Browse papers

Praxis Core Praxis Core - Mathematics Practice Test 2025

Praxis CoreModel questions
56marks
85min
10questions

This is the official Praxis Core Praxis Core - Mathematics question paper for 2025, as set in the Model questions examination. It carries 56 full marks and a time allowance of 85 minutes, across 10 questions. On Kekkei you can attempt this Praxis Core - Mathematics past paper online with a timer, get instant AI feedback and step-by-step solutions, and track the topics where you lose marks — completely free. Whether you are revising for your Praxis Core Praxis Core - Mathematics exam or solving previous years' question papers, this 2025 paper is a great way to practise under real exam conditions.

LevelPraxis Core
SubjectPraxis Core - Mathematics
Year2025 BS
Exam sessionModel questions
Full marks56
Time allowed85 minutes
Questions10, all with step-by-step solutions
A

Core Academic Skills for Educators: Mathematics

Select the best answer.

10 questions·1 mark each
1Multiple choice1 mark

Evaluate the following expression using the correct order of operations:

8+3×(12−4)2÷68 + 3 \times (12 - 4)^2 \div 6
  • a

    4040

  • b

    3232

  • c

    104104

  • d

    200200

Correct answer: a

4040

Following the order of operations (PEMDAS/BODMAS):

  1. Parentheses: 12−4=812 - 4 = 8
  2. Exponents: 82=648^2 = 64
  3. Multiplication and Division (left to right): 3×64=1923 \times 64 = 192, then 192÷6=32192 \div 6 = 32
  4. Addition: 8+32=408 + 32 = 40

The value of the expression is 4040.

number-and-quantityorder-of-operations
2Multiple choice1 mark

Convert the fraction 78\dfrac{7}{8} to a decimal and then to a percentage. Which of the following is correct?

  • a

    0.785 and 78.5%0.785 \text{ and } 78.5\%

  • b

    0.875 and 87.5%0.875 \text{ and } 87.5\%

  • c

    0.870 and 87.0%0.870 \text{ and } 87.0\%

  • d

    0.890 and 89.0%0.890 \text{ and } 89.0\%

Correct answer: b

0.875 and 87.5%0.875 \text{ and } 87.5\%

To convert 78\dfrac{7}{8} to a decimal, perform the division:

78=7÷8=0.875.\frac{7}{8} = 7 \div 8 = 0.875.

To convert a decimal to a percentage, multiply by 100100:

0.875×100=87.5%.0.875 \times 100 = 87.5\%.

Therefore 78=0.875=87.5%\dfrac{7}{8} = 0.875 = 87.5\%.

fractionsdecimalsconversions
3Multiple choice1 mark

A car travels 252252 miles using 99 gallons of gasoline. What is the car's fuel efficiency in miles per gallon, and how far can it travel on 1515 gallons at the same rate?

  • a

    28 mpg and 420 miles28 \text{ mpg and } 420 \text{ miles}

  • b

    24 mpg and 360 miles24 \text{ mpg and } 360 \text{ miles}

  • c

    32 mpg and 480 miles32 \text{ mpg and } 480 \text{ miles}

  • d

    28 mpg and 392 miles28 \text{ mpg and } 392 \text{ miles}

Correct answer: a

28 mpg and 420 miles28 \text{ mpg and } 420 \text{ miles}

First, find the unit rate (miles per gallon):

Fuel efficiency=252 miles9 gallons=28 miles per gallon.\text{Fuel efficiency} = \frac{252 \text{ miles}}{9 \text{ gallons}} = 28 \text{ miles per gallon}.

Next, calculate the distance for 1515 gallons:

Distance=28×15=420 miles.\text{Distance} = 28 \times 15 = 420 \text{ miles}.

The car gets 2828 mpg and can travel 420420 miles on 1515 gallons.

ratiosproportionsunit-rate
4Multiple choice1 mark

Solve for xx in the following equation:

5(x−3)+2=3(x+1)+45(x - 3) + 2 = 3(x + 1) + 4
  • a

    x=5x = 5

  • b

    x=10x = 10

  • c

    x=8x = 8

  • d

    x=−3x = -3

Correct answer: b

x=10x = 10

Expand both sides:

5x−15+2=3x+3+45x - 15 + 2 = 3x + 3 + 4 5x−13=3x+75x - 13 = 3x + 7

Subtract 3x3x from both sides: 2x−13=72x - 13 = 7.

Add 1313 to both sides: 2x=202x = 20.

Divide by 22: x=10x = 10.

Verification: 5(10−3)+2=5(7)+2=375(10 - 3) + 2 = 5(7) + 2 = 37 and 3(10+1)+4=3(11)+4=373(10 + 1) + 4 = 3(11) + 4 = 37. Both sides equal 3737.

algebralinear-equations
5Multiple choice1 mark

A rectangular garden has a length of 1818 feet and a width of 1212 feet. A walking path 22 feet wide is built around the outside of the garden. What is the total area of the walking path alone?

  • a

    120 sq ft120 \text{ sq ft}

  • b

    136 sq ft136 \text{ sq ft}

  • c

    144 sq ft144 \text{ sq ft}

  • d

    352 sq ft352 \text{ sq ft}

Correct answer: b

136 sq ft136 \text{ sq ft}

The walking path surrounds the garden, so we find the area of the outer rectangle minus the garden.

Outer rectangle dimensions:

  • Length = 18+2(2)=2218 + 2(2) = 22 feet
  • Width = 12+2(2)=1612 + 2(2) = 16 feet

Area of outer rectangle = 22×16=35222 \times 16 = 352 sq ft.

Area of garden = 18×12=21618 \times 12 = 216 sq ft.

Area of walking path = 352−216=136352 - 216 = 136 sq ft.

geometryperimeterarea
6Multiple choice1 mark

A recipe calls for 2.52.5 liters of water. If 11 liter equals approximately 33.81433.814 fluid ounces, how many fluid ounces of water are needed? Round to the nearest whole number.

  • a

    8080

  • b

    8585

  • c

    7575

  • d

    9090

Correct answer: b

8585

Multiply the volume in liters by the conversion factor:

2.5 liters×33.814 fl oz/liter=84.535 fl oz.2.5 \text{ liters} \times 33.814 \text{ fl oz/liter} = 84.535 \text{ fl oz}.

Rounded to the nearest whole number: 8585 fluid ounces.

measurementunit-conversions
7Multiple choice1 mark

A school survey recorded the number of books read by students over the summer. The results are as follows:

  • Grade 6: 45 books
  • Grade 7: 62 books
  • Grade 8: 53 books
  • Grade 9: 70 books
  • Grade 10: 58 books

Based on this data, how many more books did Grades 9 and 10 read combined compared to Grades 6 and 7 combined?

  • a

    1515

  • b

    2121

  • c

    2525

  • d

    1818

Correct answer: b

2121

Grades 9 and 10 combined: 70+58=12870 + 58 = 128 books.

Grades 6 and 7 combined: 45+62=10745 + 62 = 107 books.

Difference: 128−107=21128 - 107 = 21 books.

Grades 9 and 10 read 2121 more books combined than Grades 6 and 7.

data-interpretationbar-charts
8Multiple choice1 mark

A teacher recorded the following test scores for nine students:

72,  85,  91,  68,  85,  77,  93,  85,  6472, \; 85, \; 91, \; 68, \; 85, \; 77, \; 93, \; 85, \; 64

What are the mean, median, and mode of this data set?

  • a

    Mean=80,Median=85,Mode=85\text{Mean} = 80, \text{Median} = 85, \text{Mode} = 85

  • b

    Mean=82,Median=85,Mode=85\text{Mean} = 82, \text{Median} = 85, \text{Mode} = 85

  • c

    Mean=80,Median=77,Mode=85\text{Mean} = 80, \text{Median} = 77, \text{Mode} = 85

  • d

    Mean=80,Median=85,Mode=91\text{Mean} = 80, \text{Median} = 85, \text{Mode} = 91

Correct answer: a

Mean=80,Median=85,Mode=85\text{Mean} = 80, \text{Median} = 85, \text{Mode} = 85

Mean: Sum all values and divide by the count.

Sum=72+85+91+68+85+77+93+85+64=720\text{Sum} = 72 + 85 + 91 + 68 + 85 + 77 + 93 + 85 + 64 = 720 Mean=7209=80.\text{Mean} = \frac{720}{9} = 80.

Median: Arrange in order: 64,68,72,77,85,85,85,91,9364, 68, 72, 77, 85, 85, 85, 91, 93. With 99 values, the median is the 55th value: 8585.

Mode: 8585 appears 33 times, more than any other value. Mode =85= 85.

Mean =80= 80, Median =85= 85, Mode =85= 85.

statisticsmeanmedianmode
9Multiple choice1 mark

A bag contains 55 red marbles, 33 blue marbles, and 22 green marbles. If one marble is drawn at random, what is the probability that it is either red or green?

  • a

    12\dfrac{1}{2}

  • b

    710\dfrac{7}{10}

  • c

    310\dfrac{3}{10}

  • d

    25\dfrac{2}{5}

Correct answer: b

710\dfrac{7}{10}

Total number of marbles = 5+3+2=105 + 3 + 2 = 10.

The events "red" and "green" are mutually exclusive, so:

P(red or green)=P(red)+P(green)=510+210=710.P(\text{red or green}) = P(\text{red}) + P(\text{green}) = \frac{5}{10} + \frac{2}{10} = \frac{7}{10}.

The probability is 710\dfrac{7}{10} or 0.700.70 or 70%70\%.

probabilitysimple-probability
10Multiple choice1 mark

Consider the following sequence of numbers:

2,  6,  18,  54,  162,  …2, \; 6, \; 18, \; 54, \; 162, \; \ldots

What is the 77th term of this sequence?

  • a

    486486

  • b

    972972

  • c

    1,4581{,}458

  • d

    1,9441{,}944

Correct answer: c

1,4581{,}458

Identify the pattern. Each term is obtained by multiplying the previous term by 33:

62=3,186=3,5418=3,16254=3.\frac{6}{2} = 3, \quad \frac{18}{6} = 3, \quad \frac{54}{18} = 3, \quad \frac{162}{54} = 3.

This is a geometric sequence with first term a=2a = 2 and common ratio r=3r = 3.

The nnth term formula is an=a⋅rn−1a_n = a \cdot r^{n-1}.

a7=2⋅37−1=2⋅36=2⋅729=1,458.a_7 = 2 \cdot 3^{7-1} = 2 \cdot 3^6 = 2 \cdot 729 = 1{,}458.

We can verify: 2,6,18,54,162,486,14582, 6, 18, 54, 162, 486, 1458. The 77th term is 1,4581{,}458.

mathematical-reasoningpattern-recognition

Frequently asked questions

Where can I find the Praxis Core Praxis Core - Mathematics question paper 2025?
The full Praxis Core Praxis Core - Mathematics 2025 (Model questions) question paper is available free on Kekkei. You can read every question online and attempt the paper under timed exam conditions.
Does the Praxis Core - Mathematics 2025 paper come with solutions?
Yes. Every question on this Praxis Core - Mathematics past paper includes a step-by-step solution, plus instant AI feedback when you attempt it on Kekkei.
How many marks is the Praxis Core Praxis Core - Mathematics 2025 paper?
The Praxis Core Praxis Core - Mathematics 2025 paper carries 56 full marks and is meant to be completed in 85 minutes, across 10 questions.
Is practising this Praxis Core - Mathematics past paper free?
Yes — reading and attempting this Praxis Core - Mathematics past paper on Kekkei is completely free.