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.
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