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ACT Math: Algebra (Drill 1)

Drill 1 · Math · Algebra

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About This Drill

ACT Math: Algebra (Drill 1) is a Math practice drill covering Algebra. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

ACT Algebra questions ask you to solve and interpret linear equations, factor algebraic expressions, solve systems of two equations, simplify rational expressions, and work with exponential relationships. This drill covers the full range of Algebra skills tested on the ACT.

Questions & Explanations

Question 1. If 4x − 7 = 21, what is the value of x?

  • A) 3.5
  • B) 5
  • C) 7 ✓
  • D) 9

Explanation: Add 7 to both sides: 4x = 28. Divide by 4: x = 7. Choice A results from dividing 21 by 4 before adding 7: 21 ÷ 4 = 5.25, rounded to 3.5. Choice B results from the same error with a different rounding: 21 ÷ 4 ≈ 5. Choice D results from adding 7 to both sides twice: treating the equation as 4x = 21 + 7 + 7 = 35, then dividing to get about 9. The key step is adding 7 first, then dividing.

Question 2. Which of the following is equivalent to x2 + 3x − 28?

  • A) (x + 4)(x − 7)
  • B) (x − 4)(x + 7) ✓
  • C) (x + 2)(x − 14)
  • D) (x − 2)(x + 14)

Explanation: To factor x2 + 3x − 28, find two numbers that multiply to −28 and add to +3. Those numbers are −4 and +7: (−4)(7) = −28 and −4 + 7 = 3. So the factored form is (x − 4)(x + 7). Choice A reverses the signs: (x + 4)(x − 7) gives a middle term of −3x, not +3x. Choices C and D use factor pairs of 28 (2 and 14) that do not sum to 3.

Question 3. What is the value of y in the solution to the system of equations below?
3x + 2y = 16
x − y = 2

  • A) 2 ✓
  • B) 4
  • C) 6
  • D) 8

Explanation: From the second equation, x = y + 2. Substitute into the first: 3(y + 2) + 2y = 16 → 3y + 6 + 2y = 16 → 5y = 10 → y = 2. Then x = 2 + 2 = 4. Choice B is the value of x, not y, a common mix-up. Choice C results from an arithmetic error when combining like terms: treating 3y + 2y as 4y. Choice D results from forgetting to substitute and solving 2y = 16 directly.

Question 4. Which of the following is equivalent to (x2 − 9) / (x + 3), for x ≠ −3?

  • A) x − 3 ✓
  • B) x + 3
  • C) x − 9
  • D) x2 − 3

Explanation: Factor the numerator as a difference of squares: x2 − 9 = (x + 3)(x − 3). Then cancel the common factor: (x + 3)(x − 3) / (x + 3) = x − 3. Choice B results from canceling incorrectly and keeping (x + 3) rather than (x − 3). Choice C results from subtracting 3 from x2 ÷ (x + 3) without factoring first. Choice D results from failing to cancel and simply subtracting 3 from the numerator's exponent.

Question 5. If 2x + 3 = 8x − 1, what is the value of x?

  • A) 2
  • B) 3
  • C) 4
  • D) 6 ✓

Explanation: Rewrite both sides with the same base. Since 8 = 23, rewrite the right side: 8x − 1 = (23)x − 1 = 23x − 3. Set exponents equal: x + 3 = 3x − 3. Solve: 6 = 2x, so x = 3. Check: 26 = 64 and 82 = 64 ✓. Choice A results from an arithmetic error when solving the linear equation, yielding x = 2. Choice C results from adding instead of subtracting when isolating x, yielding 4x = 6. Choice D results from solving x + 3 = 3x − 3 as −x = −6 and dropping the negative sign.