Praxis 5272 cheat sheet

The exam covers three areas: number and operations, algebraic thinking, and geometry and measurement with data; know which area each item targets before computing.

Number and operations items test place value, factors and multiples, integer and rational operations, and proportional reasoning rather than long computation alone.

Algebraic thinking includes patterns, expressions, equations, inequalities, and functional relationships; expect items requiring interpretation of representations, not only solving.

Geometry and measurement includes angle relationships, area and volume formulas, coordinate geometry, and unit conversion within and across customary and metric systems.

Data items require reading and comparing displays (dot plots, histograms, box plots, scatter plots) and choosing appropriate measures of center and spread.

Show work on constructed-response items: a correct answer with no supporting reasoning may earn partial credit, and a reasoning error with consistent work may earn partial credit.

Multiple-choice items are scored without penalty for guessing, so answer every item; eliminate clearly wrong options first.

Calculator use is permitted, but verify order of operations and unit labels because most errors on calculator items come from entry or labeling, not arithmetic.

The eight Standards for Mathematical Practice frame process items: persevering, reasoning, constructing arguments, modeling, using tools, attending to precision, using structure, and repeated reasoning.

A modeling cycle is: identify quantities in a real context, formulate a representation, compute, interpret results in context, then validate or revise the model.

Proportional reasoning decision rule: two quantities are proportional only if their ratio is constant and the graph passes through the origin.

Distinguish additive from multiplicative comparison: "how many more" is subtraction; "how many times as many" is division or scaling.

Justification items require a general argument, not a single example; one counterexample disproves a general claim.

Estimation and reasonableness checks belong in explanations: state why an answer is plausible given the magnitudes involved.

When comparing strategies, name the property or structure used (distributive, commutative, associative, inverse) rather than describing steps vaguely.

Precision items penalize rounding too early; carry exact values through intermediate steps and round only at the end.

Order of operations: grouping symbols, exponents, multiplication and division left to right, addition and subtraction left to right.

Divisibility rules: 3 and 9 by digit sum; 4 by last two digits; 8 by last three digits; 6 requires divisibility by both 2 and 3.

Fraction division rule: a/b ÷ c/d = a/b × d/c; interpret as "how many groups of c/d are in a/b."

Percent change = (new − old)/old × 100; successive percent changes do not add, they multiply as factors.

Unit rate comparison: convert to a common unit before comparing; the better buy has the lower cost per unit.

Integer rules: product or quotient is negative for an odd number of negative factors and positive for an even number.

Scientific notation: a × 10^n where 1 ≤ |a| < 10; multiplying adds exponents, dividing subtracts them.

Rational versus irrational: a decimal that terminates or repeats is rational; non-repeating, non-terminating decimals such as √2 or π are irrational.

Slope = (y2 − y1)/(x2 − x1); slope-intercept form y = mx + b; point-slope form y − y1 = m(x − x1).

Parallel lines have equal slopes; perpendicular lines have slopes whose product is −1 (negative reciprocals).

Solving linear equations: apply inverse operations to both sides; check by substitution because extraneous or sign errors are common.

A system of two linear equations has one solution when slopes differ, none when slopes are equal and intercepts differ, and infinitely many when the equations are equivalent.

Distributive property a(b + c) = ab + ac underpins factoring and expanding; watch signs when subtracting a binomial.

Inequalities: multiplying or dividing both sides by a negative number reverses the inequality symbol.

Function notation f(x) means the output for input x; a relation is a function if each input has exactly one output (passes the vertical line test).

Exponential growth is y = a(1 + r)^t and decay is y = a(1 − r)^t, where r is the rate per period and t the number of periods.

Triangle angle sum is 180°; exterior angle equals the sum of the two remote interior angles.

Area formulas: triangle ½bh, parallelogram bh, trapezoid ½(b1 + b2)h, circle πr²; circumference is 2πr.

Volume: prism or cylinder Bh; pyramid or cone ⅓Bh; sphere (4/3)πr³. Surface area sums the areas of all faces.

Pythagorean theorem a² + b² = c² applies only to right triangles; the converse tests whether a triangle is right.

Similar figures have equal corresponding angles and proportional sides; scale factor k multiplies lengths by k, area by k², volume by k³.

Mean is affected by outliers; median and mode are resistant. Range = max − min; interquartile range = Q3 − Q1.

Probability of a compound independent event is the product of individual probabilities; mutually exclusive events add.

Metric conversions use powers of ten (kilo-, centi-, milli-); customary conversions to know include 12 in = 1 ft, 3 ft = 1 yd, 16 oz = 1 lb, 1 gal = 4 qt.