Digital SAT chapter 1: Math · Algebra practice questions with answers

By Team Megalecture · Updated 4 Nov 2026

119 exam-style questions on Math · Algebra, 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.

119 questions · 5 topics · 10 per test

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What chapter 1 covers

Ten Math · Algebra questions with answers

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

1. A student sells handmade cards for $3.50 each. Each card costs $0.80 in materials, and the student also paid a one-time $60 fee for a booth. What is the minimum number of cards the student must sell to earn a profit of at least $200?

  1. A
    75
  2. B
    96
  3. C
    97
  4. D
    130
Show answer

Answer: C. Profit is 3.5c − 0.8c − 60 ≥ 200, so 2.7c ≥ 260 and c ≥ 96.3. The minimum whole number is 97. Choosing 96 rounds down and 75 ignores the cost of materials.

2. A caterer can spend at most $600 on sandwiches that cost $6 each and salads that cost $8 each. She needs at least 80 items in all. Which system of inequalities represents this situation, where s is the number of sandwiches and d is the number of salads?

  1. A
    6s + 8d ≥ 600 and s + d ≤ 80
  2. B
    6s + 8d ≤ 600 and s + d ≤ 80
  3. C
    8s + 6d ≤ 600 and s + d ≥ 80
  4. D
    6s + 8d ≤ 600 and s + d ≥ 80
Show answer

Answer: D. "At most $600" means the cost 6s + 8d is less than or equal to 600, and "at least 80 items" means s + d ≥ 80. The system with both signs flipped reverses both conditions.

3. 4(x − 2) = 4x − 8
How many solutions does the given equation have?

  1. A
    Exactly one
  2. B
    Exactly two
  3. C
    Infinitely many
  4. D
    Zero
Show answer

Answer: C. Distributing gives 4x − 8 = 4x − 8, which is true for every value of x, so the equation has infinitely many solutions.

4. ax + 2y = 14
3x − by = −3
In the given system of equations, a and b are constants. If the solution to the system is (2, 3), what is the value of a + b?

  1. A
    1
  2. B
    4
  3. C
    7
  4. D
    11
Show answer

Answer: C. Substitute x = 2 and y = 3. The first equation gives 2a + 6 = 14, so a = 4. The second gives 6 − 3b = −3, so b = 3. Then a + b = 7. A sign slip in the second equation gives b = −3 and the value 1.

5. kx + 4y = 10
x + ky = 5
In the given system of equations, k is a constant. For which value of k does the system have no solution?

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

Answer: B. Equal slopes require k2 = 4, so k = 2 or k = −2. For k = 2 the first equation is 2x + 4y = 10, which simplifies to x + 2y = 5, the same line as the second, so there are infinitely many solutions. For k = −2 it simplifies to x − 2y = −5, parallel to x − 2y = 5, so there is no solution.

6. cx + 6 = 2x + 3c
In the given equation, c is a constant. For which value of c does the equation have infinitely many solutions?

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

Answer: A. Rewrite the equation as (c − 2)x = 3(c − 2). If c = 2, both sides are 0 for every x, so there are infinitely many solutions. For any other c, dividing by c − 2 gives the single solution x = 3.

7. Starting on day 0, the number of copies of a novel in a warehouse decreased at a constant rate each day. On day 5 there were 410 copies, and on day 12 there were 270 copies. How many copies were in the warehouse on day 0?

  1. A
    310
  2. B
    430
  3. C
    510
  4. D
    550
Show answer

Answer: C. The number fell by 140 copies in 7 days, which is 20 copies per day. Going back 5 days from day 5 adds 5 × 20 = 100 copies, giving 510. Subtracting the 100 instead gives 310.

8. Which of the following values of x satisfies the inequality 5x − 3 > 17?

  1. A
    2
  2. B
    3
  3. C
    4
  4. D
    5
Show answer

Answer: D. Adding 3 and dividing by 5 gives x > 4, and 5 is the only choice greater than 4. The value 4 makes 5x − 3 equal to 17, which is not greater than 17.

9. 3x + y = 17
x − y = 3
The solution to the given system of equations is (x, y). What is the value of x?

  1. A
    2
  2. B
    5
  3. C
    7
  4. D
    20
Show answer

Answer: B. Adding the equations eliminates y: 4x = 20, so x = 5 (and y = 2). The value 20 is 4x, and 2 is the value of y.

10. Line ℓ is parallel to the line y = −(2/3)x + 7 and passes through the point (6, 1). The y-intercept of line ℓ is (0, b). What is the value of b?

  1. A
    −8
  2. B
    −3
  3. C
    5
  4. D
    7
Show answer

Answer: C. Parallel lines have equal slopes, so ℓ is y = −(2/3)x + b. Substituting (6, 1) gives 1 = −4 + b, so b = 5. The value −8 comes from using the perpendicular slope 3/2.

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Ways to practise this chapter

Math · Algebra: questions students ask

How many Math · Algebra practice questions are there?

119, each with the answer and a short explanation, across 5 topics: Linear equations in one variable, Linear functions, Linear equations in two variables, Systems of two linear equations, Linear inequalities. Every chapter test draws ten of them, so you can take it many times.

Is the Digital SAT chapter 1 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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