SAT MATH - Practice Test with Fully Worked
Solutions
30 original practice questions, each with a step-by-step worked
explanation
For students preparing for the SAT Math section. This is original practice material written for
study purposes. It is NOT a copy of real SAT questions and is not affiliated with or endorsed by
the College Board.
How to use this document
• Answer all 30 questions on paper first, without looking at the solutions. Each question has 4
options (A-D), written in the style of the SAT Math section.
• Then check yourself in the Worked Solutions section, where every question is solved step by
step so you can see exactly where a mistake happened.
• A quick answer grid and a self-scoring guide are included at the end.
• Topics covered, following the SAT Math blueprint: Heart of Algebra (linear equations,
inequalities, systems of equations), Problem Solving and Data Analysis (ratios, percentages,
unit conversion, averages), Passport to Advanced Math (quadratics, polynomials, functions,
exponentials, rational expressions), and geometry with basic right-triangle trigonometry.
Heart of Algebra
1. Solve for x: 3(x - 4) = 2x + 5
A) x = 13
B) x = 17
C) x = 21
D) x = 22
2. Which values of x satisfy the inequality -2x + 7 > 15?
A) x < -4
B) x > -4
C) x < 4
D) x > -8
3. The system 2x + 3y = 12 and x - y = 1 has one solution. What is the value of x + y?
, A) 3
B) 4
C) 5
D) 6
4. A line passes through the points (2, 5) and (6, 13). What is the y-intercept of the line?
A) -1
B) 1
C) 2
D) 5
5. Solve for x: 3x + 7 = 2(2x - 1)
A) x = 5
B) x = 7
C) x = 9
D) x = 11
6. A copy shop charges a setup fee of $40 plus $0.25 for each printed page. How much does it
cost to print 300 pages?
A) $100
B) $110
C) $115
D) $145
7. Which values of x satisfy the inequality 3x - 5 <= 4x + 7?
A) x >= -12
B) x <= -12
C) x >= 12
D) x <= 2
8. If y = 3x - 4 and 2x + y = 21, what is the value of y?
A) 5
B) 7
C) 9
D) 11
Solutions
30 original practice questions, each with a step-by-step worked
explanation
For students preparing for the SAT Math section. This is original practice material written for
study purposes. It is NOT a copy of real SAT questions and is not affiliated with or endorsed by
the College Board.
How to use this document
• Answer all 30 questions on paper first, without looking at the solutions. Each question has 4
options (A-D), written in the style of the SAT Math section.
• Then check yourself in the Worked Solutions section, where every question is solved step by
step so you can see exactly where a mistake happened.
• A quick answer grid and a self-scoring guide are included at the end.
• Topics covered, following the SAT Math blueprint: Heart of Algebra (linear equations,
inequalities, systems of equations), Problem Solving and Data Analysis (ratios, percentages,
unit conversion, averages), Passport to Advanced Math (quadratics, polynomials, functions,
exponentials, rational expressions), and geometry with basic right-triangle trigonometry.
Heart of Algebra
1. Solve for x: 3(x - 4) = 2x + 5
A) x = 13
B) x = 17
C) x = 21
D) x = 22
2. Which values of x satisfy the inequality -2x + 7 > 15?
A) x < -4
B) x > -4
C) x < 4
D) x > -8
3. The system 2x + 3y = 12 and x - y = 1 has one solution. What is the value of x + y?
, A) 3
B) 4
C) 5
D) 6
4. A line passes through the points (2, 5) and (6, 13). What is the y-intercept of the line?
A) -1
B) 1
C) 2
D) 5
5. Solve for x: 3x + 7 = 2(2x - 1)
A) x = 5
B) x = 7
C) x = 9
D) x = 11
6. A copy shop charges a setup fee of $40 plus $0.25 for each printed page. How much does it
cost to print 300 pages?
A) $100
B) $110
C) $115
D) $145
7. Which values of x satisfy the inequality 3x - 5 <= 4x + 7?
A) x >= -12
B) x <= -12
C) x >= 12
D) x <= 2
8. If y = 3x - 4 and 2x + y = 21, what is the value of y?
A) 5
B) 7
C) 9
D) 11
