Integrated math 1
The Mathematics 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; Introductory statistics; and Geometric transformations and congruence. Khan Academy's Mathematics 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!
18 units338 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
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
Equivalent systems of equations
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
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
Graphs of two-variable inequalities word problem ✓ Check-ins4:59
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
Analyzing structure with linear inequalities: fruits ✓ Check-ins3:53
Analyzing structure with linear inequalities: balls ✓ Check-ins2:20
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: Scatterplots
Creating and interpreting scatterplots
Unit 10: Data distributions
Displays of distributions
Summarizing center of distributions (central tendency)
Box and whisker plots
Comparing distributions
Unit 11: Two-way tables
Two-way relative frequency tables
Unit 12: Sequences
Introduction to arithmetic sequences
Constructing arithmetic sequences
Introduction to geometric sequences
Constructing geometric sequences
Modeling with sequences
Unit 13: Exponents & radicals
Exponent properties review
Radicals
Unit 14: 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 15: Performing transformations
Introduction to rigid transformations
Translations
Reflections
Unit 16: Transformation properties and proofs
Rigid transformations overview
Dilation preserved properties
Properties & definitions of transformations
Symmetry
Proofs with transformations
Unit 17: Congruence
Transformations & congruence
Triangle congruence from transformations
Proving the SSS triangle congruence criterion using transformations ✓ Check-ins5:47
Proving the SAS triangle congruence criterion using transformations ✓ Check-ins4:31
Proving the ASA and AAS triangle congruence criteria using transformations ✓ Check-ins7:24
Why SSA isn't a congruence postulate/criterion ✓ Check-ins7:24
Congruent triangles
Theorems concerning triangle properties
Working with triangles
Theorems concerning quadrilateral properties
Proof: Opposite sides of a parallelogram ✓ Check-ins8:30
Proof: Diagonals of a parallelogram ✓ Check-ins9:06
Proof: Opposite angles of a parallelogram ✓ Check-ins4:08
Proof: The diagonals of a kite are perpendicular ✓ Check-ins11:06
Proof: Rhombus diagonals are perpendicular bisectors ✓ Check-ins4:04
Proof: Rhombus area ✓ Check-ins5:07
Proofs of general theorems that use triangle congruence
Constructing lines & angles
Geometric constructions: congruent angles ✓ Check-ins4:09
Geometric constructions: parallel line ✓ Check-ins2:03
Geometric constructions: perpendicular bisector ✓ Check-ins1:26
Geometric constructions: perpendicular line through a point on the line ✓ Check-ins1:12
Geometric constructions: perpendicular line through a point not on the line ✓ Check-ins2:42
Geometric constructions: angle bisector ✓ Check-ins2:17
Unit 18: Analytic geometry
Distance and midpoints
Dividing line segments
Problem solving with distance on the coordinate plane
Parallel & perpendicular lines on the coordinate plane
Equations of parallel & perpendicular lines
Parallel lines from equation ✓ Check-ins3:48
Parallel lines from equation (example 2) ✓ Check-ins3:03
Parallel lines from equation (example 3) ✓ Check-ins2:42
Perpendicular lines from equation ✓ Check-ins3:29
Writing equations of perpendicular lines ✓ Check-ins3:01
Writing equations of perpendicular lines (example 2) ✓ Check-ins1:45
Proof: parallel lines have the same slope ✓ Check-ins5:49
Proof: perpendicular lines have opposite reciprocal slopes ✓ Check-ins8:55
Learn this with a class
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