Praxis Core Math Practice Test: Algebra and Functions
- Algebra and Functions
- 10 questions
- 14 minutes
Ten algebra questions like those on the Praxis Core Mathematics test. Tip: after you solve an equation, put your answer back into the original equation to check it.
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.
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Question 1
Solve for x: 3x − 7 = 2x + 5
Correct answer: C
Subtract 2x from both sides and add 7: x = 12. Check: 36 − 7 = 29 and 24 + 5 = 29.
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Question 2
Solve for x: 4(x − 2) = 2x + 6
Correct answer: D
Distribute: 4x − 8 = 2x + 6, so 2x = 14 and x = 7. Multiplying only the x by 4 (4x − 2) gives the wrong answer 4.
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Question 3
If f(x) = 2x2 − 3x, what is f(−2)?
Correct answer: A
f(−2) = 2(4) − 3(−2) = 8 + 6 = 14. Forgetting that −3 × (−2) is positive gives 8 − 6 = 2.
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Question 4
A taxi charges a $3 pickup fee plus $2 for each mile. Which equation gives the cost C, in dollars, of a ride of m miles?
Correct answer: B
The $3 is charged once, and $2 is charged for each of the m miles. Switching the numbers would charge $3 per mile.
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Question 5
What is the slope of the line through the points (1, 4) and (5, 12)?
Correct answer: D
Slope = (12 − 4) ÷ (5 − 1) = 8 ÷ 4 = 2. Dividing the change in x by the change in y gives 12.
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Question 6
Which inequality is equivalent to −2x + 5 > 11?
Correct answer: C
Subtract 5: −2x > 6. Divide by −2 and reverse the sign: x < −3. Forgetting to reverse the sign gives x > −3.
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Question 7
If x + y = 10 and x − y = 4, what is the value of y?
Correct answer: B
Adding the equations gives 2x = 14, so x = 7, and then y = 10 − 7 = 3. The answer 7 is the value of x.
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Question 8
The sum of two consecutive integers is 51. What is the larger integer?
Correct answer: A
Let the integers be n and n + 1: 2n + 1 = 51, so n = 25 and the larger one is 26. The answer 25 is the smaller integer.
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Question 9
The pattern 5, 9, 13, 17, … continues by adding the same number each time. What is the 20th term?
Correct answer: C
The first term is 5 and the difference is 4, so the 20th term is 5 + 19 × 4 = 81. Using 20 × 4 instead of 19 × 4 gives 85.
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Question 10
The table shows values of x and y:
x: 1, 2, 3, 4
y: 5, 8, 11, 14
Which equation fits all the values in the table?Correct answer: B
y rises by 3 each time x rises by 1, so the slope is 3, and 3(1) + 2 = 5. y = x + 4 works for the first pair only.
Questions you leave blank are not counted as wrong.
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