Comparing amounts across categories

Parts of a whole (the slices add to 100%)

The shape of grouped numerical data

The relationship/correlation between two variables

How long is the Praxis Core Math test?

You have 90 minutes for the 56 questions — about 96 seconds per question on average. The test is delivered on computer in one section, so you can move forward and back and flag questions to revisit.

What is a passing score on the Praxis Core Math (5733)?

Praxis Core Math is reported on a scaled score of 100–200. The most commonly cited qualifying score is 150, but the official passing score is set by each individual state, agency, or teacher-preparation program — always confirm the requirement where you plan to be certified.

Can you use a calculator on the Praxis Core Math test?

Yes. An on-screen four-function calculator is provided within the test for every question. You may not bring your own calculator; the built-in tool is the only one allowed.

What topics are on the Praxis Core Math (5733)?

Three content categories: Number and Quantity (about 36%) — fractions, decimals, percents, ratios, and number properties; Data Interpretation and Representation, Statistics, and Probability (about 32%) — graphs, mean/median/mode, spread, and probability; and Algebra and Geometry (about 32%) — equations, inequalities, lines, area, volume, and triangles.

How hard is the Praxis Core Math test?

The math is roughly high-school level — arithmetic, basic statistics, beginning algebra, and geometry — with no trigonometry or calculus. Most test-takers find the challenge is pacing and avoiding careless errors rather than advanced content. Steady, mixed practice with full review of every miss is the most reliable way to pass.

How should I use this Praxis Core Math study guide?

Work through the three content categories in order — Number and Quantity, then Data and Statistics, then Algebra and Geometry. After each module take the checkpoint quiz to find gaps, then drill that category with our free practice questions and flashcards, and revisit flagged sections before test day.

Is this Praxis Core Math study guide free?

Yes — the full guide, the checkpoints, the glossary, the practice questions, and the flashcards are 100% free, with no account required.

Is the Praxis Core Math the same as the combined Core test?

The Mathematics test (5733) is one of three Praxis Core Academic Skills for Educators tests, alongside Reading (5713) and Writing (5723). You can take it on its own or as part of the combined Core (5752) battery, depending on what your program or state requires.

How do you add or subtract fractions with different denominators?

Find a common denominator (often the least common multiple of the two denominators), rewrite each fraction with it, then add or subtract the numerators and keep the denominator. For 3/4 + 5/6, the common denominator is 12: 9/12 + 10/12 = 19/12. This is a Number and Quantity skill. The denominators must match before you combine the numerators — only the tops are added or subtracted. Always simplify the result, and convert an improper fraction to a mixed number if the question asks for one.

How do you divide fractions?

Multiply by the reciprocal of the second fraction — keep, change, flip. Keep the first fraction, change division to multiplication, and flip the second. So 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8. This is a Number and Quantity skill. Dividing by a fraction is the same as multiplying by its reciprocal (multiplicative inverse). A quick check: dividing by a number less than 1 makes the result larger, which is why 3/4 ÷ 2/5 is greater than 3/4.

How do you calculate percent change?

Percent change equals the change divided by the original amount, times 100. If a value rises from 80 to 100, the change is 20, so the increase is 20 ÷ 80 = 25%. Always divide by the starting value, not the new one. Percentages, ratios, and rates are core Number and Quantity skills. A common error is dividing by the new value instead of the original. To increase a number by 25%, multiply by 1.25; to decrease by 25%, multiply by 0.75.

What is the difference between the greatest common factor and the least common multiple?

The greatest common factor (GCF) is the largest number that divides two values evenly — GCF of 48 and 60 is 12. The least common multiple (LCM) is the smallest number both divide into — LCM of 8 and 12 is 24. GCF splits things into equal groups; LCM lines up repeating events. These are Number and Quantity skills. Use the GCF for 'identical kits using all items' problems and the LCM for 'when do they coincide again' problems. Prime factorization makes both quick: the GCF takes the lowest shared powers, the LCM the highest.

How do you solve a proportion?

Set the two ratios equal and cross-multiply: for a/b = c/d, a × d = b × c. To solve 2/3 = x/12, cross-multiply to get 3x = 24, so x = 8. Proportions handle scaling, unit conversions, and similar-figure problems. Ratios and proportional reasoning are core Number and Quantity skills. Keep the units in the same position (top and bottom) on both sides. A unit rate is just a proportion with a denominator of 1 — found by dividing.

What is the difference between the mean and the median?

The mean is the average — add all values and divide by how many there are. The median is the middle value when the data is ordered. The median resists outliers, so for skewed data like incomes or home prices it better represents a typical value than the mean. Measures of center are core Statistics skills. An extreme value pulls the mean toward it but barely moves the median. On a right-skewed data set the mean is greater than the median; on a left-skewed set it is less.

How do you find the probability of two independent events both happening?

For independent events — where one outcome does not affect the other — multiply their probabilities. If P(A) = 0.6 and P(B) = 0.8, then P(A and B) = 0.6 × 0.8 = 0.48. Each probability is a value from 0 (impossible) to 1 (certain). Probability is a core Statistics and Probability skill. 'And' for independent events means multiply; 'or' means add and subtract the overlap. The complement rule helps too: P(not A) = 1 − P(A).

What does standard deviation tell you?

Standard deviation measures how spread out data is around its mean. A small standard deviation means values cluster close to the mean; a large one means they are widely spread. A standard deviation of zero means every value in the set is identical. Measures of spread are a core Statistics topic, alongside the range and interquartile range. Two data sets can share the same mean yet have very different standard deviations — always compare both center and spread.

How do you read a scatterplot and describe correlation?

A scatterplot plots paired data as points to show how two variables relate. If the points trend upward to the right, the variables have a positive correlation; downward to the right is negative. A correlation, though, does not by itself prove that one variable causes the other. Interpreting graphs is a core Data Interpretation skill. A line of best fit summarizes the trend and lets you estimate values. Remember: correlation is not causation — a hidden third factor may drive both variables.

How do you find the slope of a line?

Slope is rise over run — the change in y divided by the change in x between two points: (y₂ − y₁) ÷ (x₂ − x₁). Through (2, 3) and (6, 11), the slope is (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2. In y = mx + b, the slope is m. Slope is one of the most important Algebra ideas. Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals. A horizontal line has slope 0; a vertical line has an undefined slope.

How do you solve a two-step linear equation?

Undo the operations in reverse order: clear addition or subtraction first, then multiplication or division. For 4x − 7 = 21, add 7 to both sides to get 4x = 28, then divide by 4 to get x = 7. Whatever you do to one side, do to the other. Solving linear equations is a core Algebra skill. The goal is to isolate the variable on one side. When the variable appears on both sides, collect the variable terms on one side and the constants on the other first.

When do you flip the sign while solving an inequality?

Solve an inequality just like an equation, with one rule: reverse the inequality symbol whenever you multiply or divide both sides by a negative number. So −3x > 12 becomes x < −4 — the sign flips when you divide by −3. This is a core Algebra skill. Adding or subtracting never flips the sign; only multiplying or dividing by a negative does. A common error is solving correctly but forgetting to reverse the symbol — a frequent trap on the test.

What is the Pythagorean theorem and when do you use it?

For a right triangle with legs a and b and hypotenuse c, a² + b² = c². Use it to find a missing side when you know the other two. A 3-4-5 triangle works because 3² + 4² = 9 + 16 = 25 = 5². The hypotenuse is always the longest side, opposite the right angle. This is a core Geometry skill. It applies only to right triangles — those with a 90° angle. Memorize common Pythagorean triples (3-4-5, 5-12-13) to recognize answers quickly.

How do you find the area of a circle?

The area of a circle is π times the radius squared: A = π × r². With a radius of 5 and π ≈ 3.14, the area is about 3.14 × 25 ≈ 79 square units. The circumference (distance around) is 2 × π × r, or π times the diameter. Area and perimeter are core Geometry skills. The 5733 does not give a formula sheet, so know these by heart. Watch the difference between radius and diameter — the diameter is twice the radius.

How do you find the volume of a rectangular box?

The volume of a rectangular prism (box) is length × width × height, measured in cubic units. A box that is 5 cm long, 3 cm wide, and 4 cm tall has a volume of 5 × 3 × 4 = 60 cubic centimeters. Volume is a core Geometry skill. Volume uses cubic units; area uses square units — keep them straight. For a cylinder, the volume is the circle's area times the height: π × r² × height.

What is the correct order of operations?

PEMDAS: Parentheses, Exponents, then Multiplication and Division left to right, then Addition and Subtraction left to right. Multiplication and division share a rank, as do addition and subtraction — work each pair from left to right, not strictly one before the other. Order of operations underlies almost every Number and Quantity computation. Misreading it is a frequent careless error. Inside parentheses, the same order applies — work from the innermost grouping outward.

The Praxis Core Academic Skills for Educators tests — Reading (5713), Writing (5723), and Mathematics (5733) — used by many teacher-preparation programs and states to certify basic academic skills.

The ETS code for the current Praxis Core Academic Skills for Educators: Mathematics test, a 56-question, 90-minute computer-delivered test.

Question formats where you choose or enter an answer: single-select multiple choice, multiple-select (choose all that apply), and numeric entry. The 5733 has no essay.

A converted score on a 100–200 scale. 150 is the most commonly cited qualifying score, but each state or program sets its own required cut score.

A whole number greater than 1 with exactly two distinct factors, 1 and itself (2, 3, 5, 7, 11...). The number 1 is not prime.

A whole number greater than 1 with more than two factors, such as 4, 6, 9, or 12.

Greatest common factor (GCF)

The largest factor shared by two or more numbers. The GCF of 48 and 60 is 12.

Least common multiple (LCM)

The smallest multiple shared by two or more numbers. The LCM of 8 and 12 is 24.

The multiplicative inverse of a number — flip the fraction. The reciprocal of 2/5 is 5/2; dividing by a fraction means multiplying by its reciprocal.

The change in a quantity divided by its original value, times 100. Always divide by the starting amount.

A comparison of two quantities, written 3:5, 3 to 5, or 3/5.

An equation stating that two ratios are equal, such as 2/3 = x/12; solve by cross-multiplying.

PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

The average — the sum of the values divided by how many there are.

The middle value of an ordered data set; it resists outliers.

The value that appears most often in a data set; a set can have no mode or more than one.

The largest value minus the smallest value in a data set.

A measure of how spread out data is around its mean; larger means more spread, zero means all values are equal.

A value far from the rest of the data; it strongly affects the mean and range but barely moves the median.

The chance an event occurs, written as favorable outcomes ÷ total outcomes, a value from 0 (impossible) to 1 (certain).

Events where one outcome does not affect the other; their probabilities multiply.

FREE Praxis Core Math Study Guide 2026 + Readiness Score

This free Praxis Core Math study guide teaches to the — every content category the test measures, organized the way ETS builds the exam.^[1] The Mathematics test is one of three tests (with Reading and Writing) that many states and teacher-preparation programs require.^[2]

The math here is roughly high-school level — fractions, percents, basic statistics, beginning algebra, and geometry, with notrigonometry or calculus. It’s interactive, not a wall of text: every category has a built-in checkpoint quiz, hover-able glossary terms, worked examples, and concept questions, so you learn by doing.

Read this guide category by category, test yourself at each checkpoint, then round out your free Praxis Core Math prep with our practice questions and flashcards.

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

Praxis Core Math (5733) Exam Snapshot

Praxis Core Math (5733) at a glance (2026)
Detail	Praxis Core Mathematics (5733)
Questions	56 selected-response (multiple choice, multiple-select, numeric entry)
Time	90 minutes, one section
Format	Computer-delivered; no essay
Calculator	On-screen four-function calculator provided (no personal calculator)
Score scale	100–200 (scaled)
Qualifying score	150 commonly cited; the official cut score is set by each state/program
Content categories	Number & Quantity · Data, Statistics & Probability · Algebra & Geometry
Part of	Praxis Core (with Reading 5713 and Writing 5723)
Publisher	ETS

How the Praxis Core Math (5733) is built

One untimed test section of 56 questions in 90 minutes, delivered on computer with a built-in calculator.

56 selected-response questionsSingle-select multiple choice, multiple-select, and numeric-entry questions across three content categories.
90 minutes of testingAbout 96 seconds per question on average. Pace yourself and flag hard ones to return to.
On-screen four-function calculatorProvided inside the test for every question. No personal calculator is allowed.
Scaled score 100–200Your raw score is converted to a 100–200 scale. 150 is the most commonly cited qualifying score, but each state or program sets its own cut score.

Praxis Core Math is one of three Core Academic Skills tests (with Reading and Writing). You can take it on its own or as part of the combined Core test.

Because Number and Quantity is the largest category — about a third of the test — fraction, percent, and ratio fluency pays off most.^[3] Spend your study time across all three categories, but build arithmetic confidence first:

Praxis Core Math content categories (2026 approximate shares)

Number and Quantity36% · ~36% · ≈20 questions

Data, Statistics & Probability32% · ~32% · ≈18 questions

Algebra & Geometry32% · ~32% · ≈18 questions

Praxis Core Math content categories (2026 shares)

Number & Quantity

~36%≈20 Q

Data, Statistics & Probability

~32%≈18 Q

Algebra & Geometry

~32%≈18 Q

Number & Quantity is the single largest category — about a third of the test — so build fraction, percent, and ratio fluency first.

ETS reports category shares as approximate ranges, so the exact mix shifts slightly each form.^[3] This guide teaches all three content categories — Number and Quantity first, then Data and Statistics, then Algebra and Geometry — as three study modules.

1 · Number and Quantity

About 36% of the test — the single largest category. This is arithmetic done well: fractions and decimals, percents and ratios, number properties, exponents and roots, and estimation. Get fluent here and you bank the most points.^[3]

Fractions, Decimals & Operations

To add or subtract fractions, use a common denominator; to multiply, multiply across; to divide, multiply by the (keep–change–flip). Convert freely among fractions, decimals, and percents.

The four fraction operations
Operation	Rule	Example
Add / subtract	Common denominator, then add/subtract numerators	3/4 + 5/6 = 9/12 + 10/12 = 19/12
Multiply	Multiply numerators and denominators, simplify	2/3 × 9/10 = 18/30 = 3/5
Divide	Multiply by the reciprocal (keep–change–flip)	3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8
Convert	Fraction → decimal by dividing top by bottom	3/4 = 3 ÷ 4 = 0.75 = 75%

Percents, Ratios & Proportions

A is the change divided by the original value, times 100. Set up a for ratio, rate, and scaling problems and solve by cross-multiplying.

Factors, Primes, GCF & LCM

A has exactly two factors; the number 1 is not prime. The splits items into the largest equal groups, and the tells you when repeating events line up again.

GCF vs LCM — which to use
Tool	What it finds	Word-problem signal
GCF	Largest factor two numbers share (48 & 60 → 12)	Identical kits/groups using ALL items
LCM	Smallest multiple two numbers share (8 & 12 → 24)	When two cycles coincide AGAIN

Exponents, Roots & Estimation

Know the exponent rules and how to estimate a root, and use rounding to check that an answer is reasonable.

Exponent and root rules you should know cold
Rule	Statement
Product of powers	$x^m \cdot x^n = x^{m+n}$
Quotient of powers	$x^m \div x^n = x^{m-n}$
Power of a power	$(x^m)^n = x^{mn}$
Zero exponent	$x^0 = 1$ (for $x \neq 0$ )
Negative exponent	$x^{-n} = \dfrac{1}{x^n}$

Order of operations — PEMDAS

PParenthesesDo everything inside grouping symbols first.
EExponentsThen powers and roots.
MDMultiply / DivideLeft to right, whichever comes first.
ASAdd / SubtractLeft to right, whichever comes first.

Multiplication and division share a rank (left to right), and so do addition and subtraction — they are not strictly “multiply before divide.”

Checkpoint · Category 1 · Number & Quantity

Question 1 of 10

Which of the following numbers is prime?

2 · Data, Statistics & Probability

About 32% of the test. Reading graphs and tables, the measures of center and spread, interpreting distributions, and basic probability.^[3]

Reading Graphs & Tables

Know what each display is for and always read the scale before estimating a value. A circle (pie) graph shows parts of a whole; a bar graph compares categories; a line graph shows change over time; a scatterplot shows the relationship between two variables.

Which graph shows what
Display	Best for
Bar graph	Comparing amounts across categories
Line graph	Showing a trend over time
Circle (pie) graph	Parts of a whole (the slices add to 100%)
Histogram	The shape of grouped numerical data
Scatterplot	The relationship/correlation between two variables

Mean, Median & Mode

The three measures of center each describe a “typical” value differently. The is the average, the is the middle value, and the is the most frequent value.

Measures of center
Measure	How to find it	Note
Mean	Add the values, divide by the count	Pulled by outliers
Median	Middle value of ordered data (average two if even count)	Resists outliers
Mode	Value that occurs most often	Can be none or several

Range, Spread & Skew

The (largest minus smallest) and the (spread around the mean) describe how scattered the data is. An stretches the range and the mean but barely moves the median.

Probability

is favorable outcomes divided by total outcomes, a value from 0 to 1. For two , multiply the probabilities.

Checkpoint · Category 2 · Data, Statistics & Probability

Question 1 of 10

A histogram shows the frequency distribution of the weights of 60 cats. If the mean weight is 10 pounds and the median weight is 9 pounds, which of the following is true about the distribution?

3 · Algebra & Geometry

About 32% of the test. Solving equations and inequalities, working with lines and the coordinate plane, and the core geometry of perimeter, area, volume, and triangles.^[3]

Equations & Inequalities

Solve a linear equation by undoing operations in reverse order until the variable is alone. Solve an the same way, with one rule: flip the symbol when you multiply or divide by a negative.

Slope, Lines & the Coordinate Plane

is rise over run. Between two points it is $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ . In $y = mx + b$ , $m$ is the slope and $b$ is the .

Perimeter, Area & Volume

is the distance around a figure, is the surface it covers (square units), and is the space it fills (cubic units). The 5733 gives no formula sheet, so memorize the workhorses:

Area, perimeter & volume formulas to know cold

RectangleArea = length × widthPerimeter = 2(l + w)

TriangleArea = ½ × base × heightAngles sum to 180°

CircleArea = π × r²Circumference = 2 × π × r

Rectangular boxVolume = length × width × heightSurface area = 2(lw + lh + wh)

CylinderVolume = π × r² × heightUse the on-screen calculator for π

The 5733 does not give a formula sheet — memorize these few workhorses so you can apply them quickly.

Triangles & the Pythagorean Theorem

A triangle’s interior angles sum to 180°. The $a^2 + b^2 = c^2$ relates the legs and the of a right triangle.

The Pythagorean theorem — a² + b² = c²

Legs
a and b form the right angle

Hypotenuse
c is opposite the right angle (longest)

3-4-5 triangle
9 + 16 = 25, so 3² + 4² = 5²

Given two sides of a right triangle, the theorem finds the third: a² + b² = c².

Recognize the common Pythagorean triples — 3-4-5 and 5-12-13 — and their multiples, so you can spot a missing side without computing.

Checkpoint · Category 3 · Algebra & Geometry

Question 1 of 10

What is the area of a rectangle that is 9 centimeters long and 4 centimeters wide?

How to Use This Study Guide

A study guide is a map, not the whole territory — use it alongside the official ETS Praxis materials and our free tools. Because the 5733 rewards steady accuracy under a 90-minute clock, spaced, mixed practice beats one long cram. Lead with — it’s the largest category and underpins the rest — then layer in statistics, algebra, and geometry.

A study loop that actually works

1
Read a category here
Work through one content category at a time — Number & Quantity, then Data & Statistics, then Algebra & Geometry.
2
Take the checkpoint
The quick check at the end of each category exposes what didn't stick.
3
Drill the gaps
Send your weak category straight into the free practice questions and flashcards.
4
Take full, timed practice
Sit a full timed set to build pacing for 56 questions in 90 minutes, then review every miss.

Praxis Core Math Concept Questions

Common math skills the Praxis Core Math test actually measures — at least one per content category. Tap any card for a short, exam-ready answer backed by an official source (ETS), then test yourself on them as flashcards.

Praxis Core Math Glossary

Quick definitions for the terms you’ll see most across the Praxis Core Math (5733) test:

Area: The amount of surface a 2-D figure covers, measured in square units (rectangle = length × width).
Composite number: A whole number greater than 1 with more than two factors, such as 4, 6, 9, or 12.
Greatest common factor (GCF): The largest factor shared by two or more numbers. The GCF of 48 and 60 is 12.
Hypotenuse: The longest side of a right triangle, opposite the right angle.
Independent events: Events where one outcome does not affect the other; their probabilities multiply.
Inequality: A statement comparing two quantities with <, >, ≤, or ≥. Flip the symbol when you multiply or divide by a negative.
Least common multiple (LCM): The smallest multiple shared by two or more numbers. The LCM of 8 and 12 is 24.
Mean: The average — the sum of the values divided by how many there are.
Median: The middle value of an ordered data set; it resists outliers.
Mode: The value that appears most often in a data set; a set can have no mode or more than one.
Order of operations: PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
Outlier: A value far from the rest of the data; it strongly affects the mean and range but barely moves the median.
Percent change: The change in a quantity divided by its original value, times 100. Always divide by the starting amount.
Perimeter: The total distance around a figure — the sum of its side lengths.
Praxis Core: The Praxis Core Academic Skills for Educators tests — Reading (5713), Writing (5723), and Mathematics (5733) — used by many teacher-preparation programs and states to certify basic academic skills.
Prime number: A whole number greater than 1 with exactly two distinct factors, 1 and itself (2, 3, 5, 7, 11...). The number 1 is not prime.
Probability: The chance an event occurs, written as favorable outcomes ÷ total outcomes, a value from 0 (impossible) to 1 (certain).
Proportion: An equation stating that two ratios are equal, such as 2/3 = x/12; solve by cross-multiplying.
Pythagorean theorem: For a right triangle with legs a and b and hypotenuse c, a² + b² = c².
Range: The largest value minus the smallest value in a data set.
Ratio: A comparison of two quantities, written 3:5, 3 to 5, or 3/5.
Reciprocal: The multiplicative inverse of a number — flip the fraction. The reciprocal of 2/5 is 5/2; dividing by a fraction means multiplying by its reciprocal.
Scaled score: A converted score on a 100–200 scale. 150 is the most commonly cited qualifying score, but each state or program sets its own required cut score.
Selected-response: Question formats where you choose or enter an answer: single-select multiple choice, multiple-select (choose all that apply), and numeric entry. The 5733 has no essay.
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-intercept form: The linear equation y = mx + b, where m is the slope and b is the y-intercept.
Standard deviation: A measure of how spread out data is around its mean; larger means more spread, zero means all values are equal.
Test code 5733: The ETS code for the current Praxis Core Academic Skills for Educators: Mathematics test, a 56-question, 90-minute computer-delivered test.
Volume: The space a 3-D figure occupies, measured in cubic units (box = length × width × height).
Y-intercept: The point where a line crosses the y-axis, where x = 0.

Free Praxis Core Math Study Materials & Resources

Everything you need to prepare for the Praxis Core Math test is free here — no paywall, no sign-up. This guide is the foundation; pair it with the rest of our free Praxis Core Math study materials for active recall, timed practice, and last-minute review:

Praxis Core Math Practice Test — exam-style questions across all three content categories, with explanations.
Praxis Core Math Flashcards — active-recall decks for the high-yield arithmetic, statistics, algebra, and geometry facts.

Praxis Core Math Study Guide FAQ

The Praxis Core Academic Skills for Educators: Mathematics test (5733) has 56 selected-response questions — a mix of single-select multiple choice, multiple-select, and numeric-entry items. There is no essay; it is entirely selected-response.

References

1.ETS. “Praxis Core Academic Skills for Educators: Mathematics (5733).” ETS. ↑
2.ETS. “About The Praxis Tests — Core Academic Skills for Educators.” ETS. ↑
3.ETS. “Praxis Core Academic Skills for Educators — Tests at a Glance.” ETS. ↑
4.ETS. “Praxis Tests — Scores and Score Reporting.” ETS. ↑
5.ETS. “Praxis Core — How the Tests Are Scored.” ETS. ↑

Sources for the concept answers

Every answer in the Praxis Core Math concept questions above is drawn from an official primary source:

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