FREE Digital SAT Maths Practice Set 3

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Question 1

Consider the function [Tex]h(x) = \frac{1}{x^2 - 1}[/Tex]. What are the vertical asymptotes of the function [Tex]h(x)[/Tex]?

  • [Tex]x = -1[/Tex] and [Tex]x = 1[/Tex]

  • [Tex]x = -2[/Tex] and [Tex]x = 2[/Tex]

  • [Tex]x = -1[/Tex], [Tex]x = 0[/Tex], and [Tex]x = 1[/Tex]

  • [Tex]x = -2[/Tex], [Tex]x = 0[/Tex], and [Tex]x = 2[/Tex]

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Question 2

Which of the following functions represents a parabola that opens downward?

  • [Tex]f(x) = x^2 - 3x + 2[/Tex]

  • [Tex]f(x) = -2x^2 + 4x - 1[/Tex]

  • [Tex]f(x) = 3x^2 - 2x + 5[/Tex]

  • [Tex]f(x) = -4x^2 + 2x - 1[/Tex]

  • [Tex]f(x) = x^2 + 3x - 2[/Tex]

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Question 3

Consider the function [Tex]f(x) = \frac{x^2 - 4x}{x - 2}[/Tex]. What are the x-values where the function [Tex]f(x)[/Tex] is undefined?

  • [Tex]x = -2[/Tex]

  • [Tex]x = -4[/Tex]

  • [Tex]x = 2[/Tex]

  • [Tex]x = -2[/Tex] and [Tex]x = 2[/Tex]

  • [Tex]x = -4[/Tex] and [Tex]x = 2[/Tex]

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Question 4

Given the function [Tex]g(x) = x^3 - 3x + 2[/Tex], what is the maximum value of the function?

  • 1

  • 2

  • 3

  • 4

  • There is no maximum value

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Question 5

Consider the function [Tex]h(x) = \frac{1}{x^2 + 1}[/Tex]. What are the vertical asymptotes of the function [Tex]h(x)[/Tex]?

  • [Tex]x = -1[/Tex] and [Tex]x = 1[/Tex]

  • [Tex]x = -2[/Tex] and [Tex]x = 2[/Tex]

  • [Tex]x = -1[/Tex], [Tex]x = 0[/Tex], and [Tex]x = 1[/Tex]

  • [Tex]x = -2[/Tex], [Tex]x = 0[/Tex], and [Tex]x = 2[/Tex]

  • [Tex]x = -1[/Tex] and [Tex]x = 0[/Tex]

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Question 6

Which of the following equations has no real solutions?

  • [Tex]x^2 - 2x + 2 = 0[/Tex]

  • [Tex]x^2 - 4x + 4 = 0[/Tex]

  • [Tex]x^2 + 3x + 2 = 0[/Tex]

  • [Tex]x^2 + 4x + 5 = 0[/Tex]

  • [Tex]x^2 - 6x + 13 = 0[/Tex]

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Question 7

What is the solution to the equation [Tex]3x^2 - 6x - 9 = 0[/Tex]?

  • [Tex]x = -1[/Tex] or [Tex]x = 3[/Tex]

  • [Tex]x = -1[/Tex] or [Tex]x = 2[/Tex]

  • [Tex]x = -3[/Tex] or [Tex]x = 2[/Tex]

  • [Tex]x = -3[/Tex] or [Tex]x = 3[/Tex]

  • [Tex]x = -2[/Tex] or [Tex]x = 3[/Tex]

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Question 8

Which of the following expressions is equivalent to [Tex]\frac{{x^2 + 2x - 8}}{{x + 4}}[/Tex]?

  • [Tex]x - 2[/Tex]

  • [Tex]x + 2[/Tex]

  • [Tex]x - 2x + 16[/Tex]

  • [Tex]x - 2x + 4[/Tex]

  • [Tex]x - 2x - 16[/Tex]

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Question 9

Which of the following expressions is equivalent to [Tex]3x^2 + 6x + 3[/Tex]?

  • [Tex]3(x^2 + 2x + 1)[/Tex]

  • [Tex]3(x^2 + 3x + 1)[/Tex]

  • [Tex]3(x^2 + 2x)[/Tex]

  • [Tex]3(x^2 + 3x)[/Tex]

  • [Tex]3(x^2 + x + 1)[/Tex]

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Question 10

Which of the following expressions is equivalent to [Tex]4x^2 - 16[/Tex]?

  • [Tex]2(x^2 - 4)[/Tex]

  • [Tex]2(x^2 - 8)[/Tex]

  • [Tex]4(x^2 - 4)[/Tex]

  • [Tex]4(x^2 - 8)[/Tex]

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