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Praxis Middle School Math study materials
Praxis Middle School Math study resources

Praxis Middle School Math practice questions

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Question 1Numbers and Operations

What is the value of -7 + 12 - 5?

  1. -10
  2. 0 Correct answer.
  3. 10
  4. -24

Explanation

Work from left to right: -7 + 12 = 5, and then 5 - 5 = 0. Subtracting a positive number is the same as adding its opposite, so the final step moves 5 units left from 5.

Question 2Numbers and Operations

What is the value of |-15| - |6|?

  1. 21
  2. 9 Correct answer.
  3. -9
  4. -21

Explanation

Absolute value gives the distance from zero, so |-15| = 15 and |6| = 6. Subtracting gives 15 - 6 = 9.

Question 3Numbers and Operations

What is the value of 20 - 2 x 3^2 + 4?

  1. 42
  2. 2
  3. -12
  4. 6 Correct answer.

Explanation

Exponents come first: 3^2 = 9. Then multiply: 2 x 9 = 18, so the expression is 20 - 18 + 4, which equals 6.

Question 4Numbers and Operations

Which fraction is 18/24 written in simplest form?

  1. 5/6
  2. 4/5
  3. 2/3
  4. 3/4 Correct answer.

Explanation

The greatest common factor of 18 and 24 is 6. Dividing numerator and denominator by 6 gives 18/6 = 3 and 24/6 = 4, so the simplest form is 3/4.

Question 5Numbers and Operations

In the number 4.072, in which place value is the digit 7?

  1. tenths
  2. hundredths Correct answer.
  3. thousandths
  4. ones

Explanation

Reading to the right of the decimal point, the first digit is tenths, the second is hundredths, and the third is thousandths. In 4.072 the 0 is tenths, the 7 is hundredths, and the 2 is thousandths.

Question 6Numbers and Operations

What is the value of the square root of 144?

  1. 72
  2. 12 Correct answer.
  3. 14
  4. 24

Explanation

A square root is a number that gives the radicand when multiplied by itself. Since 12 x 12 = 144, the square root of 144 is 12.

Question 7Numbers and Operations

Which of these numbers is divisible by 3?

  1. 415
  2. 721
  3. 834 Correct answer.
  4. 220

Explanation

A whole number is divisible by 3 exactly when the sum of its digits is a multiple of 3. For 834 the digit sum is 8 + 3 + 4 = 15, and 15 is a multiple of 3, so 834 is divisible by 3.

Question 8Numbers and Operations

What is the sum 3.6 + 0.47?

  1. 3.107
  2. 3.93
  3. 4.7
  4. 4.07 Correct answer.

Explanation

Line up the decimal points and write 3.6 as 3.60. Adding 3.60 + 0.47 gives 4.07, with hundredths 0 + 7, tenths 6 + 4 = 10 (write 0, carry 1), and ones 3 + 0 + 1 = 4.

Question 9Numbers and Operations

What is the greatest common factor of 36 and 48?

  1. 12 Correct answer.
  2. 144
  3. 6
  4. 4

Explanation

Both numbers factor as 36 = 2^2 x 3^2 and 48 = 2^4 x 3. Taking the lowest power of each shared prime gives 2^2 x 3 = 12.

Question 10Numbers and Operations

What is the least common multiple of 8 and 12?

  1. 24 Correct answer.
  2. 48
  3. 4
  4. 96

Explanation

Multiples of 12 are 12, 24, 36, ... and multiples of 8 are 8, 16, 24, ... The first value appearing in both lists is 24, so the least common multiple is 24.

Question 11Numbers and Operations

What is the value of 3/4 divided by 2/5?

  1. 3/10
  2. 15/8 Correct answer.
  3. 8/15
  4. 5/6

Explanation

Dividing by a fraction is the same as multiplying by its reciprocal, so 3/4 divided by 2/5 equals 3/4 x 5/2. Multiplying across gives 15/8.

Question 12Numbers and Operations

What is 15% of 80?

  1. 8
  2. 15
  3. 4
  4. 12 Correct answer.

Explanation

Convert the percent to a decimal and multiply: 0.15 x 80 = 12. Equivalently, 10% of 80 is 8 and 5% of 80 is 4, and 8 + 4 = 12.

Question 13Numbers and Operations

Which number is 0.00042 written in scientific notation?

  1. 4.2 x 10^-5
  2. 4.2 x 10^-4 Correct answer.
  3. 4.2 x 10^4
  4. 4.2 x 10^-3

Explanation

Scientific notation writes a number as a factor between 1 and 10 times a power of 10. Moving the decimal point in 0.00042 four places to the right gives 4.2, so the exponent is -4.

Question 14Numbers and Operations

Which expression is equal to 2^3 x 2^4?

  1. 4^12
  2. 4^7
  3. 2^12
  4. 2^7 Correct answer.

Explanation

When multiplying powers with the same base, keep the base and add the exponents: 2^3 x 2^4 = 2^(3+4) = 2^7. Checking, 8 x 16 = 128 = 2^7.

Question 15Numbers and Operations

Which of these numbers is irrational?

  1. -5
  2. 0.75
  3. The square root of 9
  4. The square root of 7 Correct answer.

Explanation

An irrational number cannot be written as a fraction of two integers. The square root of 7 is not a perfect square and its decimal form never terminates or repeats, so it is irrational.

Question 16Numbers and Operations

A 12-ounce box of cereal costs $3.60. What is the cost per ounce?

  1. $0.30 Correct answer.
  2. $0.25
  3. $3.00
  4. $0.36

Explanation

A unit rate is found by dividing the total cost by the number of ounces: 3.60 divided by 12 = 0.30. So the cereal costs $0.30 per ounce.

Question 17Numbers and Operations

Which of these numbers has the greatest value: -2/3, -0.7, -0.65, -5/8?

  1. -2/3
  2. -0.7
  3. -0.65
  4. -5/8 Correct answer.

Explanation

Write each value as a decimal: -2/3 is about -0.667, -5/8 = -0.625, and the others are -0.7 and -0.65. Among negatives, the one closest to zero is greatest, which is -0.625, or -5/8.

Question 18Numbers and Operations

Which expression is equivalent to 6(2x - 5)?

  1. 12x + 30
  2. 12x - 30 Correct answer.
  3. 2x - 30
  4. 12x - 5

Explanation

The distributive property multiplies each term inside the parentheses by 6: 6 x 2x = 12x and 6 x (-5) = -30. The result is 12x - 30.

Question 19Numbers and Operations

What is the prime factorization of 84?

  1. 2^2 x 3 x 7 Correct answer.
  2. 4 x 3 x 7
  3. 2^2 x 7^2
  4. 2 x 3^2 x 7

Explanation

Divide by primes until only primes remain: 84 = 2 x 42 = 2 x 2 x 21 = 2 x 2 x 3 x 7. Grouping the repeated 2s gives 2^2 x 3 x 7.

Question 20Numbers and Operations

A submarine is at a depth of -85 meters. It rises 40 meters and then dives 25 meters. What is its final depth in meters?

  1. -70 Correct answer.
  2. -100
  3. -150
  4. -45

Explanation

Rising means adding to the position and diving means subtracting. Starting at -85, the rise gives -85 + 40 = -45, and the dive gives -45 - 25 = -70 meters.

Question 21Numbers and Operations

What is the value of (2/3)^-2?

  1. 9/4 Correct answer.
  2. 4/9
  3. -9/4
  4. -4/9

Explanation

A negative exponent takes the reciprocal of the base: (2/3)^-2 = (3/2)^2. Squaring gives 9/4.

Question 22Numbers and Operations

Which fraction equals the repeating decimal 0.363636...?

  1. 4/11 Correct answer.
  2. 2/5
  3. 11/4
  4. 36/100

Explanation

Let x = 0.363636... Then 100x = 36.363636..., and subtracting gives 99x = 36. So x = 36/99, which simplifies by a factor of 9 to 4/11.

Question 23Numbers and Operations

What is the value of (3/4 - 1/2) divided by 1/8?

  1. 8
  2. 3/8
  3. 1/32
  4. 2 Correct answer.

Explanation

First subtract inside the parentheses: 3/4 - 1/2 = 3/4 - 2/4 = 1/4. Then divide by 1/8 by multiplying by its reciprocal: 1/4 x 8 = 2.

Question 24Numbers and Operations

What is the product (3 x 10^5)(4 x 10^-8) expressed in scientific notation?

  1. 1.2 x 10^-2 Correct answer.
  2. 1.2 x 10^2
  3. 1.2 x 10^-4
  4. 1.2 x 10^-3

Explanation

Multiply the coefficients and add the exponents: 3 x 4 = 12 and 5 + (-8) = -3, giving 12 x 10^-3. Rewriting 12 as 1.2 x 10^1 and combining exponents gives 1.2 x 10^-2.

Question 25Numbers and Operations

A store raises the price of an item by 20% and later lowers the new price by 20%. Compared with the original price, what is the overall change?

  1. A 4% decrease Correct answer.
  2. No change
  3. A 4% increase
  4. A 20% decrease

Explanation

Multiply the two multipliers: 1.20 x 0.80 = 0.96. The final price is 96% of the original, which is a 4% decrease.

Question 26Numbers and Operations

What is the value of 8 − 3 × (2 + 1)?

  1. 9
  2. 17
  3. 15
  4. -1 Correct answer.

Explanation

The order of operations requires evaluating the parentheses first: 2 + 1 = 3. Multiplication comes before subtraction, so 3 × 3 = 9, and then 8 − 9 = -1.

Question 27Numbers and Operations

What is the value of |−7| + |3 − 9|?

  1. 1
  2. -13
  3. 13 Correct answer.
  4. 10

Explanation

Absolute value gives the distance from zero, so |−7| = 7. Simplify inside the second bars first: 3 − 9 = -6 and |−6| = 6, then add 7 + 6 = 13.

Question 28Numbers and Operations

Which decimal is equivalent to the fraction 5/8?

  1. 1.6
  2. 0.65
  3. 0.625 Correct answer.
  4. 0.58

Explanation

A fraction equals its numerator divided by its denominator, so divide 5 by 8. Since 8 × 0.625 = 5, the decimal is 0.625.

Question 29Numbers and Operations

When 0.04672 is rounded to the nearest thousandth, what is the result?

  1. 0.0467
  2. 0.05
  3. 0.046
  4. 0.047 Correct answer.

Explanation

The thousandths digit is the third digit after the decimal point, which is 6 in 0.04672. The following digit is 7, so the thousandths digit rounds up from 6 to 7, giving 0.047.

Question 30Numbers and Operations

What is the value of 2/3 + 3/4 − 1/6?

  1. 17/12
  2. 5/4 Correct answer.
  3. 4/5
  4. 11/12

Explanation

Rewrite each fraction with the least common denominator 12: 8/12 + 9/12 − 2/12. Combining gives 15/12, which simplifies to 5/4.

Question 31Numbers and Operations

A recipe uses 2 1/4 cups of flour to make 12 cookies. At the same rate, how many cups of flour are needed for 20 cookies?

  1. 3 1/4
  2. 3 3/4 Correct answer.
  3. 2 3/4
  4. 4 1/4

Explanation

Set up the proportion (9/4)/12 = x/20 and solve for x. The unit rate is 3/16 cup per cookie, and 20 × 3/16 = 15/4, which is 3 3/4 cups.

Question 32Numbers and Operations

A jacket priced at $80 is discounted 25%, and then an additional 10% is taken off the sale price. What is the final price of the jacket?

  1. $56
  2. $60
  3. $52
  4. $54 Correct answer.

Explanation

The successive discounts multiply: 80 × 0.75 = $60 after the first discount, then 60 × 0.90 = $54. The combined effect is a 32.5% reduction, not a 35% reduction.

Question 33Numbers and Operations

Which expression has the same value as (2^3)^2 ÷ 2^4?

  1. 2
  2. 8
  3. 16
  4. 4 Correct answer.

Explanation

A power raised to a power multiplies exponents, so (2^3)^2 = 2^6. Dividing powers with the same base subtracts exponents: 2^6 ÷ 2^4 = 2^2 = 4.

Question 34Numbers and Operations

What is the value of 0.36 ÷ 0.004?

  1. 0.9
  2. 900
  3. 90 Correct answer.
  4. 9

Explanation

Multiply both numbers by 1000 to clear the decimals: 360 ÷ 4 = 90. Scaling both the dividend and divisor by the same power of ten leaves the quotient unchanged.

Question 35Numbers and Operations

Between which two consecutive integers does the square root of 50 lie?

  1. 8 and 9
  2. 7 and 8 Correct answer.
  3. 6 and 7
  4. 24 and 26

Explanation

Since 7^2 = 49 and 8^2 = 64, and 50 is between 49 and 64, the square root of 50 is between 7 and 8. It is just slightly greater than 7.

Question 36Numbers and Operations

What is 3.07 × 10^-4 written in standard decimal form?

  1. 30,700
  2. 0.0000307
  3. 0.000307 Correct answer.
  4. 0.00307

Explanation

A negative exponent of -4 moves the decimal point four places to the left. Moving the point in 3.07 four places left gives 0.000307.

Question 37Numbers and Operations

A number is increased by 12%, and the result is 56. What is the original number?

  1. 48
  2. 44
  3. 50 Correct answer.
  4. 52.5

Explanation

An increase of 12% means the new value is 1.12 times the original, so solve 1.12x = 56. Dividing gives x = 50, and checking: 50 × 1.12 = 56.

Question 38Numbers and Operations

What is the value of (3/4 + 5/6) ÷ 2/3?

  1. 19/18
  2. 8/19
  3. 19/12
  4. 19/8 Correct answer.

Explanation

First add inside the parentheses using the common denominator 12: 9/12 + 10/12 = 19/12. Dividing by 2/3 means multiplying by its reciprocal 3/2, so 19/12 × 3/2 = 57/24 = 19/8.

Question 39Numbers and Operations

What is the value of (−3)^2 − (−2)^3?

  1. 13
  2. -17
  3. 17 Correct answer.
  4. 1

Explanation

A negative number squared is positive, so (−3)^2 = 9. A negative number cubed is negative, so (−2)^3 = -8, and subtracting it gives 9 − (-8) = 9 + 8 = 17.

Question 40Numbers and Operations

A pipe fills 3/5 of a tank in 9 minutes. Working at the same constant rate, how long does it take to fill 2 identical tanks?

  1. 18 minutes
  2. 30 minutes Correct answer.
  3. 27 minutes
  4. 22.5 minutes

Explanation

Divide the time by the fraction of the tank filled to get the time for one full tank: 9 ÷ 3/5 = 9 × 5/3 = 15 minutes. Two tanks then take 2 × 15 = 30 minutes.

Question 41Algebra

Solve for x: 3x + 7 = 22

  1. 5 Correct answer.
  2. 15
  3. 29/3
  4. 3

Explanation

Undo the addition first by subtracting 7 from both sides, which gives 3x = 15. Then divide both sides by 3 to isolate x, giving x = 5. Checking the result: 3(5) + 7 = 22 is true.

Question 42Algebra

What is the slope of the line that passes through the points (2, 3) and (6, 11)?

  1. -2
  2. 8
  3. 2 Correct answer.
  4. 1/2

Explanation

Slope equals the change in y divided by the change in x: (11 - 3)/(6 - 2). This simplifies to 8/4, which is 2. The slope is positive because y increases as x increases.

Question 43Algebra

Evaluate the expression 2x² - 3x + 1 when x = -2.

  1. 23
  2. 15 Correct answer.
  3. 3
  4. 13

Explanation

Substitute -2 for every x, remembering that (-2)² = 4: 2(4) - 3(-2) + 1. This becomes 8 + 6 + 1, which equals 15. The product -3(-2) is positive 6, not -6.

Question 44Algebra

Which expression is equivalent to 4(2x - 3) - 5x?

  1. 3x - 3
  2. 13x - 12
  3. 3x + 12
  4. 3x - 12 Correct answer.

Explanation

Distributing the 4 gives 8x - 12, so the expression becomes 8x - 12 - 5x. Combining like terms gives 3x - 12. Only the x-terms combine; the constant stays as -12.

Question 45Algebra

If f(x) = 3x - 5, what is the value of f(-2)?

  1. -1
  2. 1
  3. 11
  4. -11 Correct answer.

Explanation

Function notation means substitute -2 wherever x appears, giving 3(-2) - 5. This equals -6 - 5, which is -11. The negative input is preserved throughout the computation.

Question 46Algebra

What is the y-intercept of the graph of 2x + 3y = 12?

  1. -2/3
  2. 4 Correct answer.
  3. 6
  4. 12

Explanation

The y-intercept is found by setting x = 0, which gives 3y = 12, so y = 4. The intercept is the point (0, 4). Substituting x = 0 is the standard method for finding where a graph crosses the y-axis.

Question 47Algebra

Evaluate -3² + (-2)³.

  1. -17 Correct answer.
  2. 1
  3. 17
  4. -1

Explanation

In -3² the exponent applies only to 3, so the value is -(3²) = -9. The cube of -2 is -8 because a negative base with an odd exponent stays negative. Adding gives -9 + (-8) = -17.

Question 48Algebra

The quantity y varies directly with x. If y = 12 when x = 3, what is y when x = 5?

  1. 60
  2. 24
  3. 15
  4. 20 Correct answer.

Explanation

Direct variation means y = kx, so first find k = 12/3 = 4. Then y = 4(5) = 20. Direct variation requires finding the constant of proportionality before substituting the new value.

Question 49Algebra

Solve the inequality -2x + 5 > 11.

  1. x < 3
  2. x < -3 Correct answer.
  3. x > -3
  4. x > 3

Explanation

Subtract 5 from both sides to get -2x > 6. Dividing both sides by -2 reverses the direction of the inequality, giving x < -3. Reversing the symbol is required whenever you divide or multiply by a negative number.

Question 50Algebra

What is the solution to the system of equations y = 2x + 1 and 3x + y = 16?

  1. (7, 3)
  2. (-3, -5)
  3. (2, 5)
  4. (3, 7) Correct answer.

Explanation

Substituting y = 2x + 1 into the second equation gives 3x + 2x + 1 = 16, so 5x = 15 and x = 3. Then y = 2(3) + 1 = 7. The solution must satisfy both equations, and 3(3) + 7 = 16 confirms it.