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Contemplanda

Core mathematics

Algebra 1

A full first year of algebra, from linear equations to quadratics, with answers you build on a graph.

10 units · 69 lessons · 559 practice items

Algebra 1 covers a full first year of algebra across ten units. You start with expressions and the real numbers, then solve linear equations, inequalities, and systems. From there the course builds through functions, exponents and exponential growth, polynomials and factoring, and quadratic equations, and closes with radical and rational expressions and a unit on data analysis and statistics. Each unit rests on the algebra the earlier ones established.

This is the course where the constructed formats do the most work: you place points, shade the solution set of an inequality, transform a function, or fit a line to a scatter of data, so an answer is something you produce rather than pick. Three quarters of the problems carry hints.

Syllabus

Every published lesson in this course, by unit.

Expressions, variables, and the real numbers6 lessons
  1. 1Variables and expressions
  2. 2Order of operations
  3. 3The real numbers
  4. 4Operations with rational numbers
  5. 5Properties of real numbers
  6. 6Evaluating and translating expressions
Linear equations and inequalities7 lessons
  1. 1Solving one- and two-step equations
  2. 2Multi-step equations and special cases
  3. 3Literal equations and formulas
  4. 4Absolute-value equations
  5. 5Linear inequalities
  6. 6Compound inequalities
  7. 7Absolute-value inequalities
Functions and linear functions7 lessons
  1. 1Relations and functions
  2. 2Function notation and evaluation
  3. 3Domain, range, and interval notation
  4. 4Slope as rate of change
  5. 5Slope-intercept and point-slope forms
  6. 6Graphing linear equations
  7. 7Linear models
Systems of linear equations and inequalities7 lessons
  1. 1Solving systems by graphing
  2. 2Solving systems by substitution
  3. 3Solving systems by elimination
  4. 4Special systems and choosing a method
  5. 5Applications of linear systems
  6. 6Linear inequalities in two variables
  7. 7Systems of linear inequalities
Exponents and exponential functions7 lessons
  1. 1Product and power properties of exponents
  2. 2Quotient and negative exponents
  3. 3Scientific notation
  4. 4Exponential functions and their graphs
  5. 5Exponential growth
  6. 6Exponential decay
  7. 7Linear versus exponential
Polynomials and factoring7 lessons
  1. 1Adding and subtracting polynomials
  2. 2Multiplying polynomials
  3. 3Special products
  4. 4GCF and factoring by grouping
  5. 5Factoring trinomials
  6. 6Factoring with leading coefficients
  7. 7Special patterns and factoring completely
Quadratic functions and equations7 lessons
  1. 1Quadratic functions and parabolas
  2. 2Graphing from standard form
  3. 3Vertex form and transformations
  4. 4Solving by graphing and square roots
  5. 5Solving by factoring
  6. 6Completing the square and the quadratic formula
  7. 7Choosing a method and modeling with quadratics
Radical expressions and equations7 lessons
  1. 1Square roots and cube roots
  2. 2Simplifying radical expressions
  3. 3Adding and subtracting radical expressions
  4. 4Multiplying radical expressions
  5. 5Dividing radicals and rationalizing denominators
  6. 6Square-root functions and their graphs
  7. 7Solving radical equations
Rational expressions and equations7 lessons
  1. 1Simplifying rational expressions
  2. 2Multiplying and dividing rational expressions
  3. 3Adding and subtracting rational expressions
  4. 4Dividing polynomials and complex fractions
  5. 5Solving rational equations
  6. 6Rational functions and inverse variation
  7. 7Applications: work and rate problems
Data analysis and statistics7 lessons
  1. 1Mean, median, and mode
  2. 2Dot plots, histograms, and shape
  3. 3The five-number summary and box plots
  4. 4Range and standard deviation
  5. 5Two-way tables
  6. 6Scatter plots and trend lines
  7. 7Checkpoint: analyzing a data set