Hard SAT Math Worksheet

12 multiple-choice questions with blank space for calculations, with answers and explanations.

Paper size

8 pages. Print pages 1–6 for students; the answer key is on pages 7–8.

First student page of the Hard SAT Math Worksheet — Student page 1 of 6

For more SAT practice questions, visit the free 1600.now question bank.

Try two questions before you print

Question 1

The equation $x^{2} - k x + 48 = 0$ has two positive solutions. One solution is three times the other. What is $k$ ?

Show answer and explanation

B. Write the roots as $r$ and $3 r$ . Their product is 48, so $3 r^{2} = 48$ and $r = 4$ because both roots are positive. The roots are 4 and 12. Their sum equals $k$ , so $k = 16$ .

Question 2

The square root of $2 x + 9$ is equal to $x - 3$ . What value of $x$ satisfies the equation?

Show answer and explanation

A. Because a square root is nonnegative, $x$ must be at least 3. Squaring gives $2 x + 9 = x^{2} - 6 x + 9$ , so $x (x - 8) = 0$ . The candidate 0 violates $x \geq 3$ . The valid solution is 8: the square root of 25 equals $8 - 3$ .

Share with your class

Paste this into Google Classroom, an email, or your next assignment.

Printing and classroom use

Select Letter or A4 before downloading. Use the student page range shown beside the download button and print at actual size. The answer key starts on a separate page. The layout works in black and white and leaves blank space for calculations.

These are original 1600.now questions for classroom or personal use. They are not official College Board items. Students may use a calculator for these math exercises.

Skill labels follow the College Board content domains.

More math worksheets

All printable SAT worksheets