Praxis Middle School Mathematics Practice Test
Middle school mathematics practice covers numerical operations, algebraic relationships, geometry, and data reasoning. Sample questions involve evaluating functions, extending sequences, calculating discounts, and working with probability and averages. These tasks call for accurate computation as well as recognizing which mathematical relationship or operation fits a situation.
Exam overview
About the Praxis Middle School Mathematics Exam
Mathematical problem solving involves translating words into expressions, selecting operations, and checking whether results make sense in context. Algebraic work includes substituting values into functions and applying rules to generate sequence terms. Number skills include operations with decimals, exponents, and factors; proportional reasoning supports percent calculations such as finding a sale price. Geometry and measurement require interpreting figures and quantities, while statistics and probability involve summarizing data, comparing values, and describing outcomes. For example, a range remains unchanged when the same amount is added to every data value, whereas a mean requires combining observations and dividing by their count. In classroom settings, these concepts support explaining strategies, identifying computational errors, and connecting numerical procedures to visual or real-world representations.
Sample Practice Questions
Review a selection from this exam's published US Practice Tests practice bank.
A function is defined by f(x) = x² − 3x. What is f(5) − f(2)?
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Correct answer: Cf(5) = 25 − 15 = 10, and f(2) = 4 − 6 = −2. Therefore f(5) − f(2) = 10 − (−2) = 12.
A sequence starts at 3 and each term is obtained by multiplying the previous term by 2, then subtracting 1. What is the fourth term?
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Correct answer: CStarting with 3, the next terms are 3 × 2 − 1 = 5, then 5 × 2 − 1 = 9, then 9 × 2 − 1 = 17. Thus the fourth term is 17.
A store reduces the price of a $64 backpack by 25%. What is the sale price before tax?
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Correct answer: CA 25% reduction is one quarter of $64, which is $16. Subtract the reduction: $64 − $16 = $48.
What is the value of 2.5 × 0.4?
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Correct answer: BSince 25 × 4 = 100 and there are two decimal places total in the factors, 2.5 × 0.4 = 1.00, or 1.
A fair six-sided number cube is rolled once. What is the probability of rolling a number greater than 4?
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Correct answer: BThe outcomes greater than 4 are 5 and 6, so there are 2 favorable outcomes out of 6 equally likely outcomes. The probability is 2/6 = 1/3.
What is the value of 4³ − 2⁴?
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Correct answer: BEvaluate the powers first: 4³ = 64 and 2⁴ = 16. Then subtract: 64 − 16 = 48.
A class has 18 students. Each student chooses one of 4 different book titles, and all titles are selected by the class. What is the average number of students per title?
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Correct answer: AThe average is the total number of students divided by the number of titles: 18 ÷ 4 = 4.5 students per title.
How to use this practice test
The free practice session draws up to 20 random questions from the 50-question bank. Work through each item by identifying the relevant concept before calculating, then use the displayed results to spot areas for further practice, such as percentages, functions, or data measures.
Preparation tips
- For function questions, substitute the input carefully, preserve parentheses, and evaluate each function value before finding a difference.
- Practice percent-change problems by converting the percent to a decimal and distinguishing the discount amount from the final price.
- For sequences, write each term in order and apply the stated rule to the previous term exactly once per step.
- Compare mean, range, and probability tasks: identify the required data operation or favorable outcomes before calculating.
- Check decimal and exponent calculations separately; use estimation to catch misplaced decimal points or incorrect powers.