SAT MATHS PRACTICE ASSIGNMENT
20 High-Yield Repeated Questions & Detailed Explanations
Student Name: Date : Target Score:
INSTRUCTIONS & EXAM PARAMETERS
This diagnostic practice contains 20 questions closely modeled after the most frequently tested concepts on the Digital
SAT Math sections.
• Calculator Policy: Use of an approved calculator is permitted on all questions.
• Formulas: Use standard SAT geometric formulas for area and volume where applicable.
• Timing: Aim to complete this assignment in 35 minutes (approximately 1 minute and 45 seconds per question).
Section 1: Multiple-Choice Questions (1–15)
1. If 3x + 7 = 22 , what is the value of 6x - 5?
A) 25 B) 29
C) 39 D) 44
2. A system of equations is shown below:
ky - 3x=4
6x - 8y=12
For which value of the constant k does the system of equations have no solution?
A) -4 B) -3
C) 4 D) 8
3. The function f is defined by f(x) = x² - 6x + 11 . Which of the following is an equivalent form of the function that
displays the minimum value of f(x) as a constant or coefficient?
A) f(x) = (x - 3)² + 2 B) f(x) = (x + 3)² - 2
C) f(x) = x(x - 6) + 11 D) f(x) = (x - 3)² + 11
Page 1 of 7
, 4.An online bookstore sells hardcover books for $18 each and paperback books for $10 each. A customer wants
to buy at least 5 books and spend at most $120. If h represents the number of hardcover books and p represents
the number of paperback books, which of the following systems of inequalities models this scenario?
A) h + p ≤ 5 B) h + p ≥ 5 18h
18h + 10p ≥ 120 + 10p ≤ 120
C) h + p ≥ 5 D) h + p ≤ 120
10h + 18p ≤ 120 18h + 10p ≥ 5
5.The population of a bacteria colony triples every 4 hours. If the initial population of the colony was 150, which of
the following functions best models the population, P(t), after t hours?
4t t/4
A) P(t) = 150(3) B) P(t) = 150(3)
C) P(t) = 150 + 3(4)t D) P(t) = 150(4) t/3
6. In the xy-plane, the circle with equation x² + y² - 8x + 6y = 11 has center (h, k) and radius r . What is the value of
r?
A) √11 B) 5
C) 6 D) 36
a² b² 16
7. If x > 0 and (x / x ) = x , where a - b = 4 , what is the value of a + b?
A) 2 B) 4
C) 8 D) 12
8. The table below shows the distribution of registered voters by political party and age group in a certain town.
Age Group Democratic Republican Independent Total
18-35 120 80 100 300
36+ 180 220 100 500
Total 300 300 200 800
If a registered voter is selected at random from those who are in the 18-35 age group, what is the probability
that the voter is registered as an Independent?
A) B)
C) 1/8 D) 1/4
1/3 1/2
9.For a certain gas, the volume V is inversely proportional to the pressure P. If the volume of the gas is 24 liters
when the pressure is 1.5 atmospheres, what is the volume of the gas, in liters, when the pressure is 3.0
atmospheres?
A) 12 B) 18
C) 36 D) 48
Page 2 of 7
20 High-Yield Repeated Questions & Detailed Explanations
Student Name: Date : Target Score:
INSTRUCTIONS & EXAM PARAMETERS
This diagnostic practice contains 20 questions closely modeled after the most frequently tested concepts on the Digital
SAT Math sections.
• Calculator Policy: Use of an approved calculator is permitted on all questions.
• Formulas: Use standard SAT geometric formulas for area and volume where applicable.
• Timing: Aim to complete this assignment in 35 minutes (approximately 1 minute and 45 seconds per question).
Section 1: Multiple-Choice Questions (1–15)
1. If 3x + 7 = 22 , what is the value of 6x - 5?
A) 25 B) 29
C) 39 D) 44
2. A system of equations is shown below:
ky - 3x=4
6x - 8y=12
For which value of the constant k does the system of equations have no solution?
A) -4 B) -3
C) 4 D) 8
3. The function f is defined by f(x) = x² - 6x + 11 . Which of the following is an equivalent form of the function that
displays the minimum value of f(x) as a constant or coefficient?
A) f(x) = (x - 3)² + 2 B) f(x) = (x + 3)² - 2
C) f(x) = x(x - 6) + 11 D) f(x) = (x - 3)² + 11
Page 1 of 7
, 4.An online bookstore sells hardcover books for $18 each and paperback books for $10 each. A customer wants
to buy at least 5 books and spend at most $120. If h represents the number of hardcover books and p represents
the number of paperback books, which of the following systems of inequalities models this scenario?
A) h + p ≤ 5 B) h + p ≥ 5 18h
18h + 10p ≥ 120 + 10p ≤ 120
C) h + p ≥ 5 D) h + p ≤ 120
10h + 18p ≤ 120 18h + 10p ≥ 5
5.The population of a bacteria colony triples every 4 hours. If the initial population of the colony was 150, which of
the following functions best models the population, P(t), after t hours?
4t t/4
A) P(t) = 150(3) B) P(t) = 150(3)
C) P(t) = 150 + 3(4)t D) P(t) = 150(4) t/3
6. In the xy-plane, the circle with equation x² + y² - 8x + 6y = 11 has center (h, k) and radius r . What is the value of
r?
A) √11 B) 5
C) 6 D) 36
a² b² 16
7. If x > 0 and (x / x ) = x , where a - b = 4 , what is the value of a + b?
A) 2 B) 4
C) 8 D) 12
8. The table below shows the distribution of registered voters by political party and age group in a certain town.
Age Group Democratic Republican Independent Total
18-35 120 80 100 300
36+ 180 220 100 500
Total 300 300 200 800
If a registered voter is selected at random from those who are in the 18-35 age group, what is the probability
that the voter is registered as an Independent?
A) B)
C) 1/8 D) 1/4
1/3 1/2
9.For a certain gas, the volume V is inversely proportional to the pressure P. If the volume of the gas is 24 liters
when the pressure is 1.5 atmospheres, what is the volume of the gas, in liters, when the pressure is 3.0
atmospheres?
A) 12 B) 18
C) 36 D) 48
Page 2 of 7
