)(6) = 32π.

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?

Answer: 15

Total = 80; Math total = 50; Science total = 30; Science-afternoon = 30 − 15 = 15.