Are flashcards effective for the Praxis Core Math test?

Yes. Flashcards use active recall — retrieving an answer from memory — which research shows is one of the most effective study methods, especially in short, spaced sessions. Because the Praxis Core Math test rewards instant recall of fraction and percent rules, statistics definitions, and area and volume formulas, the cards make that knowledge automatic.

What topics do the Praxis Core Math flashcards cover?

All three content categories: Number and Quantity (fractions, decimals, percents, ratios, factors, exponents), Data Interpretation, Statistics and Probability (graphs, mean/median/mode, range, standard deviation, probability), and Algebra and Geometry (equations, inequalities, slope, perimeter, area, volume, and the Pythagorean theorem).

How should I study with these Praxis Core Math flashcards?

Lead with Number and Quantity — about 36% of the test — then drill the statistics definitions and the algebra and geometry formulas. Mix the modes: flip to learn, type to test recall, match for speed, and quiz to check yourself before working full practice questions.

Are the Praxis Core Math flashcards free?

Yes — 100% free, all four study modes, no paywall and no sign-up.

Do these flashcards match the current Praxis Core Math (5733) test?

Yes. The cards are organized to the ETS Praxis Core Math (5733) content categories and reflect the current 56-question, 90-minute computer-delivered test with its on-screen calculator and 100–200 scaled score.

A whole number greater than 1 with exactly two distinct factors: 1 and itself (2, 3, 5, 7, 11, 13...).

A whole number greater than 1 that has more than two factors (4, 6, 8, 9, 10...). It is not prime.

No. A prime has exactly two distinct factors; 1 has only one factor (itself), so it is neither prime nor composite.

Yes. 2 is the only even prime number — every other even number is divisible by 2.

A whole number that divides another evenly with no remainder. Factors of 12 are 1, 2, 3, 4, 6, 12.

The product of a number and any whole number. Multiples of 5 are 5, 10, 15, 20, 25...

Greatest common factor (GCF)

The largest factor shared by two numbers. GCF of 48 and 60 is 12. Find it by listing factors or using prime factorization.

Least common multiple (LCM)

The smallest multiple shared by two numbers. LCM of 8 and 12 is 24. Useful for adding fractions and 'when do events line up again' problems.

Writing a number as a product of primes. 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.

Number of factors of a product of two distinct primes

Exactly 4. If x and y are distinct primes, xy has factors 1, x, y, and xy.

A whole number and its opposite, including zero: ..., −2, −1, 0, 1, 2, ... No fractions or decimals.

Any number that can be written as a fraction a/b where a and b are integers and b ≠ 0. Includes terminating and repeating decimals.

A number that cannot be written as a fraction; its decimal never ends and never repeats. Examples: √2, π.

The distance of a number from zero on the number line; always nonnegative. |−7| = 7 and |7| = 7.

Order of operations (PEMDAS)

Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Find a common denominator, rewrite each fraction, add the numerators, keep the denominator, then simplify. 3/4 + 5/6 = 9/12 + 10/12 = 19/12.

Subtracting fractions

Use a common denominator, subtract numerators, keep the denominator, simplify. 11/12 − 1/4 = 11/12 − 3/12 = 8/12 = 2/3.

Multiplying fractions

Multiply numerators and multiply denominators, then simplify. 2/3 × 9/10 = 18/30 = 3/5.

Multiply by the reciprocal of the second fraction (keep–change–flip). 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.

The multiplicative inverse — flip the fraction. The reciprocal of 2/5 is 5/2; the reciprocal of 4 is 1/4. A number times its reciprocal equals 1.

Simplifying a fraction

Divide the numerator and denominator by their GCF. 18/30 ÷ 6/6 = 3/5.

A fraction whose numerator is greater than or equal to its denominator, such as 7/4. It can be written as the mixed number 1¾.

A whole number plus a fraction, such as 2½. Convert to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 2½ = 5/2.

Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75.

Write the decimal over its place value, then simplify. 0.75 = 75/100 = 3/4.

Divide by 100 (move the decimal two places left). 45% = 0.45.

Multiply by 100 (move the decimal two places right). 0.6 = 60%.

Multiply the number by the percent as a decimal. 20% of 80 = 0.20 × 80 = 16.

Finding the whole from a percent

Divide the part by the percent as a decimal. If 15 is 25% of a number, the number is 15 ÷ 0.25 = 60.

Change ÷ original × 100. Always divide by the starting value. From 80 to 100: 20 ÷ 80 = 25% increase.

Percent increase shortcut

To increase a number by 25%, multiply by 1.25; to decrease by 25%, multiply by 0.75.

A comparison of two quantities, written 3:5, 3 to 5, or 3/5. Reduce ratios like fractions.

An equation stating two ratios are equal, such as 2/3 = x/12. Solve by cross-multiplying: 3x = 24, so x = 8.

For a/b = c/d, multiply diagonally: a × d = b × c. Used to solve proportions.

A rate with a denominator of 1, such as miles per hour or cost per item. Find it by dividing. $12 for 4 lbs = $3 per lb.

The ratio used to enlarge or reduce; multiply each measurement by it. A 1:50 map scale means 1 unit on the map equals 50 real units.

A small number telling how many times to multiply the base by itself. 2³ = 2 × 2 × 2 = 8.

Any nonzero number raised to the 0 power equals 1. 7⁰ = 1.

A negative exponent means take the reciprocal: x⁻ⁿ = 1/xⁿ. So 2⁻³ = 1/8.

Product of powers rule

When multiplying like bases, add the exponents: xᵐ · xⁿ = xᵐ⁺ⁿ. So 2³ · 2⁴ = 2⁷.

Quotient of powers rule

When dividing like bases, subtract the exponents: xᵐ ÷ xⁿ = xᵐ⁻ⁿ. So 2⁵ ÷ 2² = 2³.

Power of a power rule

Raise a power to a power by multiplying the exponents: (xᵐ)ⁿ = xᵐⁿ. So (2³)² = 2⁶.

A value that, multiplied by itself, gives the number. √36 = 6 because 6 × 6 = 36.

The product of an integer with itself: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100... Their square roots are whole numbers.

A number written as a value between 1 and 10 times a power of 10. 47,000 = 4.7 × 10⁴.

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Praxis Core Math Flashcards

Prime number: A whole number greater than 1 with exactly two distinct factors: 1 and itself (2, 3, 5, 7, 11, 13...).
Composite number: A whole number greater than 1 that has more than two factors (4, 6, 8, 9, 10...). It is not prime.
Is 1 prime?: No. A prime has exactly two distinct factors; 1 has only one factor (itself), so it is neither prime nor composite.
Is 2 prime?: Yes. 2 is the only even prime number — every other even number is divisible by 2.
Factor: A whole number that divides another evenly with no remainder. Factors of 12 are 1, 2, 3, 4, 6, 12.
Multiple: The product of a number and any whole number. Multiples of 5 are 5, 10, 15, 20, 25...
Greatest common factor (GCF): The largest factor shared by two numbers. GCF of 48 and 60 is 12. Find it by listing factors or using prime factorization.
Least common multiple (LCM): The smallest multiple shared by two numbers. LCM of 8 and 12 is 24. Useful for adding fractions and 'when do events line up again' problems.
Prime factorization: Writing a number as a product of primes. 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
Number of factors of a product of two distinct primes: Exactly 4. If x and y are distinct primes, xy has factors 1, x, y, and xy.
Integer: A whole number and its opposite, including zero: ..., −2, −1, 0, 1, 2, ... No fractions or decimals.
Rational number: Any number that can be written as a fraction a/b where a and b are integers and b ≠ 0. Includes terminating and repeating decimals.
Irrational number: A number that cannot be written as a fraction; its decimal never ends and never repeats. Examples: √2, π.
Absolute value: The distance of a number from zero on the number line; always nonnegative. |−7| = 7 and |7| = 7.
Order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
Adding fractions: Find a common denominator, rewrite each fraction, add the numerators, keep the denominator, then simplify. 3/4 + 5/6 = 9/12 + 10/12 = 19/12.
Subtracting fractions: Use a common denominator, subtract numerators, keep the denominator, simplify. 11/12 − 1/4 = 11/12 − 3/12 = 8/12 = 2/3.
Multiplying fractions: Multiply numerators and multiply denominators, then simplify. 2/3 × 9/10 = 18/30 = 3/5.
Dividing fractions: Multiply by the reciprocal of the second fraction (keep–change–flip). 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.
Reciprocal: The multiplicative inverse — flip the fraction. The reciprocal of 2/5 is 5/2; the reciprocal of 4 is 1/4. A number times its reciprocal equals 1.
Simplifying a fraction: Divide the numerator and denominator by their GCF. 18/30 ÷ 6/6 = 3/5.
Improper fraction: A fraction whose numerator is greater than or equal to its denominator, such as 7/4. It can be written as the mixed number 1¾.
Mixed number: A whole number plus a fraction, such as 2½. Convert to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 2½ = 5/2.
Fraction to decimal: Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75.
Decimal to fraction: Write the decimal over its place value, then simplify. 0.75 = 75/100 = 3/4.
Percent to decimal: Divide by 100 (move the decimal two places left). 45% = 0.45.
Decimal to percent: Multiply by 100 (move the decimal two places right). 0.6 = 60%.
Percent of a number: Multiply the number by the percent as a decimal. 20% of 80 = 0.20 × 80 = 16.
Finding the whole from a percent: Divide the part by the percent as a decimal. If 15 is 25% of a number, the number is 15 ÷ 0.25 = 60.
Percent change: Change ÷ original × 100. Always divide by the starting value. From 80 to 100: 20 ÷ 80 = 25% increase.
Percent increase shortcut: To increase a number by 25%, multiply by 1.25; to decrease by 25%, multiply by 0.75.
Ratio: A comparison of two quantities, written 3:5, 3 to 5, or 3/5. Reduce ratios like fractions.
Proportion: An equation stating two ratios are equal, such as 2/3 = x/12. Solve by cross-multiplying: 3x = 24, so x = 8.
Cross-multiplication: For a/b = c/d, multiply diagonally: a × d = b × c. Used to solve proportions.
Unit rate: A rate with a denominator of 1, such as miles per hour or cost per item. Find it by dividing. $12 for 4 lbs =$ 3 per lb.
Scale factor: The ratio used to enlarge or reduce; multiply each measurement by it. A 1:50 map scale means 1 unit on the map equals 50 real units.
Exponent: A small number telling how many times to multiply the base by itself. 2³ = 2 × 2 × 2 = 8.
Zero exponent rule: Any nonzero number raised to the 0 power equals 1. 7⁰ = 1.
Negative exponent: A negative exponent means take the reciprocal: x⁻ⁿ = 1/xⁿ. So 2⁻³ = 1/8.
Product of powers rule: When multiplying like bases, add the exponents: xᵐ · xⁿ = xᵐ⁺ⁿ. So 2³ · 2⁴ = 2⁷.
Quotient of powers rule: When dividing like bases, subtract the exponents: xᵐ ÷ xⁿ = xᵐ⁻ⁿ. So 2⁵ ÷ 2² = 2³.
Power of a power rule: Raise a power to a power by multiplying the exponents: (xᵐ)ⁿ = xᵐⁿ. So (2³)² = 2⁶.
Square root: A value that, multiplied by itself, gives the number. √36 = 6 because 6 × 6 = 36.
Perfect square: The product of an integer with itself: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100... Their square roots are whole numbers.
Scientific notation: A number written as a value between 1 and 10 times a power of 10. 47,000 = 4.7 × 10⁴.
Estimating with rounding: Replace numbers with nearby easy values to check that an answer is reasonable. 19 × 21 ≈ 20 × 20 = 400.
Rounding to a place value: Look at the digit to the right: 5 or more rounds up, 4 or less rounds down. 3.47 to the tenths = 3.5.
Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. 132 → 1+3+2 = 6, divisible by 3.
Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. 729 → 7+2+9 = 18, divisible by 9.
Divisibility by 4: A number is divisible by 4 if its last two digits form a number divisible by 4. 1,316 → 16 is divisible by 4.
Even and odd numbers: Even numbers are divisible by 2 (end in 0, 2, 4, 6, 8); odd numbers are not. Even × any = even; odd × odd = odd.
Adding integers with different signs: Subtract the absolute values and keep the sign of the larger one. −8 + 5 = −3.
Multiplying signed numbers: Same signs give a positive product; different signs give a negative product. (−4)(−3) = 12; (−4)(3) = −12.
Subtracting integers: Add the opposite: a − b = a + (−b). 5 − (−3) = 5 + 3 = 8.
Number line ordering: Numbers increase from left to right. −5 is less than −2, which is less than 0, which is less than 3.
Comparing fractions: Use a common denominator or cross-multiply. For 3/4 vs 5/7: 3×7 = 21 vs 5×4 = 20, so 3/4 is larger.
Equivalent fractions: Fractions that name the same value, found by multiplying or dividing top and bottom by the same number. 1/2 = 2/4 = 3/6.
Reducing a fraction part of a recipe: To make 2/3 of a recipe needing 3/4 cup, multiply: 2/3 × 3/4 = 6/12 = 1/2 cup.
Place value: The value of a digit based on its position. In 3,482 the 4 means 400 (hundreds place).
Rounding money: Round to the nearest cent (hundredths) by looking at the thousandths digit. $4.567 ≈$ 4.57.
Whole number: The counting numbers plus zero: 0, 1, 2, 3, 4, ... No negatives, fractions, or decimals.
Twin primes: A pair of prime numbers that differ by 2, such as 11 and 13 or 17 and 19.
Factors of a prime number: Exactly two: 1 and the number itself. That is the definition of prime.
Estimating a square root: Find the perfect squares it falls between. √50 is between √49 = 7 and √64 = 8, so about 7.1.
Converting units (length): Multiply or divide by the conversion factor. 3 feet = 36 inches (×12); 250 cm = 2.5 m (÷100).
Converting units (time): 60 seconds = 1 minute, 60 minutes = 1 hour. 150 minutes = 2 hours 30 minutes.
Dimensional analysis: Multiply by conversion fractions so unwanted units cancel, leaving the desired unit. Lets you convert miles/hour to feet/second, etc.
Percent greater than 100: A percent over 100% means more than the whole. 150% of 40 = 1.5 × 40 = 60.
Markup and discount: Markup adds a percent to a price; discount subtracts one. A $50 item at 20% off costs 50 × 0.80 =$ 40.
Simple interest: I = Prt, where P is principal, r is the annual rate (as a decimal), and t is time in years. $1,000 at 5% for 2 years earns$ 100.
GCF supply-kit problem: To split items into identical groups using all of them, find the GCF of the counts. 54 pencils and 72 erasers → GCF 18 kits.
LCM 'line up again' problem: To find when two repeating events coincide, find the LCM of their periods. Laps of 6 and 9 minutes meet again at 18 minutes.
Fraction of a fraction: 'Of' means multiply. 1/2 of 1/3 = 1/2 × 1/3 = 1/6.
Sum of consecutive even multiples: The sum 2a + 4a + ... + 2na is n(n+1)a, since 2a(1 + 2 + ... + n) = 2a · n(n+1)/2.
Repeating decimal: A decimal with a digit or block that repeats forever, written with a bar. 1/3 = 0.333... = 0.3̄.
Terminating decimal: A decimal that ends. A fraction terminates when its denominator (in lowest terms) has only 2s and 5s as factors. 3/8 = 0.375.
Opposite (additive inverse): The number that adds to a given number to make 0. The opposite of 7 is −7.
Cube of a number: Multiply the number by itself three times. 4³ = 4 × 4 × 4 = 64.
Square of a number: Multiply the number by itself. 9² = 9 × 9 = 81.
Properties: commutative: Order does not change a sum or product. a + b = b + a; a × b = b × a.
Properties: associative: Grouping does not change a sum or product. (a + b) + c = a + (b + c).
Properties: distributive: a(b + c) = ab + ac. So 3(x + 4) = 3x + 12.
Counting principle: If one choice has m options and another has n options, the number of combined outcomes is m × n. 3 shirts × 4 pants = 12 outfits.
Estimating a percent of a number: Use friendly benchmarks. 10% of a number moves the decimal one place left; 50% is half; 25% is a quarter.
Rate problem (distance): Distance = rate × time, so rate = distance ÷ time. 150 miles in 3 hours = 50 mph.
Work / per-unit rate: Divide total by quantity to get a per-unit value. 240 copies in 8 minutes = 30 copies per minute.
Reading mixed numbers on a ruler: Each inch is divided into halves, quarters, eighths, sixteenths. A mark halfway between 2 and 3 is 2½ inches.
Estimating fractions near a benchmark: Compare to 0, ½, or 1. 7/15 is just under ½; 9/10 is near 1.
Order of magnitude: The power of ten closest to a number. 6,200 is on the order of 10³ (thousands).
Negative number subtraction trap: Subtracting a negative is the same as adding. 3 − (−5) = 3 + 5 = 8 — a common careless error.
Percent of change vs percentage points: Going from 20% to 25% is a rise of 5 percentage points, but a 25% relative increase (5 ÷ 20). Keep them distinct.
Comparing rational and irrational: Rational numbers terminate or repeat; irrationals (π, √2) do neither. π ≈ 3.14159... never repeats.
Estimating to check a calculation: Round each value first to confirm an exact answer is reasonable. If 4.9 × 9.8 ≈ 5 × 10 = 50, then 48.02 is sensible.
Splitting a quantity by a ratio: Add the ratio parts, divide the total by that sum, then multiply. Share $60 in a 1:2:3 ratio → parts of$ 10, $20,$ 30.
Fraction word problem keywords: 'Of' means multiply, 'per' means divide, 'is' means equals. Translate the words into an operation.
Like fractions vs unlike fractions: Like fractions share the same denominator and can be added directly; unlike fractions need a common denominator first.
Estimating products and quotients: Round each factor to a friendly number to predict the size of the answer before computing exactly.
Comparing decimals: Line up the decimal points and compare digit by digit from the left. 0.4 > 0.38 because 0.40 > 0.38.
Estimating a tip: 10% is the decimal moved one place; 20% is double that. A 20% tip on $30 is about$ 6.
Average rate over a whole trip: Total distance ÷ total time, not the average of the speeds. Compute each leg's distance and time first.
Mean (average): Add all the values and divide by how many there are. The mean of 6, 8, 8, 10, 13 is 45 ÷ 5 = 9.
Median: The middle value of an ordered data set. With an even count, average the two middle numbers. Median of 12, 15, 19, 22, 27, 31 is (19+22)/2 = 20.5.
Mode: The value that appears most often. In 14, 16, 16, 15, 16, 14, 17 the mode is 16. A set can have no mode or several.
Range: The largest value minus the smallest. For 8, 3, 7, 14, 10, 6, 2, 9 the range is 14 − 2 = 12.
Mean vs median with outliers: The mean is pulled toward extreme values; the median resists them. For skewed data (incomes, home prices) the median better represents the center.
Standard deviation: A measure of how spread out data is around the mean. A larger standard deviation means more spread; a value of 0 means all data points are identical.
Effect of removing a value on the mean: Removing a number above the mean lowers the average; removing one below it raises the average. Recompute with the new sum and count.
Weighted average: Multiply each value by its weight (or count), add, then divide by the total weight. A grade with a heavier final counts that score more.
Probability of an event: Favorable outcomes ÷ total equally likely outcomes, a value from 0 to 1. Rolling a 4 on a die has probability 1/6.
Probability of independent events (AND): Multiply the probabilities. P(A and B) = P(A) × P(B). Two events with 0.6 and 0.8 → 0.48.
Probability of either event (OR): Add and subtract the overlap. P(A or B) = P(A) + P(B) − P(A and B).
Complement of an event: The chance the event does NOT happen: P(not A) = 1 − P(A). If P(rain) = 0.3, P(no rain) = 0.7.
Independent events: Events where one outcome does not affect the other, like separate coin flips. Their probabilities multiply.
Dependent events: Events where the first outcome changes the second's probability, like drawing cards without replacing them.
Theoretical vs experimental probability: Theoretical comes from equally likely outcomes; experimental comes from actual trial results. Over many trials, experimental approaches theoretical.
Bar graph: Uses rectangular bars to compare amounts across categories. Bar length shows the value; read the axis scale carefully.
Line graph: Shows how a quantity changes over time using points connected by line segments. Good for trends.
Circle (pie) graph: Shows parts of a whole as sectors; the whole circle is 100%. A 25% slice is a quarter of the circle (90°).
Histogram: A bar graph for grouped numerical data; bars touch and each covers an interval (bin). Shows the shape of a distribution.
Scatterplot: Plots paired data as points to show the relationship between two variables. A rising pattern suggests a positive correlation.
Positive correlation: As one variable increases, the other tends to increase. On a scatterplot the points trend upward to the right.
Negative correlation: As one variable increases, the other tends to decrease. On a scatterplot the points trend downward to the right.
Correlation is not causation: Two variables moving together does not prove one causes the other; a third factor may explain both.
Line of best fit (trend line): A straight line through scatterplot points that summarizes the trend, used to estimate and predict values.
Two-way (frequency) table: Organizes data by two categories in rows and columns. Read the correct row and column to find a count or a conditional rate.
Skewed data: Data with a long tail to one side. Right-skewed: mean > median; left-skewed: mean < median. The tail points toward the mean.
Positively (right) skewed: A distribution with a long right tail caused by a few large values. The mean is greater than the median.
Negatively (left) skewed: A distribution with a long left tail caused by a few small values. The mean is less than the median.
Symmetric distribution: A distribution where the two halves mirror each other; the mean and median are approximately equal.
Outlier: A value far from the rest of the data. Outliers strongly affect the mean and the range but barely move the median.
Quartiles: Three values (Q1, Q2/median, Q3) that split ordered data into four equal parts. Q1 is the 25th percentile, Q3 the 75th.
Interquartile range (IQR): Q3 − Q1, the spread of the middle 50% of the data. It resists outliers.
Box plot (box-and-whisker): Displays the five-number summary: minimum, Q1, median, Q3, and maximum. The box spans the IQR.
Percentile: The percent of data values at or below a given value. Scoring in the 80th percentile means you did as well as or better than 80% of test takers.
Sample vs population: A population is the entire group; a sample is the subset actually studied. A good sample is random and representative.
Random sample: A sample in which every member of the population has an equal chance of being chosen, reducing bias.
Biased sample: A sample that is not representative of the population, giving misleading results. A survey only of volunteers is biased.
Frequency: The number of times a value or category occurs in a data set. A frequency table lists each value with its count.
Relative frequency: A category's count divided by the total, often written as a fraction, decimal, or percent. It estimates probability.
Measures of center: Mean, median, and mode — each describes a 'typical' value differently. The best one depends on the shape of the data.
Measures of spread: Range, interquartile range, and standard deviation — they describe how spread out the data is.
Reading a graph's scale: Check the axis intervals before estimating values; gridlines may count by 2s, 5s, 10s, etc.
Misleading graph: A graph can distort data with a truncated axis, unequal intervals, or 3-D effects. Always read the actual numbers.
Expected value (long-run average): Multiply each outcome by its probability and add. The long-run average result of a repeated random process.
Probability with 'and replacement': Replacing the item keeps each draw independent, so probabilities stay the same and multiply.
Probability without replacement: Not replacing the item changes the totals, making draws dependent; recompute the probability for each later draw.
Combination vs permutation: A permutation counts ordered arrangements; a combination counts groups where order does not matter. 'Choosing 3' usually means a combination.
Probability of mutually exclusive events: Events that cannot happen together; their joint probability is 0, so P(A or B) = P(A) + P(B).
Interpreting a survey percentage: Apply the percent to the relevant total. If 30% of 250 students walk to school, that is 0.30 × 250 = 75 students.
Comparing two data sets: Compare both center (mean/median) and spread (range/standard deviation). Equal means can hide very different spreads.
Cumulative frequency: A running total of frequencies; each entry adds the previous counts. Used to find medians and percentiles.
Stem-and-leaf plot: Splits each value into a stem (leading digits) and a leaf (last digit) to show the distribution while keeping the data.
Probability scale: Probabilities range from 0 (impossible) to 1 (certain). 0.5 means equally likely to happen or not.
Sample space: The set of all possible outcomes of an experiment. For one die roll the sample space is {1, 2, 3, 4, 5, 6}.
Odds vs probability: Probability compares favorable outcomes to the total; odds compare favorable to unfavorable. Probability 1/4 is odds of 1 to 3.
Estimating from a circle graph: Multiply the slice's percent by the total. A 40% slice of a $2,000 budget is 0.40 × 2,000 =$ 800.
Trend in a line graph: A rising line shows increase, a falling line shows decrease, and a flat line shows no change over the interval.
Mean of a frequency table: Multiply each value by its frequency, add those products, and divide by the total frequency.
Bimodal data set: A data set with two values that tie for most frequent; it has two modes. The distribution shows two peaks.
Predicting from a line of best fit: Read the trend line at the desired x-value to estimate y. Extrapolating far beyond the data is unreliable.
Variable: A letter that represents an unknown or changing number, such as x or n in an expression or equation.
Algebraic expression: A combination of numbers, variables, and operations with no equals sign, such as 3x + 5.
Equation: A statement that two expressions are equal, containing an equals sign, such as 2x + 3 = 11.
Like terms: Terms with the same variable raised to the same power; only like terms can be combined. 3x and 5x combine to 8x.
Solving a one-step equation: Undo the operation on both sides. For x + 7 = 12, subtract 7: x = 5.
Solving a two-step equation: Undo addition/subtraction first, then multiplication/division. For 4x − 7 = 21: add 7 (4x = 28), divide by 4 (x = 7).
Solving equations with variables on both sides: Collect variables on one side and numbers on the other. 3(x + 2) = 5x − 4 → 3x + 6 = 5x − 4 → x = 5.
Inequality symbols: < less than, > greater than, ≤ less than or equal to, ≥ greater than or equal to.
Solving an inequality: Solve like an equation, with one rule: flip the inequality sign when you multiply or divide both sides by a negative number.
Inequality sign-flip rule: Multiplying or dividing by a negative reverses the inequality. −3x > 12 → x < −4 (sign flips).
Slope: The steepness of a line: rise over run, the change in y divided by the change in x. In y = mx + b, the slope is m.
Slope formula: For points (x₁, y₁) and (x₂, y₂): slope = (y₂ − y₁) ÷ (x₂ − x₁). Through (2, 3) and (6, 11): (11−3)/(6−2) = 2.
Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).
Y-intercept: The point where a line crosses the y-axis, where x = 0. In y = 2x + 5 the y-intercept is 5.
X-intercept: The point where a line crosses the x-axis, where y = 0. Set y = 0 and solve for x.
Slopes of horizontal and vertical lines: A horizontal line has slope 0; a vertical line has an undefined slope.
Parallel lines: Lines that never meet; they have equal slopes but different y-intercepts.
Perpendicular lines: Lines that meet at a right angle; their slopes are negative reciprocals (their product is −1).
System of equations: Two or more equations solved together; the solution is the point satisfying all of them — where the graphs intersect.
Substitution method: Solve one equation for a variable, substitute it into the other, and solve. Good when a variable is already isolated.
Elimination method: Add or subtract the equations to cancel one variable, then solve. Multiply an equation first if needed to match coefficients.
Evaluating an expression: Substitute the given value for the variable and simplify. For 3x + 4 when x = 5: 3(5) + 4 = 19.
Translating words to algebra: 'More than' is +, 'less than' is −, 'product' is ×, 'quotient' is ÷. 'Five less than twice a number' is 2x − 5.
Function: A rule that assigns exactly one output to each input. Written f(x); f(3) means evaluate the rule at x = 3.
Distributing then solving: Use the distributive property to clear parentheses before combining like terms. 2(x + 3) = 10 → 2x + 6 = 10 → x = 2.
Perimeter: The distance around a figure — the sum of all side lengths. A rectangle's perimeter is 2(length + width).
Area of a rectangle: length × width. A 9 cm by 4 cm rectangle has an area of 36 square centimeters.
Area of a triangle: ½ × base × height. A triangle with base 10 and height 6 has area ½ × 10 × 6 = 30 square inches.
Area of a circle: π × radius². With radius 5 and π ≈ 3.14, area ≈ 3.14 × 25 ≈ 79 square units.
Circumference of a circle: π × diameter (or 2 × π × radius). A circle with diameter 8 and π ≈ 3.14 has circumference ≈ 25 units.
Area of a parallelogram: base × height, where height is the perpendicular distance between the parallel sides.
Area of a trapezoid: ½ × (base₁ + base₂) × height — the average of the parallel sides times the height between them.
Volume of a rectangular prism (box): length × width × height. A 5 × 3 × 4 box has a volume of 60 cubic units.
Volume of a cylinder: π × radius² × height. A cylinder with radius 3 and height 4 has volume π × 9 × 4 = 36π cubic units.
Surface area: The total area of all faces of a 3-D figure, measured in square units. Add the areas of each face.
Pythagorean theorem: For a right triangle with legs a and b and hypotenuse c: a² + b² = c². A 3-4-5 triangle satisfies it (9 + 16 = 25).
Hypotenuse: The longest side of a right triangle, opposite the right angle. The Pythagorean theorem finds it from the two legs.
Types of triangles by sides: Equilateral (3 equal sides), isosceles (2 equal sides), scalene (no equal sides).
Types of triangles by angles: Acute (all angles < 90°), right (one 90° angle), obtuse (one angle > 90°).
Sum of a triangle's interior angles: Always 180°. If two angles are 50° and 60°, the third is 180° − 110° = 70°.

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By Career EmployerUpdated Jun 21, 2026

200+ free Praxis Core Math flashcards — 4 ways to study

Praxis Core Math Flashcard of the Day

The classic card. Do you know this one?

Click Study Flashcards above to open the flashcard hub — 200 Praxis Core Math cards you can flip, match, type, or quiz yourself on. Every card is drawn from the ETS Praxis Core Math (5733) content categories, so you study exactly what the test measures.^[1] Pair them with our free practice test and study guide.

Praxis Core Math is one of the 7 Praxis exams — explore our Praxis flashcards to compare and prep across the whole family.

Praxis Core Math Flashcard Study Modes

Most flashcard sites give you one thing: a card to flip. Ours has four modes so you can both learn the material and prove you know it — the difference between recognizing an answer and recalling it under exam pressure.

Flip (Study) — the classic card. Flip term ↔ definition, shuffle the deck, and mark each card “Got it” or “Still learning.”
Match (Game) — a timed game: pair each term to its definition as fast as you can. Great for cementing formulas, fraction rules, and statistics terms.
Type (Recall) — read the definition and type the term. Typing forces true active recall instead of passive recognition.
Quiz (Test) — multiple-choice questions generated from the cards, so you self-test exactly like exam day.

$Free Praxis Core Math flashcards from Career Employer — active recall for the ETS 5733 test$

Why Flashcards Work for the Praxis Core Math Test

Flashcards aren’t busywork — they’re built on active recall: pulling an answer out of memory strengthens it far more than re-reading notes. Pair that with spacing — short sessions across several days rather than one cram — and you retain more in less time.

The Praxis Core Math test rewards instant recall of fraction and percent rules, statistics definitions, and area and volume formulas.^[2] Spaced flashcards are the most efficient way to make that knowledge automatic. Used alongside our practice test and study guide, they turn review time into measurable progress.

Praxis Core Math Flashcards by Category

The cards are organized by the test’s three ETS content categories. Drill Number and Quantity first — it’s the largest share of the test — then the statistics definitions and the algebra and geometry formulas:^[1]

Praxis Core Math flashcards by content category
Content category	What the cards cover
Number and Quantity	Fractions, decimals, percents, ratios, factors, primes, GCF/LCM, exponents
Data, Statistics & Probability	Graphs and tables, mean/median/mode, range, spread, probability
Algebra & Geometry	Equations, inequalities, slope, perimeter, area, volume, triangles

How to Get the Most Out of These Flashcards

Lead with Number and Quantity. It’s about 36% of the test and underpins the rest — start with fractions, percents, and ratios.
Master the formulas. Use Match and Type to lock in area, volume, slope, percent change, and the Pythagorean theorem.
Use Type and Quiz, not just Flip. Recognizing the right answer is easy; recalling and choosing it under pressure is the real test.
Then prove it. When the cards feel easy, confirm with the full practice test — read every rationale before exam day.

Praxis Core Math Flashcards FAQ

Two hundred free Praxis Core Math (5733) flashcards, organized across all three ETS content categories — Number and Quantity, Data Interpretation and Representation/Statistics/Probability, and Algebra and Geometry. They're free with no account required.

References

1.ETS. “Praxis Core Academic Skills for Educators: Mathematics (5733).” ETS. ↑
2.ETS. “About The Praxis Tests — Core Academic Skills for Educators.” ETS. ↑

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