Precalculus (TX TEKS)
13 units256 videos25 hours
Learn it live with a class on Puzzicle · Teachers: use it with your class
Unit 1: Graphs, attributes, and applications of functions
Parent functions
Graph 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
Graphs of nonlinear piecewise functions ✓ Check-ins4:23
Function symmetry
Discontinuities
Unit 2: Compositions and inverses of functions
Determine and represent an inverse function
Domain restrictions for functionality
Represent functions as compositions
Intro to composing functions ✓ Check-ins6:15
Evaluating composite functions ✓ Check-ins4:10
Evaluating composite functions: using tables ✓ Check-ins4:10
Evaluating composite functions: using graphs ✓ Check-ins3:02
Finding composite functions ✓ Check-ins2:57
Evaluating composite functions (advanced) ✓ Check-ins4:11
Composition of functions to prove inverses
Use compositions to model & solve real world problems
Unit 3: Polynomial and power functions, equations, and inequalities
Graph polynomial functions & analyze key features
Zeros of polynomials introduction ✓ Check-ins5:09
Zeros of polynomials: plotting zeros ✓ Check-ins3:19
Zeros of polynomials: matching equation to zeros ✓ Check-ins3:51
Zeros of polynomials: matching equation to graph ✓ Check-ins3:01
Zeros of polynomials (with factoring): grouping ✓ Check-ins4:55
Zeros of polynomials (with factoring): common factor ✓ Check-ins3:32
Positive and negative intervals of polynomials
End behavior and relative extrema
Graph polynomials with transformations and applications
Solve polynomial equations
The Fundamental theorem of Algebra ✓ Check-ins5:34
Number of possible real roots of a polynomial ✓ Check-ins3:46
Solving polynomial functions using their graphs ✓ Check-ins3:15
Solving polynomials using a table ✓ Check-ins3:23
Factoring quadratics: common factor + grouping ✓ Check-ins4:46
Factoring quadratics: negative common factor + grouping ✓ Check-ins5:17
Factoring higher degree polynomials ✓ Check-ins3:58
Factoring higher degree polynomials: Common factor ✓ Check-ins3:39
Polynomial division and the rational root theorem
Solve polynomial inequalities
Unit 4: Rational functions, equations, and inequalities
Rational function key features
End behavior of rational functions ✓ Check-ins10:07
Analyzing horizontal asymptotes of rational functions ✓ Check-ins5:51
Analyzing vertical asymptotes of rational functions ✓ Check-ins7:06
Estimating an oblique asymptote graphically ✓ Check-ins1:49
Finding oblique asymptotes of a rational function ✓ Check-ins5:16
Discontinuities of rational functions ✓ Check-ins6:46
Graph rational functions
Graphing rational functions according to asymptotes ✓ Check-ins11:22
Graphs of rational functions: y-intercept ✓ Check-ins3:08
Graphs of rational functions: horizontal asymptote ✓ Check-ins3:16
Graphs of rational functions: vertical asymptotes ✓ Check-ins5:33
Graphs of rational functions: zeros ✓ Check-ins7:47
Solve rational equations and inequalities
Rational equations intro ✓ Check-ins3:12
Equations with rational expressions ✓ Check-ins5:12
Equations with rational expressions (example 2) ✓ Check-ins7:12
Solving rational inequalities from a graph ✓ Check-ins ✎ Fixed a slip1:57
Solving factored form rational inequalities by testing intervals ✓ Check-ins ✎ Fixed a slip8:02
Solving rational inequalities by testing intervals in terms of a constant ✓ Check-ins ✎ Fixed a slip10:17
Solving rational inequalities with rational expressions on both sides ✓ Check-ins7:59
Algebraically construct rational models
Unit 5: Exponential and logarithmic functions and equations
Exponential and logarithmic inverses
Exponential key features
Graph exponential functions with transformations
Graph logarithmic functions with transformations
Properties of logarithms
Evaluating logarithms (advanced) ✓ Check-ins4:20
Intro to logarithm properties (1 of 2) ✓ Check-ins9:16
Intro to logarithm properties (2 of 2) ✓ Check-ins10:04
Using the logarithmic product rule ✓ Check-ins5:04
Using the logarithmic power rule ✓ Check-ins4:49
Using the properties of logarithms: multiple steps ✓ Check-ins2:10
Proof of the logarithm product rule ✓ Check-ins7:08
Proof of the logarithm quotient and power rules ✓ Check-ins7:59
The change of base formula for logarithms
Generate and solve logarithmic equations
Generate exponential equations
Solve exponential equations
Unit 6: Sequences, series, and binomial expansion
Sequences intro
Convert and use sequence formulas
Arithmetic series (pt. 1)
Arithmetic series (pt. 2)
Geometric series
Partial and finite sums with applications
Binomial theorem and connected theorems
Unit 7: Problem solving with trigonometric ratios
Trigonometric ratios in right triangles
Law of sines and cosines
Solving for a side with the law of sines ✓ Check-ins5:58
Solving for an angle with the law of sines ✓ Check-ins5:34
Proof of the law of sines ✓ Check-ins6:34
Solving for a side with the law of cosines ✓ Check-ins4:38
Solving for an angle with the law of cosines ✓ Check-ins6:41
Proof of the law of cosines ✓ Check-ins9:26
Trig word problem: stars ✓ Check-ins6:00
Unit 8: Trigonometric functions
Conversions
Reference angles and standard position
Trigonometric functions key features
Transform sinusoidal graphs
Graph trigonometric functions
Unit 9: Trigonometric equations and identities
Trigonometric identities
Sine & cosine identities: symmetry ✓ Check-ins7:58
Tangent identities: symmetry ✓ Check-ins7:15
Sine & cosine identities: periodicity ✓ Check-ins6:13
Tangent identities: periodicity ✓ Check-ins4:02
Proof of the Pythagorean trig identity ✓ Check-ins6:12
Using the Pythagorean trig identity ✓ Check-ins6:15
Using the quotient identities to prove trig identities ✓ Check-ins2:02
Trigonometric identities 2
Trig angle addition identities ✓ Check-ins11:07
Using the cosine angle addition identity ✓ Check-ins5:14
Using the cosine double-angle identity ✓ Check-ins3:28
Proof of the sine angle addition identity ✓ Check-ins8:26
Proof of the cosine angle addition identity ✓ Check-ins6:02
Proof of the tangent angle sum and difference identities ✓ Check-ins6:55
Finding trig values using angle addition identities ✓ Check-ins8:35
Using the tangent angle addition identity ✓ Check-ins6:29
Using trig angle addition identities: finding side lengths ✓ Check-ins5:20
Using trig angle addition identities: manipulating expressions ✓ Check-ins6:12
Using trigonometric identities ✓ Check-ins3:07
Solve trigonometric equations
Solving sinusoidal equations of the form sin(x)=d ✓ Check-ins6:10
Cosine equation algebraic solution set ✓ Check-ins6:13
Cosine equation solution set in an interval ✓ Check-ins6:22
Sine equation algebraic solution set ✓ Check-ins5:36
Solving cos(θ)=1 and cos(θ)=-1 ✓ Check-ins5:18
Interpreting solutions of trigonometric equations ✓ Check-ins4:09
Trig word problem: solving for temperature ✓ Check-ins8:23
Unit 10: Vectors
Describe vectors and their components
Vector magnitude and direction
Vector magnitude from graph ✓ Check-ins3:38
Vector magnitude from components ✓ Check-ins3:06
Vector magnitude from initial & terminal points ✓ Check-ins5:23
Direction of vectors from components: 1st & 2nd quadrants ✓ Check-ins9:01
Direction of vectors from components: 3rd & 4th quadrants ✓ Check-ins6:42
Vector components from magnitude & direction ✓ Check-ins10:16
Vector components from magnitude & direction: word problem ✓ Check-ins8:56
Vector operations
Scalar multiplication: component form ✓ Check-ins5:42
Scalar multiplication: magnitude and direction ✓ Check-ins4:53
Adding & subtracting vectors ✓ Check-ins7:42
Adding & subtracting vectors end-to-end ✓ Check-ins6:22
Parallelogram rule for vector addition ✓ Check-ins2:20
Subtracting vectors end-to-end ✓ Check-ins1:44
Subtracting vectors with parallelogram rule ✓ Check-ins2:46
Vector addition & magnitude ✓ Check-ins5:30
Adding vectors in magnitude and direction form ✓ Check-ins8:21
Combined vector operations ✓ Check-ins5:59
Unit 11: Parametric equations
Graph parametric equations
Parametric vs. rectangular equations
Real world applications
Unit 12: Polar equations
Graph polar coordinates
Unit 13: Conics
General conic characteristics
Write equations of circles and analyze key features
Write rectangular equations of ellipses and analyze key features
Equations and key features of ellipses
Write rectangular equations of parabolas and analyze key features
Write rectangular equations of hyperbolas and analyze key features
Intro to hyperbolas ✓ Check-ins13:34
Vertices & direction of a hyperbola ✓ Check-ins5:15
Vertices & direction of a hyperbola (example 2) ✓ Check-ins2:21
Graphing hyperbolas (old example) ✓ Check-ins7:30
Foci of a hyperbola from equation ✓ Check-ins15:24
Proof of the hyperbola foci formula ✓ Check-ins14:50
Equation of a hyperbola not centered at the origin ✓ Check-ins10:29
Conic section from expanded equation: circle & parabola ✓ Check-ins11:34
Conic section from expanded equation: ellipse ✓ Check-ins9:11
Conic section from expanded equation: hyperbola ✓ Check-ins ✎ Fixed a slip11:28
Learn this with a class
With a class on Puzzicle this course runs as a timetable of live study parties: your batch watches together and answers the check-ins, sometimes with a teacher leading.
Course content © Khan Academy, used under CC BY-NC-SA. See this course on Khan Academy.