Materials for SAT Math Prep
Practice Questions for the Digital SAT
Provided by the College Board:
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Previous Test Questions and Answers
- PSAT 11 - Oct. 2020: Math - Calculator questions with answers and explanations and Math - No Calculator questions with answers and explanations
- PSAT 11 - Oct. 2019: Math - Calculator questions with answers and explanations and Math - No Calculator questions with answers and explanations
- PSAT 10 - Apr. 2019: Math - Calculator questions with answers and explanations and Math - No Calculator questions with answers and explanations
- PSAT 9 - Apr. 2019 Math - Calculator questions with answers and explanations and Math - No Calculator questions with answers and explanations
- PSAT 11 - Oct. 2018: Math - Calculator questions with answers and explanations and Math - No Calculator questions with answers and explanations
- PSAT 10 - Apr. 2018: Math - all questions from booklet
- PSAT 9 - Apr. 2018: Math - all questions from booklet
- PSAT 11 - Oct. 2017: Math - Calculator questions with answers and explanations and Math - No Calculator questions with answers and explanations
- PSAT 11 - Oct. 2016: Math - Calculator questions with answers and explanations and Math - No Calculator questions with answers and explanations
- PSAT 10 - Apr. 2016: Math - Calculator questions with answers and explanations and Math - No Calculator questions with answers and explanations
Sample Questions
Click to download additional sample questions for all 3 areas on PowerPoint slides.
Heart of Algebra (with calculator):
When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?
A) p = 0.44d + 0.77
B) p = 0.44d + 14.74
C) p = 2.2d – 1.1
D) p = 2.2d – 9.9
Answer and Explanation:
Choice B is correct. To determine the linear model, one can first determine the rate at which the pressure due to the atmosphere and surrounding water is increasing as the depth of the diver increases. Calculating this gives [fraction numerator 20.9 −18.7 over denominator 14 − 9 end fraction] equals [fraction numerator 2.2 over denominator 5 end fraction] comma or 0.44. Then one needs to determine the pressure due to the atmosphere or, in other words, the pressure when the diver is at a depth of 0. Solving the equation 18.7 = 0.44 ( 9 ) + b gives b = 14.74. Therefore, the model that can be used to relate the pressure and the depth is p = 0.44 d + 14.74.
When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?
A) p = 0.44d + 0.77
B) p = 0.44d + 14.74
C) p = 2.2d – 1.1
D) p = 2.2d – 9.9
Answer and Explanation:
Choice B is correct. To determine the linear model, one can first determine the rate at which the pressure due to the atmosphere and surrounding water is increasing as the depth of the diver increases. Calculating this gives [fraction numerator 20.9 −18.7 over denominator 14 − 9 end fraction] equals [fraction numerator 2.2 over denominator 5 end fraction] comma or 0.44. Then one needs to determine the pressure due to the atmosphere or, in other words, the pressure when the diver is at a depth of 0. Solving the equation 18.7 = 0.44 ( 9 ) + b gives b = 14.74. Therefore, the model that can be used to relate the pressure and the depth is p = 0.44 d + 14.74.
Problem-Solving and Data Analysis
A typical image taken of the surface of Mars by a camera is 11.2 gigabits in size. A tracking station on Earth can receive data from the spacecraft at a data rate of 3 megabits per second for a maximum of 11 hours each day. If 1 gigabit equals 1,024 megabits, what is the maximum number of typical images that the tracking station could receive from the camera each day?
A) 3
B) 10
C) 56
D) 144
Answer and Explanation:
A typical image taken of the surface of Mars by a camera is 11.2 gigabits in size. A tracking station on Earth can receive data from the spacecraft at a data rate of 3 megabits per second for a maximum of 11 hours each day. If 1 gigabit equals 1,024 megabits, what is the maximum number of typical images that the tracking station could receive from the camera each day?
A) 3
B) 10
C) 56
D) 144
Answer and Explanation:
Passport to Advanced Math
The function f is defined by f (x) = 2x³ + 3x² + cx + 8, where c is a constant. In the xy-plane, the graph of f intersects the x-axis at the three points (−4, 0), (1/2, 0 ), and
( p, 0). What is the value of c?
A) –18
B) –2
C) 2
D) 10
Answer and Explanation:
Choice A is correct. The given zeros can be used to set up an equation to solve for c. Substituting –4 for x and 0 for y yields –4c = 72, or c = –18.
Alternatively, since –4, 1/2, and p are zeros of the polynomial function
f (x) = 2x³ + 3x² + cx + 8, it follows that f (x) = (2x − 1)(x + 4)(x − p).
Were this polynomial multiplied out, the constant term would be
(−1)(4)(− p) = 4 p. (We can see this without performing the full expansion.)
Since it is given that this value is 8, it goes that 4p = 8 or rather, p = 2. Substituting 2 for p in the polynomial function yields
f (x) = (2x − 1)(x + 4)(x − 2),
and after multiplying the factors one finds that the coefficient of the x term, or the value of c, is –18
The function f is defined by f (x) = 2x³ + 3x² + cx + 8, where c is a constant. In the xy-plane, the graph of f intersects the x-axis at the three points (−4, 0), (1/2, 0 ), and
( p, 0). What is the value of c?
A) –18
B) –2
C) 2
D) 10
Answer and Explanation:
Choice A is correct. The given zeros can be used to set up an equation to solve for c. Substituting –4 for x and 0 for y yields –4c = 72, or c = –18.
Alternatively, since –4, 1/2, and p are zeros of the polynomial function
f (x) = 2x³ + 3x² + cx + 8, it follows that f (x) = (2x − 1)(x + 4)(x − p).
Were this polynomial multiplied out, the constant term would be
(−1)(4)(− p) = 4 p. (We can see this without performing the full expansion.)
Since it is given that this value is 8, it goes that 4p = 8 or rather, p = 2. Substituting 2 for p in the polynomial function yields
f (x) = (2x − 1)(x + 4)(x − 2),
and after multiplying the factors one finds that the coefficient of the x term, or the value of c, is –18
Instructional Materials
Instruction Ideas:
Project a sample question for the class and…
Reviewing and Practicing for the Multi-Step Problems:
Discuss a plan for solving these types and model how you would analyze the task…
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Lesson Resources:
Test-Taking Tips to Teach:
Web Sites for Practice:
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Practice Passages & Test Questions
From the College Board's SAT practice tests.
The above test questions (collections 1-6) are also organized by skill on this page sponsored by Ivy Global Prep. Categories of skills include:
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Delivering Instruction of SAT Skills
Use the following visible thinking questions to guide your instruction using practice SAT questions:
Claim:
What type of question is being asked? What is the student being asked to do or solve? |
Support:
What is the skill or concept needed to correctly answer the question? |
Question:
What instructional strategies can be used to teach this skill? |