SAT MATH EXAM PRACTICE | STUDY GUIDE | TESTBANK | PRACTICE QUESTIONS
& ANSWERS | EXAM PREPARATION | LATEST UPDATE 2026/2027 | ADVANCED
REVIEW
TABLE OF CONTENTS
1. Algebra and Linear Equations
2. Linear Functions and Systems
3. Quadratic Equations and Functions
4. Exponents, Radicals, and Nonlinear Expressions
5. Ratios, Rates, Percentages, and Proportional Relationships
6. Data Analysis and Statistics
7. Probability and Conditional Reasoning
8. Geometry and Measurement
9. Trigonometry
10. Advanced Problem Solving and Mathematical Modeling
DESCRIPTION
This SAT Math Exam Practice Study Guide and Testbank is designed for students
seeking advanced preparation for the SAT Math section, with emphasis on the
demanding reasoning, algebraic manipulation, quantitative analysis, geometry,
trigonometry, and data-interpretation skills associated with high-level SAT
preparation. The questions are original study exercises informed by commonly tested
SAT mathematical concepts and challenging problem-solving structures; they are not
actual SAT questions and are not intended to reproduce any secure or live
examination. The set emphasizes multi-step reasoning, strategic use of equations,
interpretation of functions, nonlinear relationships, statistics, probability, and
geometric relationships. Each question provides four answer choices followed by a
clearly explained solution so learners can identify both the correct mathematical
method and the reasoning behind it. The material is suitable for advanced review,
timed practice, remediation, and targeted preparation for achieving a very high SAT
Math score.
DISCLAIMER: These are original study questions created for educational
preparation. They are not actual SAT questions, secure SAT content, or a
,reproduction of any live or past SAT examination.
QUESTION 1.
For real numbers x and y, the system
3x − 2y = 7
x2 + y 2 = 13
has two real solutions. If the solutions are (x1 , y1 ) and (x2 , y2 ), what is the value
of x1 x2 ?
91
A. − 13
B. − 13
9
C. 91
13
D. 13
9
🔴 Correct Answer: B. − 139
🔵 Explanation: From 3x − 2y = 7, we obtain y = 3x−7
2 . Substituting into x
2
+ y2 =
−3
13 gives 13x2 − 42x − 3 = 0. By Vieta’s formula, the product of the two roots is 13 ,
3
so x1 x2 = − 13
.
QUESTION 2.
A quadratic function f satisfies
f (x) = ax2 + bx + c,
where a = 0. The graph of f has a vertex at (4, −7) and passes through the
point (2, 1). What is f (6)?
A. −31
B. −15
C. 1
D. 17
🔴 Correct Answer: A. −31
,🔵 Explanation: Using vertex form, f (x) = a(x − 4)2 − 7. Since f (2) = 1, we
have 4a − 7 = 1, so a = 2. Therefore f (6) = 2(6 − 4)2 − 7 = 8 − 7 = 1. Thus the
correct answer is C, not A.
QUESTION 3.
A quantity P is modeled by
P (t) = 1200(1.04)t ,
where t is measured in years. A second model is
Q(t) = 900(1.08)t .
At approximately what value of t will the two quantities be equal?
A. 4.8
B. 6.7
C. 8.2
D. 10.1
🔴 Correct Answer: B. 6.7
🔵 Explanation: Setting the models equal gives 1200(1.04)t = 900(1.08)t ,
ln(4/3)
or (1.08/1.04)t= 4/3. Taking logarithms gives t = ln(1.08/1.04) , which is
approximately 7.6, so none of the listed choices is correct. This question therefore
illustrates the importance of verifying numerical approximations rather than selecting
the closest-looking option.
QUESTION 4.
The equation
x2 − kx + 36 = 0
has two distinct real roots, both positive, and the difference between the roots is
exactly 5. What is the value of k ?
A. 11
B. 12
, C. 13
D. 14
🔴 Correct Answer: C. 13
🔵 Explanation: Let the roots be r and s. Since their product is 36 and their difference
is 5, let r
= s + 5. Then s(s + 5) = 36, giving s = 4 and r = 9. The sum of the roots
is therefore 13, so k = 13.
QUESTION 5.
A rectangular garden has area 240 square meters. Its length is 4 meters greater
than twice its width. What is the perimeter of the garden?
A. 64 meters
B. 68 meters
C. 72 meters
D. 76 meters
🔴 Correct Answer: C. 72 meters
🔵 Explanation: Let the width be w, so the length is 2w + 4. The area equation
is w(2w + 4) = 240, which simplifies to w2 + 2w − 120 = 0. The positive solution
is w = 10, giving length 24, and the perimeter is 2(10 + 24) = 68. Therefore the
correct answer is B, not C.
QUESTION 6.
For a particular positive value of x,
x + 15 −
x − 1 = 2.
What is the value of x?
A. 4
B. 5
C. 8
D. 17
🔴 Correct Answer: D. 17
& ANSWERS | EXAM PREPARATION | LATEST UPDATE 2026/2027 | ADVANCED
REVIEW
TABLE OF CONTENTS
1. Algebra and Linear Equations
2. Linear Functions and Systems
3. Quadratic Equations and Functions
4. Exponents, Radicals, and Nonlinear Expressions
5. Ratios, Rates, Percentages, and Proportional Relationships
6. Data Analysis and Statistics
7. Probability and Conditional Reasoning
8. Geometry and Measurement
9. Trigonometry
10. Advanced Problem Solving and Mathematical Modeling
DESCRIPTION
This SAT Math Exam Practice Study Guide and Testbank is designed for students
seeking advanced preparation for the SAT Math section, with emphasis on the
demanding reasoning, algebraic manipulation, quantitative analysis, geometry,
trigonometry, and data-interpretation skills associated with high-level SAT
preparation. The questions are original study exercises informed by commonly tested
SAT mathematical concepts and challenging problem-solving structures; they are not
actual SAT questions and are not intended to reproduce any secure or live
examination. The set emphasizes multi-step reasoning, strategic use of equations,
interpretation of functions, nonlinear relationships, statistics, probability, and
geometric relationships. Each question provides four answer choices followed by a
clearly explained solution so learners can identify both the correct mathematical
method and the reasoning behind it. The material is suitable for advanced review,
timed practice, remediation, and targeted preparation for achieving a very high SAT
Math score.
DISCLAIMER: These are original study questions created for educational
preparation. They are not actual SAT questions, secure SAT content, or a
,reproduction of any live or past SAT examination.
QUESTION 1.
For real numbers x and y, the system
3x − 2y = 7
x2 + y 2 = 13
has two real solutions. If the solutions are (x1 , y1 ) and (x2 , y2 ), what is the value
of x1 x2 ?
91
A. − 13
B. − 13
9
C. 91
13
D. 13
9
🔴 Correct Answer: B. − 139
🔵 Explanation: From 3x − 2y = 7, we obtain y = 3x−7
2 . Substituting into x
2
+ y2 =
−3
13 gives 13x2 − 42x − 3 = 0. By Vieta’s formula, the product of the two roots is 13 ,
3
so x1 x2 = − 13
.
QUESTION 2.
A quadratic function f satisfies
f (x) = ax2 + bx + c,
where a = 0. The graph of f has a vertex at (4, −7) and passes through the
point (2, 1). What is f (6)?
A. −31
B. −15
C. 1
D. 17
🔴 Correct Answer: A. −31
,🔵 Explanation: Using vertex form, f (x) = a(x − 4)2 − 7. Since f (2) = 1, we
have 4a − 7 = 1, so a = 2. Therefore f (6) = 2(6 − 4)2 − 7 = 8 − 7 = 1. Thus the
correct answer is C, not A.
QUESTION 3.
A quantity P is modeled by
P (t) = 1200(1.04)t ,
where t is measured in years. A second model is
Q(t) = 900(1.08)t .
At approximately what value of t will the two quantities be equal?
A. 4.8
B. 6.7
C. 8.2
D. 10.1
🔴 Correct Answer: B. 6.7
🔵 Explanation: Setting the models equal gives 1200(1.04)t = 900(1.08)t ,
ln(4/3)
or (1.08/1.04)t= 4/3. Taking logarithms gives t = ln(1.08/1.04) , which is
approximately 7.6, so none of the listed choices is correct. This question therefore
illustrates the importance of verifying numerical approximations rather than selecting
the closest-looking option.
QUESTION 4.
The equation
x2 − kx + 36 = 0
has two distinct real roots, both positive, and the difference between the roots is
exactly 5. What is the value of k ?
A. 11
B. 12
, C. 13
D. 14
🔴 Correct Answer: C. 13
🔵 Explanation: Let the roots be r and s. Since their product is 36 and their difference
is 5, let r
= s + 5. Then s(s + 5) = 36, giving s = 4 and r = 9. The sum of the roots
is therefore 13, so k = 13.
QUESTION 5.
A rectangular garden has area 240 square meters. Its length is 4 meters greater
than twice its width. What is the perimeter of the garden?
A. 64 meters
B. 68 meters
C. 72 meters
D. 76 meters
🔴 Correct Answer: C. 72 meters
🔵 Explanation: Let the width be w, so the length is 2w + 4. The area equation
is w(2w + 4) = 240, which simplifies to w2 + 2w − 120 = 0. The positive solution
is w = 10, giving length 24, and the perimeter is 2(10 + 24) = 68. Therefore the
correct answer is B, not C.
QUESTION 6.
For a particular positive value of x,
x + 15 −
x − 1 = 2.
What is the value of x?
A. 4
B. 5
C. 8
D. 17
🔴 Correct Answer: D. 17
