📖 SAT Math

SAT Math Practice

SAT Math practice questions with explanations

538 Practice questions
3 Difficulty levels
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📝 Sample Questions

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Medium
What is the y -intercept of the graph of the function y = 2 ^{x} − 3?
  1. A. −3
  2. B. −2 ✓
  3. C. 0
  4. D. 1
Explanation: To find the $y$-intercept, set $x = 0$ because the $y$-intercept is the point where the graph crosses the $y$-axis. Substitute this into the equation $y = 2^x - 3$ to get $y = 2^0 - 3$. Since any non-zero number raised to the power of zero equals 1, this simplifies to $y = 1 - 3$, which equals $-2$.
Easy
Samara drove on a 400-mile trip. If the first half of the trip took her 4 hours of driving to complete and the second half took her 6 hours of driving to complete, what was her average driving speed for the whole 400-mile trip?
  1. A. 20 miles per hour
  2. B. 35 miles per hour
  3. C. 40 miles per hour ✓
  4. D. 80 miles per hour
Explanation: The total amount of time that it took Samara to complete the trip is 4 + 6 = 10 hours. Use the equation Distance = Rate × Time to work with this problem. The problem asks for the average speed, which corresponds to the rate. Using that equation, the \text{Rate} = \frac{\text{Distance}}{\text{Time}}
Hard
If x + 3 = y and xy = 40, what is the sum of x and y , given that both x and y are positive?
  1. A. 5
  2. B. 8
  3. C. 13 ✓
  4. D. 15
Explanation: Substitute $y = x + 3$ into the equation $xy = 40$ to get $x(x + 3) = 40$, which simplifies to the quadratic $x^2 + 3x - 40 = 0$. Factoring this yields $(x + 8)(x - 5) = 0$, giving solutions $x = -8$ or $x = 5$; since $x$ must be positive, we select $x = 5$. This results in $y = 8$, making the sum $
Medium
5. Which of the following equivalent forms gives the x -intercepts of the parabola given by the equation above? −2 x ( x − 5) + 7( x − 5) = ax ^{2} + bx + c
  1. A. y − 24 = x ^{2} − 10 x
  2. B. y + 1 = ( x − 5) ^{2}
  3. C. y = ( x − 4)( x − 6) ✓
  4. D. y = x ( x − 10) + 24
Explanation: Getting to the Answer: The variable y expressed as the product of two factors clearly reveals the two values for which y = 0. Choice (C) is correct.
Hard
4. If the volume of a sphere is the same as that of a cylinder with radius 4 feet and height 18 feet, what is the radius, in feet, of the sphere?
  1. A. 2
  2. B. 3
  3. C. 6 ✓
  4. D. 12
Explanation: Getting to the Answer: The volume of the cylinder is π r ^{2} h = π(4) ^{2} (18) = 288π. Set the volume of the cylinder equal to the volume of the sphere: 288\text{π}=\frac{4}{3}\text{π}r^{3}. So, r^{3}=\frac{3(288\text{π})}{4\text{π}}=216, and r = 6 feet. Choice (C) is correct.

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