Bluebook SAT Test Digital SAT Math Practice 8

Question 1

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

Accepted Answer

x = 7, y = 3

Answer

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?

Accepted Answer

2/13

Answer

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?

Accepted Answer

1

Answer

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?

Accepted Answer

175 miles

Answer

3.5 × 50 = 175 miles.

Question 5

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

Accepted Answer

Any value of k except 15

Answer

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.

Bluebook SAT Practice Test