Digital SAT chapter 2: Math · Advanced Math practice questions with answers

By Team Megalecture · Updated 4 Nov 2026

103 exam-style questions on Math · Advanced Math, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

103 questions · 3 topics · 10 per test

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What chapter 2 covers

Ten Math · Advanced Math questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. The graph of y = x2 in the xy-plane is shifted 3 units to the right and 2 units down. Which equation represents the resulting graph?

  1. A
    y = (x + 3)2 − 2
  2. B
    y = (x − 2)2 − 3
  3. C
    y = (x − 3)2 − 2
  4. D
    y = (x − 3)2 + 2
Show answer

Answer: C. A shift of 3 units right replaces x with x − 3, and a shift of 2 units down subtracts 2 from the output: y = (x − 3)2 − 2. Using x + 3 would shift the graph to the left.

2. f(x) = 3x2 + kx − 4
In the given function, k is a constant and f(2) = 10. What is the value of f(−1)?

  1. A
    −2
  2. B
    0
  3. C
    2
  4. D
    6
Show answer

Answer: A. f(2) = 12 + 2k − 4 = 10 gives k = 1. Then f(−1) = 3(1) + (1)(−1) − 4 = −2. The value 0 is f(1), and 6 is f(−2).

3. f(x) = x2 + 4x − 12
Which of the following is an equivalent form of the given function that displays the x-intercepts of the graph of y = f(x) in the xy-plane as constants or coefficients?

  1. A
    f(x) = (x + 6)(x − 2)
  2. B
    f(x) = (x + 2)2 − 16
  3. C
    f(x) = x2 + 4(x − 3)
  4. D
    f(x) = (x − 6)(x + 2)
Show answer

Answer: A. In factored form the x-intercepts can be read from the factors: x = −6 and x = 2. The form (x + 2)2 − 16 is equivalent but displays the vertex instead, and (x − 6)(x + 2) is not equivalent to f(x), since its x-term is −4x.

4. y = x2 + c
y = 2x
In the given system of equations, c is a constant. The system has exactly one distinct real solution. What is the value of c?

  1. A
    −1
  2. B
    1
  3. C
    2
  4. D
    4
Show answer

Answer: B. Substituting gives x2 + c = 2x, or x2 − 2x + c = 0. Exactly one solution means the discriminant is 0: (−2)2 − 4c = 0, so c = 1. The line is then tangent to the parabola at (1, 2).

5. The expression (3x − 2)(x2 + 4x − 1) is equivalent to 3x3 + bx2 + cx + 2, where b and c are constants. What is the value of b + c?

  1. A
    −11
  2. B
    −1
  3. C
    10
  4. D
    21
Show answer

Answer: B. Expanding gives 3x3 + 12x2 − 3x − 2x2 − 8x + 2 = 3x3 + 10x2 − 11x + 2. So b = 10, c = −11, and b + c = −1. The values 10 and −11 are single coefficients.

6. Which of the following is a factor of x2 − 3x − 28?

  1. A
    x − 7
  2. B
    x + 7
  3. C
    x − 4
  4. D
    x − 28
Show answer

Answer: A. Find two numbers with product −28 and sum −3: −7 and 4. So x2 − 3x − 28 = (x − 7)(x + 4), and x − 7 is a factor. The choices x + 7 and x − 4 use the right numbers with the wrong signs.

7. f(x) = (x + 8)/2
For the given function f, if f(a) = 10, what is the value of a?

  1. A
    6
  2. B
    9
  3. C
    12
  4. D
    28
Show answer

Answer: C. Set (a + 8)/2 = 10. Then a + 8 = 20, so a = 12. The value 9 is f(10), which answers a different question.

8. The expression x2 + 10x + 18 is written in the equivalent form (x + h)2 + k, where h and k are constants. What is the value of k?

  1. A
    −25
  2. B
    −7
  3. C
    7
  4. D
    43
Show answer

Answer: B. (x + 5)2 = x2 + 10x + 25, so x2 + 10x + 18 = (x + 5)2 − 7 and k = −7. The value 43 comes from adding 25 instead of subtracting it.

9. For x > 0, which expression is equivalent to (16x8)3/4?

  1. A
    8x6
  2. B
    12x6
  3. C
    64x6
  4. D
    8x32/3
Show answer

Answer: A. 163/4 = (4√16)3 = 23 = 8 and (x8)3/4 = x6, so the expression equals 8x6. Multiplying 16 by 3/4 gives 12, which treats the exponent as a multiplier.

10. f(x) = 2x2 − 8
The function g is defined by g(x) = f(2x). What are the x-coordinates of the x-intercepts of the graph of y = g(x) in the xy-plane?

  1. A
    −2 and 2
  2. B
    −4 and 4
  3. C
    −√2 and √2
  4. D
    −1 and 1
Show answer

Answer: D. g(x) = 2(2x)2 − 8 = 8x2 − 8, which is 0 when x2 = 1, so x = −1 and x = 1. Replacing x with 2x squeezes the graph toward the y-axis, halving the zeros ±2 of f; ±4 moves them the wrong way.

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Ways to practise this chapter

Math · Advanced Math: questions students ask

How many Math · Advanced Math practice questions are there?

103, each with the answer and a short explanation, across 3 topics: Equivalent expressions, Nonlinear equations and systems, Nonlinear functions. Every chapter test draws ten of them, so you can take it many times.

Is the Digital SAT chapter 2 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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