10 Most Common Praxis Core Math Questions

3- D
Isolate and solve for \(x\).
\(\frac{2}{3} x+\frac{1}{6} = \frac{1}{3} {\Rightarrow} \frac{2}{3} x= \frac{1}{3} -\frac{1}{6} = \frac{1}{6} {\Rightarrow} \frac{2}{3} x= \frac{1}{6} \)
Multiply both sides by the reciprocal of the coefficient of \(x\).
\((\frac{3}{2}) \frac{2}{3} x= \frac{1}{6} (\frac{3}{2}) {\Rightarrow} x= \frac{3}{12}=\frac{1}{4}\)

4- D
The probability of choosing a Hearts is \(\frac{13}{52}=\frac{1}{4} \)

5- D
Change the numbers to decimals and then compare.
\(\frac{2}{3} = 0.666… \)
\(0.68 \)
\(67\% = 0.67\)
\(\frac{4}{5} = 0.80\)
Therefore
\(\frac{2}{3} < 67\% < 0.68 < \frac{4}{5}\)

6- C
average (mean)\( =\frac{(sum \space of \space terms)}{(number \space of \space terms)} {\Rightarrow} 88 = \frac{(sum \space of \space terms)}{50} {\Rightarrow} sum = 88 {\times} 50 = 4400\)
The difference between 94 and 69 is 25. Therefore, 25 should be subtracted from the sum.
\(4400 – 25 = 4375\)
\(mean = \frac{(sum of terms)}{(number of terms)} ⇒ mean = \frac{(4375)}{50}= 87.5\)

7- B
To get a sum of 6 for two dice, we can get 5 different options:
\((5, 1), (4, 2), (3, 3), (2, 4), (1, 5)\)
To get a sum of 9 for two dice, we can get 4 different options:
\((6, 3), (5, 4), (4, 5), (3, 6)\)
Therefore, there are 9 options to get the sum of 6 or 9.
Since we have \(6 × 6 = 36\) total options, the probability of getting a sum of 6 and 9 is 9 out of 36 or \(\frac{1}{4}\).

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8- C
The distance between Jason and Joe is 9 miles. Jason is running at 5.5 miles per hour, and Joe is running at the speed of 7 miles per hour. Therefore, every hour, the distance is 1.5 miles less. \(9 \div 1.5 = 6\)

9- C
The failing rate is 11 out of \(55 = \frac{11}{55} \)
Change the fraction to percent:
\( \frac{11}{55} {\times} 100\%=20\% \)
20 percent of students failed. Therefore, 80 percent of students passed the exam.

10- D
Volume of a box \(= length \times width \times height = 4 \times 5 \times 6 = 120\)

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Walking Through the 10 Most Common Praxis Core Math Question Types

The Praxis Core Math test covers arithmetic, elementary algebra, geometry, and data analysis. Success comes from recognizing patterns. Here are the 10 most frequently tested question types with full solutions.

Type 1: Multi-Step Arithmetic with Fractions

Example: \(\frac{3}{5} + \frac{1}{4} – \frac{2}{10}\) = ?

Solution: Find a common denominator (20): \(\frac{12}{20} + \frac{5}{20} – \frac{4}{20} = \frac{13}{20}\).

Frequency: Very common. Time budget: 1-2 minutes maximum.

Type 2: Percent Increase/Decrease

Example: A price rises from \$200 to \$250. What’s the percent increase?

Solution: Change is \$50. Percent increase = \(\frac{50}{200} = 0.25 = 25\%\).

Formula to remember: \(\text{Percent change} = \frac{\text{New} – \text{Old}}{\text{Old}} \times 100\%\)

Type 3: Solving a One-Variable Linear Equation

Example: \(2(x – 3) + 5 = 11\)

Solution: Distribute: \(2x – 6 + 5 = 11\). Simplify: \(2x – 1 = 11\). Add 1: \(2x = 12\). Divide: \(x = 6\).

Key: Use inverse operations. Always check by substituting back.

Type 4: Integer and Absolute Value Operations

Example: \(|-8| + (-3) – (-2) + |5|\) = ?

Solution: \(8 – 3 + 2 + 5 = 12\).

Remember: Absolute value is always non-negative. Subtracting a negative is adding.

Type 5: Order of Operations with Exponents

Example: \(3 + 2^3 \times 4 – 6\) = ?

Solution: Exponent first: \(2^3 = 8\). Then multiply: \(8 \times 4 = 32\). Then left to right: \(3 + 32 – 6 = 29\).

Type 6: Ratio and Proportion

Example: If the ratio of red to blue marbles is 3:5, and there are 18 red marbles, how many blue?

Solution: \(\frac{3}{5} = \frac{18}{x}\). Cross-multiply: \(3x = 90\). So \(x = 30\) blue marbles.

Type 7: Simple Geometry (Perimeter, Area, Volume)

Example: A rectangle has length 10 cm and width 6 cm. What’s the area?

Solution: Area = \(10 \times 6 = 60\) cm².

Know these formulas: Rectangle area = length × width. Triangle area = \(\frac{1}{2} \times \text{base} \times \text{height}\). Circle area = \(\pi r^2\).

Type 8: Data Interpretation (Mean, Median, Mode)

Example: Find the mean of 12, 15, 18, 20, 35.

Solution: Sum = \(12 + 15 + 18 + 20 + 35 = 100\). Count = 5. Mean = \(100 ÷ 5 = 20\).

Median: Middle value when ordered (18 here). Mode: Most frequent value.

Type 9: Algebraic Expression Simplification

Example: Simplify \(3x + 2(x – 4) – 5\).

Solution: Distribute: \(3x + 2x – 8 – 5\). Combine like terms: \(5x – 13\).

Type 10: Systems of Equations (Basic)

Example: \(x + y = 7\) and \(x – y = 3\). Solve for \(x\) and \(y\).

Solution: Add the equations: \(2x = 10\), so \(x = 5\). Substitute: \(5 + y = 7\), so \(y = 2\).

Praxis Core Test Strategy

You have about 90 minutes for 50-60 questions. That’s roughly 90 seconds per question, but easier questions take 30 seconds, freeing time for harder ones. Don’t spend more than 2 minutes on any single item. Flag it and move on.

Use the calculator for arithmetic when provided, but understand the underlying math. Many Praxis questions reward conceptual understanding over just grinding numbers.

Scoring and What You Need

The Praxis Core Math test scores from 100-200. Most teacher certification programs require 150+ (65th percentile). Strong performance requires both speed and accuracy. You’re not expected to finish perfectly—aim for 70-75% correct to hit 150+.

Study Resources

Systematically work through the complete Praxis Core math formula cheat sheet and Praxis math formulas to organize what you need to know. Practice order of operations daily. Build speed with math fundamentals courses that review arithmetic and algebra comprehensively.

Practice under timed conditions. After each practice test, review every single question, even ones you got right. This reveals your weak areas before test day.

Walking Through the 10 Most Common Praxis Core Math Question Types

The Praxis Core Math test covers arithmetic, elementary algebra, geometry, and data analysis. Success comes from recognizing patterns. Here are the 10 most frequently tested question types with full solutions.

Type 1: Multi-Step Arithmetic with Fractions

Example: \(\frac{3}{5} + \frac{1}{4} – \frac{2}{10}\) = ?

Solution: Find a common denominator (20): \(\frac{12}{20} + \frac{5}{20} – \frac{4}{20} = \frac{13}{20}\).

Frequency: Very common. Time budget: 1-2 minutes maximum.

Type 2: Percent Increase/Decrease

Example: A price rises from \$200 to \$250. What’s the percent increase?

Solution: Change is \$50. Percent increase = \(\frac{50}{200} = 0.25 = 25\%\).

Formula to remember: \(\text{Percent change} = \frac{\text{New} – \text{Old}}{\text{Old}} \times 100\%\)

Type 3: Solving a One-Variable Linear Equation

Example: \(2(x – 3) + 5 = 11\)

Solution: Distribute: \(2x – 6 + 5 = 11\). Simplify: \(2x – 1 = 11\). Add 1: \(2x = 12\). Divide: \(x = 6\).

Key: Use inverse operations. Always check by substituting back.

Type 4: Integer and Absolute Value Operations

Example: \(|-8| + (-3) – (-2) + |5|\) = ?

Solution: \(8 – 3 + 2 + 5 = 12\).

Remember: Absolute value is always non-negative. Subtracting a negative is adding.

Type 5: Order of Operations with Exponents

Example: \(3 + 2^3 \times 4 – 6\) = ?

Solution: Exponent first: \(2^3 = 8\). Then multiply: \(8 \times 4 = 32\). Then left to right: \(3 + 32 – 6 = 29\).

Type 6: Ratio and Proportion

Example: If the ratio of red to blue marbles is 3:5, and there are 18 red marbles, how many blue?

Solution: \(\frac{3}{5} = \frac{18}{x}\). Cross-multiply: \(3x = 90\). So \(x = 30\) blue marbles.

Type 7: Simple Geometry (Perimeter, Area, Volume)

Example: A rectangle has length 10 cm and width 6 cm. What’s the area?

Solution: Area = \(10 \times 6 = 60\) cm².

Know these formulas: Rectangle area = length × width. Triangle area = \(\frac{1}{2} \times \text{base} \times \text{height}\). Circle area = \(\pi r^2\).

Type 8: Data Interpretation (Mean, Median, Mode)

Example: Find the mean of 12, 15, 18, 20, 35.

Solution: Sum = \(12 + 15 + 18 + 20 + 35 = 100\). Count = 5. Mean = \(100 ÷ 5 = 20\).

Median: Middle value when ordered (18 here). Mode: Most frequent value.

Type 9: Algebraic Expression Simplification

Example: Simplify \(3x + 2(x – 4) – 5\).

Solution: Distribute: \(3x + 2x – 8 – 5\). Combine like terms: \(5x – 13\).

Type 10: Systems of Equations (Basic)

Example: \(x + y = 7\) and \(x – y = 3\). Solve for \(x\) and \(y\).

Solution: Add the equations: \(2x = 10\), so \(x = 5\). Substitute: \(5 + y = 7\), so \(y = 2\).

Praxis Core Test Strategy

You have about 90 minutes for 50-60 questions. That’s roughly 90 seconds per question, but easier questions take 30 seconds, freeing time for harder ones. Don’t spend more than 2 minutes on any single item. Flag it and move on.

Use the calculator for arithmetic when provided, but understand the underlying math. Many Praxis questions reward conceptual understanding over just grinding numbers.

Scoring and What You Need

The Praxis Core Math test scores from 100-200. Most teacher certification programs require 150+ (65th percentile). Strong performance requires both speed and accuracy. You’re not expected to finish perfectly—aim for 70-75% correct to hit 150+.

Study Resources

Systematically work through the complete Praxis Core math formula cheat sheet and Praxis math formulas to organize what you need to know. Practice order of operations daily. Build speed with math fundamentals courses that review arithmetic and algebra comprehensively.

Practice under timed conditions. After each practice test, review every single question, even ones you got right. This reveals your weak areas before test day.