Pre-Algebra — Free Practice Questions, Study Guides & Mock Exams

Learn the essentials of Pre-Algebra. In compliance with U.S. Public School Curriculum.

Topics covered

• MCQ
• Parsons
• True/False
• Word Bank
• Fill in the Blank

Free Pre-Algebra study guides

• Variables and Expressions — See variables as movable number-parts, identify coefficients and constants, translate words, and evaluate expressions by substitution.
• Order of Operations — Treat every expression like a route: group, power, multiply or divide, then add or subtract—with equal-priority operations moving left to right.
• Properties of Operations — Use commutative, associative, identity, inverse, and distributive properties as legal moves that preserve value—and factor by running distribution backward.
• Powers and Exponents Basics — Read powers as compressed multiplication, expand factor chains, evaluate special exponents, and use parentheses to control negative-base scope.
• Solutions to Equations — Read equations as truth claims, test candidate solutions by substitution, and undo operations without breaking the balance.
• Coordinate Plane Basics — Navigate ordered pairs from the origin, identify quadrants, reflect points, measure axis-aligned distances, and read vertical and horizontal lines.
• Integers and Absolute Value — Use signed positions, opposites, and distance from zero to interpret integers and evaluate absolute-value expressions.
• Comparing and Ordering Integers — Compare signed values by number-line position, choose inequality symbols, and arrange integers in ascending or descending order.
• Adding Integers — Add signed integers with number-line movement, same- and different-sign rules, additive inverses, and zero pairs.
• Subtracting Integers — Rewrite integer subtraction as addition of the opposite, track sign changes, and apply signed-addition rules accurately.
• Multiplying Integers — Determine product signs from sign patterns and negative-factor parity, then multiply absolute values for magnitude.
• Dividing Integers — Divide signed integers by separating quotient size from sign, checking with multiplication, and handling zero safely.
• Integer Word Problems — Translate real-world direction into signed values by identifying the start, change, target, unit, and contextual meaning.
• Fractions and Decimals — Translate between fraction and decimal notation using division, place value, simplification, and repeating-tail cancellation.
• Comparing Rational Numbers — Compare and order fractions, decimals, and negative rational numbers using common forms, benchmarks, and number-line position.
• Adding and Subtracting Fractions — Add and subtract fractions by matching denominator units, finding least common denominators, regrouping mixed numbers, and simplifying.
• Multiplying and Dividing Fractions — Multiply fractions with area models and factor cancellation, divide with reciprocals, convert mixed numbers, and simplify results.
• Adding and Subtracting Decimals — Add and subtract decimals by aligning place-value columns, using placeholder zeros, regrouping accurately, and estimating for reasonableness.
• Multiplying and Dividing Decimals — Multiply decimals by counting place values, divide by making the divisor whole, use powers of ten, and estimate decimal placement.
• Writing Expressions — Translate verbal phrases into algebraic expressions by defining variables, matching operations, and preserving order.
• Simplifying with Distributive — Use area models and the distributive property to open grouped expressions, preserve signs, combine like terms, and factor in reverse.
• Combining Like Terms — Identify matching variable parts, sort terms by type, combine coefficients and constants, and preserve signs and exponents.
• One-Step Equations Add/Subtract — Solve one-step addition and subtraction equations with inverse operations, balanced changes, and substitution checks.
• One-Step Equations Multiply/Divide — Solve one-step multiplication and division equations by separating equal groups, applying inverse operations, and checking signs.
• Two-Step Equations — Solve two-step equations by reversing their operation order, balancing both sides, handling signed and fractional coefficients, and checking the original.
• Variables on Both Sides — Collect variable terms on one side, move constants to the other, solve, check, and classify no-solution or infinitely-many cases.
• Multi-Step Equations — Clean each side by distributing and combining like terms, then collect variables, isolate, classify special cases, and check the original.
• Inequalities and Their Graphs — Map inequality solution sets with open or closed boundaries, correct shade directions, tested values, and simple or compound number-line graphs.
• Solving One-Step Inequalities — Use inverse operations, preserve or reverse the comparison correctly, graph the complete solution set, and verify it with test values.
• Solving Multi-Step Inequalities — Solve multi-step inequalities with a four-station route: simplify, collect, isolate with the negative flip rule, then graph and check.
• Ratios — Compare quantities in the requested order, distinguish part-to-part from part-to-whole, and build or simplify equivalent ratios by scaling both terms.
• Rates and Unit Rates — Find and interpret unit rates by dividing to a denominator of one, preserving units, and comparing choices on the same per-one scale.
• Proportions — Set up and solve proportions by aligning matching quantities, using equal cross products, and verifying that both ratios describe the same comparison.
• Scale Drawings and Maps — Use drawing-to-actual proportions for maps, blueprints, and enlargements; align corresponding lengths, convert units, and check whether results should shrink or grow.
• Similar Figures — Prove figures are similar by matching corresponding vertices and angles, using one scale factor for every side pair, and distinguishing similarity from congruence.
• Indirect Measurement — Measure unreachable heights with similar triangles, shadow ratios, mirror sight lines, and reliable correspondence checks.
• Percents and Fractions — Translate fractions and percents through hundred grids, equivalent fractions, division, and benchmark values while preserving the exact amount.
• Percents and Decimals — Move between decimal and percent notation with place-value reasoning, one-whole size checks, and accurate multiply-or-divide-by-100 conversions.
• The Percent Proportion — Organize percent problems by assigning part, whole, and percent roles, aligning the two fractions, solving cross products, and checking size.
• The Percent Equation — Build and rearrange the percent equation, convert percent rates to decimals, and check every result with an estimate.
• Percent of Change — Measure percent increase and decrease from the original value, compare relative change, and avoid the new-value denominator trap.
• Discount — Calculate discounts, sale prices, tax, tips, markup, and commission from the correct base while separating change amounts from final totals.
• Functions — Understand the function promise, evaluate function notation, identify domain and range, and use the vertical-line test.
• Coordinate Plane — Read ordered pairs, plot exact points, identify quadrants and axes, and handle reflections and translations on the coordinate plane.
• Graphing Linear Equations — Turn true solutions into points, then press those points into one precise straight line.
• Slope — Survey rise and run, read direction, and distinguish zero slope from undefined slope.
• Slope-Intercept Form — Use a line launchpad to start at b, fly by m, and build or decode any slope-intercept graph.
• Solving Systems by Graphing — Graph both equations, identify their shared point, classify the system, and verify the solution in both equations.
• Scatter Plots — Read paired-data clouds by direction, strength, outliers, and lines of fit while separating association from causation.
• Powers and Exponents — Read bases and exponents as repeated multiplication, evaluate powers, handle zero and negative bases, and avoid multiplying the base by the exponent.
• Negative Exponents — Use reciprocals to rewrite negative exponents, evaluate powers, track signs, and keep every denominator defined.
• Multiplying and Dividing Monomials — Simplify monomial products and quotients by separating coefficient arithmetic from matching-base exponent rules.
• Powers of Monomials — Send every factor through the Power Press: raise coefficients, multiply exponent counts, track signs, and simplify powers of products and quotients.
• Scientific Notation — Focus significant digits into the coefficient window, track decimal travel with the exponent odometer, and verify scale before transmitting the answer.
• Square Roots — Build square areas from tiles, recover their nonnegative side lengths, and estimate non-perfect roots between exact square frames.
• The Real Number System — Navigate the real number system by classifying natural, whole, integer, rational, and irrational numbers from their fractions, decimals, and radicals.
• The Pythagorean Theorem — Build, identify, and solve right triangles with a² + b² = c².
• Distance on the Coordinate Plane — Build the hidden right triangle and find exact coordinate-plane distance.
• Special Right Triangles — Recognize 45-45-90 and 30-60-90 triangles, match each side to its ratio, and scale exact lengths with confidence.
• Trigonometric Ratios — Label right-triangle sides from a chosen angle, tune the correct SOH-CAH-TOA ratio, and avoid viewpoint and unit mistakes.
• Angle Relationships — Recognize complementary, supplementary, vertical, and adjacent angles, translate diagram clues into equations, and solve missing measures.
• Triangles — Classify triangles by angles and sides, solve missing angles, connect equal sides to equal angles, and test possible side lengths.
• Quadrilaterals — Navigate the quadrilateral family map using angle sums, parallel sides, equal sides, right angles, and the most specific supported classification.
• Polygons and Angles — Classify polygons, derive interior-angle sums from hidden triangles, connect interior and exterior angles, and solve backward for side count.
• Congruent and Similar Figures — Match corresponding parts, distinguish exact copies from scaled copies, calculate scale factors and missing sides, and track perimeter and area effects.
• Transformations — Translate, reflect, rotate, and dilate figures with coordinate rules, transformation invariants, scale factors, and ordered compositions.
• Three-Dimensional Figures — Classify prisms, pyramids, cylinders, cones, and spheres by bases and surfaces; count faces, edges, and vertices; and connect solids to nets and cross-sections.
• Volume of Prisms — Calculate prism volume using V = Bh; distinguish base area and perpendicular height; and solve rectangular, triangular, oblique, and composite cases with cubic units.
• Volume of Cylinders — Calculate cylinder volume with V = πr²h; distinguish radius from diameter, use perpendicular height, preserve exact π, reverse the formula, and reason about scaling and cubic units.
• Surface Area of Prisms — Calculate prism surface area by pairing faces or using SA = 2B + Ph; unfold nets, distinguish area from perimeter, handle triangular bases, openings, reverse problems, and square units.
• Surface Area of Cylinders — Build cylinder surface area from circular bases and an unrolled wrapper; convert diameter to radius, handle open containers, reverse the formula, convert units, scale dimensions, and report square units.
• Pyramids and Cones — Compare pyramids and cones with matching prisms and cylinders; use V = ⅓Bh, choose the correct base area and perpendicular height, reverse the formula, distinguish slant height, calculate surface area, and reason about scaling.
• Measures of Center — Choose and calculate mean, median, and mode; handle odd and even medians, no-mode and bimodal data, see how outliers pull the mean, and match each measure to the context.
• Measures of Variation — Measure data spread with range, quartiles, IQR, five-number summaries, and box plots; split odd and even data sets correctly, compare outlier sensitivity, and avoid confusing range with count.
• Displaying Data — Choose and interpret bar graphs, line plots, histograms, circle graphs, stem-and-leaf plots, box plots, and line graphs; connect each display to its question, calculate percent sections, and detect misleading scales.
• Probability of Simple Events — Define experiments, outcomes, sample spaces, and events; calculate simple probability as favorable over total equally likely outcomes; use complements, convert formats, and catch unequal-likelihood and counting traps.
• Probability of Compound Events — Map multi-stage outcomes with lists, tables, and trees; count with the multiplication principle; multiply independent and dependent paths, update without-replacement probabilities, and add disjoint winning routes.
• Counting Outcomes — Count complete outcomes with organized lists, tables, trees, and the fundamental counting principle; distinguish addition from multiplication, handle shrinking no-repeat choices, permutations, ranked slots, and repetition rules.
• Statistical Sampling — Judge whether a sample represents its population; compare census, random, systematic, convenience, and voluntary methods, diagnose bias, scale proportions, and state responsible population estimates.

Units

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11
• Chapter 12
• Chapter 13

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