Algebra 1
The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience! **Teaching this course? Check out our [teacher resources](https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:alg1-ccss-teacher-resources)!**
16 units343 videos29 hours
Learn it live with a class on Puzzicle · Teachers: use it with your class
Unit 1: Algebra foundations
Overview and history of algebra
Introduction to variables
Substitution and evaluating expressions
Combining like terms
Introduction to equivalent expressions
Unit 2: Solving equations & inequalities
Linear equations with variables on both sides
Why we do the same thing to both sides: Variable on both sides ✓ Check-ins7:36
Intro to equations with variables on both sides ✓ Check-ins8:53
Equations with variables on both sides: 20-7x=6x-6 ✓ Check-ins4:06
Equation with variables on both sides: fractions ✓ Check-ins4:50
Equation with the variable in the denominator ✓ Check-ins3:24
Linear equations with parentheses
Analyzing the number of solutions to linear equations
Linear equations with unknown coefficients
Multi-step inequalities
Unit 3: Working with units
Rate conversion
Appropriate units
Unit 4: Linear equations & graphs
Two-variable linear equations intro
Slope
Horizontal & vertical lines
x-intercepts and y-intercepts
Applying intercepts and slope
Modeling with linear equations and inequalities
Unit 5: Forms of linear equations
Intro to slope-intercept form
Graphing slope-intercept equations
Writing slope-intercept equations
Point-slope form
Standard form
Summary: Forms of two-variable linear equations
Unit 6: Systems of equations
Introduction to systems of equations
Systems of equations: trolls, tolls (1 of 2) ✓ Check-ins6:51
Systems of equations: trolls, tolls (2 of 2) ✓ Check-ins5:41
Testing a solution to a system of equations ✓ Check-ins2:38
Systems of equations with graphing: y=7/5x-5 & y=3/5x-1 ✓ Check-ins2:22
Systems of equations with graphing: exact & approximate solutions ✓ Check-ins5:56
Setting up a system of equations from context example (pet weights) ✓ Check-ins1:59
Setting up a system of linear equations example (weight and price) ✓ Check-ins4:12
Interpreting points in context of graphs of systems ✓ Check-ins5:39
Solving systems of equations with substitution
Solving systems of equations with elimination
Systems of equations with elimination: King's cupcakes ✓ Check-ins9:00
Elimination strategies ✓ Check-ins7:16
Systems of equations with elimination: x-4y=-18 & -x+3y=11 ✓ Check-ins5:59
Systems of equations with elimination: potato chips ✓ Check-ins9:21
Systems of equations with elimination (and manipulation) ✓ Check-ins12:01
Equivalent systems of equations
Number of solutions to systems of equations
Systems of equations number of solutions: fruit prices (1 of 2) ✓ Check-ins9:25
Systems of equations number of solutions: fruit prices (2 of 2) ✓ Check-ins7:08
Solutions to systems of equations: consistent vs. inconsistent ✓ Check-ins5:29
Solutions to systems of equations: dependent vs. independent ✓ Check-ins5:10
Number of solutions to a system of equations ✓ Check-ins3:26
Number of solutions to a system of equations graphically ✓ Check-ins6:36
Number of solutions to a system of equations algebraically ✓ Check-ins6:01
How many solutions does a system of linear equations have if there are at least two? ✓ Check-ins2:12
Systems of equations word problems
Age word problem: Imran ✓ Check-ins3:43
Age word problem: Ben & William ✓ Check-ins6:28
Age word problem: Arman & Diya ✓ Check-ins5:21
System of equations word problem: walk & ride ✓ Check-ins7:00
System of equations word problem: no solution ✓ Check-ins5:03
System of equations word problem: infinite solutions ✓ Check-ins5:01
Systems of equations with elimination: TV & DVD ✓ Check-ins5:51
Systems of equations with elimination: apples and oranges ✓ Check-ins5:06
Systems of equations with substitution: coins ✓ Check-ins5:58
Systems of equations with elimination: coffee and croissants ✓ Check-ins4:15
Unit 7: Inequalities (systems & graphs)
Checking solutions of two-variable inequalities
Graphing two-variable inequalities
Modeling with linear inequalities
Writing two-variable inequalities word problem ✓ Check-ins2:22
Solving two-variable inequalities word problem ✓ Check-ins3:42
Interpreting two-variable inequalities word problem ✓ Check-ins4:20
Modeling with systems of inequalities ✓ Check-ins9:45
Writing systems of inequalities word problem ✓ Check-ins4:00
Solving systems of inequalities word problem ✓ Check-ins4:25
Graphs of systems of inequalities word problem ✓ Check-ins3:35
Graphs of two-variable inequalities word problem ✓ Check-ins4:59
Creativity break: What can we do to expand our creative skills? ✓ Check-ins1:28
Unit 8: Functions
Evaluating functions
Inputs and outputs of a function
Functions and equations
Interpreting function notation
Introduction to the domain and range of a function
Determining the domain of a function
Determining whether values are in domain of function ✓ Check-ins4:57
Examples finding the domain of functions ✓ Check-ins4:25
Worked example: determining domain word problem (real numbers) ✓ Check-ins2:19
Worked example: determining domain word problem (positive integers) ✓ Check-ins2:34
Worked example: determining domain word problem (all integers) ✓ Check-ins5:34
Recognizing functions
Maximum and minimum points
Intervals where a function is positive, negative, increasing, or decreasing
Interpreting features of graphs
Average rate of change
Average rate of change word problems
Unit 9: Sequences
Introduction to arithmetic sequences
Constructing arithmetic sequences
Introduction to geometric sequences
Constructing geometric sequences
Modeling with sequences
Unit 10: Absolute value & piecewise functions
Graphs of absolute value functions
Piecewise functions
Introduction to piecewise functions ✓ Check-ins3:49
Worked example: evaluating piecewise functions ✓ Check-ins4:24
Worked example: graphing piecewise functions ✓ Check-ins4:30
Worked example: domain & range of step function ✓ Check-ins2:44
Worked example: domain & range of piecewise linear functions ✓ Check-ins7:25
Unit 11: Exponents & radicals
Exponent properties review
Radicals
Unit 12: Exponential growth & decay
Exponential vs. linear growth
Exponential expressions
Graphs of exponential growth
Exponential vs. linear growth over time
Exponential growth & decay
Exponential functions from tables & graphs
Writing exponential functions ✓ Check-ins1:40
Writing exponential functions from tables ✓ Check-ins5:17
Writing exponential functions from graphs ✓ Check-ins7:25
Analyzing tables of exponential functions ✓ Check-ins7:20
Analyzing graphs of exponential functions ✓ Check-ins4:06
Analyzing graphs of exponential functions: negative initial value ✓ Check-ins6:07
Modeling with basic exponential functions word problem ✓ Check-ins5:37
Unit 13: Quadratics: Multiplying & factoring
Multiplying monomials by polynomials
Multiplying binomials
Special products of binomials
Introduction to factoring
Factoring quadratics intro
Factoring quadratics by grouping
Intro to grouping ✓ Check-ins13:57
Factoring quadratics by grouping ✓ Check-ins3:55
Factoring quadratics: common factor + grouping ✓ Check-ins4:46
Factoring quadratics: negative common factor + grouping ✓ Check-ins5:17
Creativity break: How can we combine ways of thinking in problem solving? ✓ Check-ins2:31
Factoring quadratics with difference of squares
Factoring quadratics with perfect squares
Perfect square factorization intro ✓ Check-ins5:19
Factoring perfect squares ✓ Check-ins4:54
Identifying perfect square form ✓ Check-ins4:37
Factoring perfect squares: negative common factor ✓ Check-ins3:52
Factoring perfect squares: missing values ✓ Check-ins2:39
Factoring perfect squares: shared factors ✓ Check-ins4:26
Strategy in factoring quadratics
Unit 14: Quadratic functions & equations
Intro to parabolas
Solving and graphing with factored form
Solving by taking the square root
Vertex form
Solving quadratics by factoring
Solving quadratics by factoring ✓ Check-ins6:22
Solving quadratics by factoring: leading coefficient ≠ 1 ✓ Check-ins4:35
Solving quadratics using structure ✓ Check-ins3:55
Quadratic equations word problem: triangle dimensions ✓ Check-ins8:21
Quadratic equations word problem: box dimensions ✓ Check-ins5:54
The quadratic formula
Completing the square intro
More on completing the square
Solve by completing the square: Integer solutions ✓ Check-ins6:29
Solve by completing the square: Non-integer solutions ✓ Check-ins4:02
Worked example: completing the square (leading coefficient ≠ 1) ✓ Check-ins5:44
Solving quadratics by completing the square: no solution ✓ Check-ins5:24
Proof of the quadratic formula ✓ Check-ins7:44
Strategizing to solve quadratic equations
Quadratic standard form
Features & forms of quadratic functions
Forms & features of quadratic functions ✓ Check-ins8:29
Worked examples: Forms & features of quadratic functions ✓ Check-ins6:42
Vertex & axis of symmetry of a parabola ✓ Check-ins7:22
Finding features of quadratic functions ✓ Check-ins8:23
Interpret quadratic models: Factored form ✓ Check-ins4:00
Interpret quadratic models: Vertex form ✓ Check-ins5:53
Creativity break: How does creativity play a role in your everyday life? ✓ Check-ins2:24
Comparing quadratic functions
Unit 15: Irrational numbers
Irrational numbers
Sums and products of rational and irrational numbers
Proof: sum & product of two rationals is rational ✓ Check-ins2:46
Proof: product of rational & irrational is irrational ✓ Check-ins3:15
Proof: sum of rational & irrational is irrational ✓ Check-ins3:24
Sums and products of irrational numbers ✓ Check-ins5:57
Worked example: rational vs. irrational expressions ✓ Check-ins2:36
Worked example: rational vs. irrational expressions (unknowns) ✓ Check-ins6:26
Unit 16: Creativity in algebra
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