ACT Math Practice Test: Pre-Algebra and Elementary Algebra
- Pre-Algebra and Elementary Algebra
- 12 questions
- 14 minutes
These 12 questions practice the pre-algebra and elementary algebra skills tested on the ACT: order of operations, fractions, percents, proportions, basic statistics, linear equations and inequalities, and simple polynomials. On the enhanced ACT, the Math section has 45 questions in 50 minutes with four answer choices each, and a calculator is allowed, so plan on a little over a minute per question.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
Your result
- 0 correct
- 0 wrong
- 0 blank
-
Question 1
What is the value of 18 − 3(4 − 6)2 ÷ 2?
Correct answer: A
Work inside the parentheses first: (4 − 6)2 = (−2)2 = 4. Then 3 × 4 ÷ 2 = 6 and 18 − 6 = 12. Subtracting 18 − 3 before multiplying gives 30, and treating (−2)2 as −4 gives 24.
-
Question 2
What is the value of 23 + 56 ÷ 14?
Correct answer: C
Division comes before addition: 56 ÷ 14 = 56 × 4 = 103, and 23 + 103 = 4. Adding first gives 32 ÷ 14 = 6, and multiplying by 14 instead of dividing gives 78.
-
Question 3
A pair of headphones regularly priced at $64 is on sale for 25% off. A sales tax of 6% is then added to the sale price. What is the total cost of the headphones?
Correct answer: B
The sale price is 0.75 × $64 = $48.00, and adding 6% tax gives 1.06 × $48.00 = $50.88. The choice $51.84 combines the two percents into one 19% discount (the same as taxing the original price), and $48.00 leaves out the tax.
-
Question 4
On a map, 1.5 inches represents 40 miles. Two towns are 6.3 inches apart on the map. How many miles apart are the towns?
Correct answer: B
The map distance contains 6.3 ÷ 1.5 = 4.2 units of 1.5 inches, so the actual distance is 4.2 × 40 = 168 miles. The choice 252 treats each inch as 40 miles, and 26.7 is only the number of miles per inch.
-
Question 5
The numbers of minutes that eight students spent on a homework assignment were 15, 8, 22, 11, 8, 19, 13 and 26. What is the median of these times?
Correct answer: D
In order, the times are 8, 8, 11, 13, 15, 19, 22, 26. With an even number of values, the median is the mean of the two middle values: (13 + 15) ÷ 2 = 14. The choice 9.5 averages the two middle numbers of the unsorted list, and 8 is the mode.
-
Question 6
What value of x is the solution of the equation 5 − 2(x − 3) = 3x − 9?
Correct answer: C
Distributing gives 5 − 2x + 6 = 3x − 9, so 11 − 2x = 3x − 9, 20 = 5x and x = 4. Writing −2(x − 3) as −2x − 6 leads to 85, and 20 is the value of 5x, not x.
-
Question 7
If a = −3 and b = 2, what is the value of a2b − 2ab2?
Correct answer: D
Here a2b = 9 × 2 = 18 and 2ab2 = 2(−3)(4) = −24, so the value is 18 − (−24) = 42. Forgetting that subtracting −24 means adding 24 gives −6, and squaring −3 as −9 gives 6.
-
Question 8
Which of the following is the solution set of the inequality 7 − 4x ≤ 19?
Correct answer: B
Subtracting 7 from both sides gives −4x ≤ 12. Dividing by a negative number reverses the inequality sign, so x ≥ −3. The answer x ≤ −3 divides correctly but forgets to reverse the sign.
-
Question 9
Which expression is equivalent to (3x2y)(−2xy3)?
Correct answer: A
Multiply the coefficients, 3 × (−2) = −6, and add the exponents of matching variables: x2 · x = x3 and y · y3 = y4. The expression −6x2y3 multiplies the exponents instead of adding them.
-
Question 10
Which of the following is a factor of x2 − 5x − 24?
Correct answer: A
Look for two numbers with a product of −24 and a sum of −5: they are −8 and 3, so x2 − 5x − 24 = (x − 8)(x + 3). The binomials x + 8 and x − 3 multiply to x2 + 5x − 24, which has the wrong middle term.
-
Question 11
The sum of three consecutive odd integers is 81. What is the greatest of the three integers?
Correct answer: D
Write the integers as n, n + 2 and n + 4. Then 3n + 6 = 81, so n = 25 and the integers are 25, 27 and 29. The choice 27 is the middle integer, and 28 comes from using consecutive integers (26, 27, 28) instead of consecutive odd integers.
-
Question 12
Which of the following is equal to 4.8 × 1071.6 × 10−3?
Correct answer: C
Divide the decimal parts, 4.8 ÷ 1.6 = 3.0, and subtract the exponents: 7 − (−3) = 10. Subtracting 3 instead of −3 gives 3.0 × 104, and 7.68 × 104 multiplies the two numbers instead of dividing them.
Questions you leave blank are not counted as wrong.
More Math tests
MathACT Math Practice Test: Intermediate Algebra and FunctionsIntermediate Algebra and Functions12 questions14 min MathACT Math Practice Test: Geometry and TrigonometryGeometry and Trigonometry12 questions14 minMathACT Math Practice Test: Mixed Review (20 Questions)Mixed Review: All Math Topics20 questions22 minMathACT Math Practice Test: Number, Statistics and ProbabilityNumber, Statistics and Probability15 questions17 minMathACT Math Practice Test: Coordinate GeometryCoordinate Geometry10 questions12 minMathACT Math Practice Test: Ratios, Rates and Percent Word ProblemsRatios, Rates and Percent Word Problems10 questions12 minMathACT Math Practice Test: Exponents, Radicals and PolynomialsExponents, Radicals and Polynomials10 questions12 min