Pre Algebra
Pre-Algebra bridges arithmetic and formal algebra for grades 7-8 students, covering integer and rational number operations, exponents and roots, algebraic expressions, one- and two-step equations and inequalities, proportional reasoning, linear relationships, coordinate graphing, and intro geometry with the Pythagorean theorem.
80
Minutes
64
Questions
70/100
Passing Score
Who Should Take This
Ideal for grade 7-8 students who have mastered basic arithmetic and are preparing for Algebra I, as well as adult learners who want to shore up their algebra foundations. Participants should be comfortable with fraction and decimal arithmetic and are ready to work with variables, equations, and graphing for the first time.
Course Outline
1Integers and Rational Numbers 7 topics
Describe rational numbers as fractions p/q where q ≠ 0, place them on a number line, and compare their magnitudes using inequality symbols including negative fractions and mixed numbers
Apply the four operations to rational numbers including negative fractions and mixed numbers, applying sign rules for multiplication and division and finding common denominators for addition and subtraction
Apply absolute value in context, compute absolute value expressions including those with operations inside, and use absolute value to find the distance between two numbers on the number line
Analyze which properties (commutative, associative, distributive, identity, inverse, zero product) apply to a given computation and use them to simplify expressions and justify algebraic steps
Apply scientific notation to write very large and very small numbers as a product of a decimal (1 ≤ d < 10) and a power of ten, and perform multiplication and division in scientific notation
Apply operations on rational numbers in multi-step word problems involving budgets, temperature differences, elevation changes, and debits/credits, correctly interpreting the sign and magnitude of the result
Describe the concept of opposites and additive inverses, explain that a number and its opposite sum to zero, and apply this to simplify expressions and solve equations involving subtraction of negative numbers
2Exponents and Roots 5 topics
Describe exponents as repeated multiplication, evaluate integer powers including zero and negative exponents, and apply the exponent rules for products, quotients, and powers of powers
Apply square root notation to find exact roots of perfect squares from 1 to 225 and approximate non-perfect square roots to the nearest tenth using successive squaring
Apply cube root notation to evaluate cube roots of perfect cubes and approximate cube roots of non-perfect cubes, explaining the relationship between a³ and ∛a as inverse operations
Analyze the difference between rational and irrational numbers by locating examples like √2 and π on the number line and explaining why their decimal expansions neither terminate nor repeat
Apply prime factorization using exponent notation to express composite numbers as products of prime powers, compute GCF using minimum exponents and LCM using maximum exponents from prime factorizations
3Expressions and Order of Operations 7 topics
Describe algebraic expressions by identifying constants, variables, coefficients, and terms, and explain how a variable represents an unknown or changing quantity in a real-world context
Apply evaluation of algebraic expressions by substituting given values for variables and simplifying using order of operations including expressions with exponents and negative values
Apply the distributive property to expand expressions like a(b + c) = ab + ac and factor expressions by identifying the greatest common factor among terms and rewriting in factored form
Apply combining like terms to simplify polynomial expressions by adding or subtracting terms that share the same variable and exponent, and explain why unlike terms cannot be combined
Analyze whether two algebraic expressions are equivalent by substituting multiple values for the variable and explain how the distributive and commutative properties produce equivalent forms
Apply writing algebraic expressions from verbal descriptions including phrases like 'five more than twice a number' and 'the product of a number and seven decreased by four', translating each mathematical operation to the correct algebraic symbol
Analyze the difference between an expression and an equation — an expression has no equals sign and is simplified, while an equation has an equals sign and is solved — and explain why 'simplify' and 'solve' are different instructions
4Equations and Inequalities 8 topics
Describe equations as statements of equality and apply inverse operations to solve one-step equations involving addition, subtraction, multiplication, and division with rational number coefficients
Apply the two-step equation solving process by isolating the variable term first then dividing by its coefficient, verifying solutions by substitution, and writing equations from word problems
Apply multi-step equation solving by combining like terms or using the distributive property before isolating the variable, including equations with variables on both sides
Describe inequalities and their solution sets, apply the rule that multiplying or dividing by a negative number reverses the inequality symbol, and graph solutions on a number line
Apply one-step and two-step inequality solving with rational coefficients, write solution sets in inequality notation and interval notation, and graph on a number line with open and closed endpoints
Analyze word problems to write equations or inequalities, solve them, and verify that the answer satisfies the original constraints including checking units, sign, and reasonableness
Apply equation writing to geometry problems including finding unknown angle measures from supplementary/complementary relationships, perimeter formulas, and the triangle angle sum, setting up and solving the resulting one- or two-step equation
Describe literal equations as formulas with multiple variables and apply the technique of isolating a specified variable by performing inverse operations, with examples including solving A = lw for l and d = rt for t
5Ratio, Proportion, and Percent Applications 7 topics
Apply unit rates to solve consumer math problems including price per unit, calories per serving, miles per gallon, and pay per hour, and compare value using unit rate analysis
Apply proportion equations to solve scaling, map, and similar figure problems by setting up two equivalent ratios and solving for the unknown using cross-multiplication or equivalent fractions
Apply percent equations in the form part = percent × whole to calculate tax, tip, discount, markup, commission, and percent increase or decrease, identifying which quantity is unknown
Analyze direct and inverse proportional relationships by identifying whether y = kx or y = k/x fits tabular data, compute k, and predict values using the proportionality constant
Apply simple interest formula I = Prt to calculate interest earned, total amount owed, principal, rate, or time when the other three quantities are given in loan and savings account scenarios
Apply markup and markdown calculations including computing the selling price given cost and markup percentage, and the sale price given original price and markdown percentage, as multi-step percent applications
Analyze proportional reasoning in scale model and map problems by identifying the scale ratio, converting between scale distance and actual distance, and computing areas in scale models using the square of the scale factor
6Linear Relationships and Graphing 9 topics
Describe slope as the ratio of vertical change to horizontal change between two points on a line, compute slope from a graph, table, or two points, and interpret slope as a unit rate in context
Apply slope-intercept form y = mx + b to graph linear equations by plotting the y-intercept and using slope as rise over run, and identify m and b from the equation and their real-world meanings
Apply table-to-equation methods by identifying the rate of change and initial value in a table of values and writing the linear equation in slope-intercept form
Describe a function as a rule that assigns exactly one output to each input, represent functions using tables, graphs, and equations, and identify whether a mapping diagram represents a function using the vertical line test
Apply function notation f(x) to evaluate functions for given input values and interpret f(x) = y as stating the output y when the input is x in both abstract and real-world function contexts
Analyze whether a given representation (table, graph, or equation) shows a linear function, proportional function, or non-linear relationship, and explain the distinguishing features of each
Apply point-slope form y - y₁ = m(x - x₁) to write the equation of a line through a given point with a given slope, and convert between point-slope, slope-intercept, and standard form Ax + By = C
Describe parallel lines as having equal slopes and perpendicular lines as having slopes that are negative reciprocals, identify whether two lines are parallel, perpendicular, or neither from their equations
Apply the concept of domain and range to real-world function situations including identifying input and output variables, restricting domain to a meaningful context (e.g., time must be non-negative), and listing range values from a table
7Geometry with Algebra 9 topics
Apply angle relationship equations to find unknown angle measures including supplementary, complementary, vertical angles, and interior angles of triangles and quadrilaterals
Describe the Pythagorean theorem as a² + b² = c² relating the legs and hypotenuse of a right triangle, and explain why the theorem holds using area-based visual proofs
Apply the Pythagorean theorem to find missing side lengths of right triangles in geometric and real-world problems including ladder height, diagonal of a rectangle, and distance between two points
Apply the distance formula between two coordinate points by recognizing it as a Pythagorean theorem application, compute exact distances as simplified radicals, and approximate decimal values
Apply transformation descriptions to identify translations (slide), reflections (flip), rotations (turn), and dilations (scale), and determine whether a transformation preserves congruence or similarity
Analyze similar figures by identifying corresponding sides and angles, setting up proportions from similarity ratios, and solving for unknown lengths in similar triangles and polygons
Apply the midpoint and distance formulas on the coordinate plane to find the midpoint between two points and the exact distance using the Pythagorean theorem, applying both formulas in perimeter and design problems
Apply the formula for the area of composite figures by decomposing irregular shapes into non-overlapping standard shapes, computing each sub-area, and summing or subtracting as appropriate to find the total area
Analyze the effects of dimension changes on area and volume by applying the rules that doubling a side length multiplies area by 4 and volume by 8, and generalize this to scaling by any factor k
8Statistics and Data Analysis 8 topics
Apply measures of spread including range, interquartile range (IQR), and mean absolute deviation (MAD) to describe how spread out a data set is and identify data sets with greater or lesser variability
Apply five-number summary (minimum, Q1, median, Q3, maximum) to construct and interpret box-and-whisker plots, identifying outliers using the 1.5 × IQR rule
Apply scatter plot analysis by plotting bivariate data, drawing an approximate line of best fit, describing the direction and strength of the association, and using the line to make predictions
Analyze sampling methods including random, stratified, systematic, and convenience sampling, identify sources of sampling bias, and explain how sample size affects the reliability of statistical conclusions
Apply measures of central tendency and spread comparison across two data sets by computing mean, median, IQR, and MAD for each, and write a paragraph interpreting what the statistics say about the difference between the groups
Describe simple random sampling as each member of the population having an equal chance of selection, explain why a convenience sample of only online users underrepresents the full population, and identify how to improve a biased sampling design
Apply theoretical probability calculations for simple events using the formula P(event) = favorable outcomes / total outcomes, and compute probabilities for compound independent events by multiplying individual probabilities
Analyze misleading statistics and graphs in media reports by identifying cherry-picked time windows, truncated y-axes, and inappropriate comparisons, and reframe the data presentation to give a more accurate picture
Exam Structure
Question Types
- Multiple Choice
- Multiple Response
What's Included in AccelaStudy® AI
Adaptive Knowledge Graph
Practice Questions
Lesson Modules
Console Simulator Labs
Exam Tips & Strategy
72 Activity Formats
Scope
Included Topics
- Integer operations review and extension, rational numbers (fractions, decimals, mixed numbers on the number line), square roots and perfect squares, cube roots, integer exponents, scientific notation, order of operations with variables, writing and evaluating algebraic expressions, one-step and two-step equations, one-step and two-step inequalities, ratio and proportion review, percent applications (tax, discount, markup, percent change), coordinate plane with linear relationships, slope as rate of change, graphing linear equations, introduction to functions as input-output relationships, basic geometric relationships with algebra (angle equations, Pythagorean theorem), introduction to transformations (translations, rotations, reflections, dilations)
Not Covered
- Multi-variable systems of equations (covered in Algebra I/II)
- Quadratic functions and factoring (covered in Algebra I/II)
- Trigonometric ratios (covered in Geometry and Trigonometry)
- Formal proof-based geometry (covered in Geometry)
- Statistical inference beyond data description (covered in Statistics)
Official Exam Page
Learn more at Mathematics
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