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Algebra
Introduction to algebra

1Origins of algebra

2Abstractness

3The beauty of algebra

4Intro to the coordinate plane

5Why all the letters in algebra?

6What is a variable?

7Why aren't we using the multiplication sign?

8Evaluating an expression with one variable

9Evaluating expressions with two variables

10Evaluating expressions with two variables

11Evaluating expressions with variables: temperature

12Evaluating expressions with variables: exponents

13Writing basic expressions with variables

14Writing expressions with variables

15Writing expressions with variables & parentheses

16Equivalent expressions

17Dependent & independent variables

18Dependent & independent variables: graphing

19Dependent & independent variables: equation

20Intro to combining like terms

21Combining like terms with negative coefficients & distribution

22Combining like terms with distribution

23Combining like terms with negative coefficients

24Combining like terms with rational coefficients

25Combining like terms with negative coefficients

26Combining like terms with rational coefficients
Solving basic equations & inequalities (one variable, linear)

27Variables, expressions, & equations

28Testing solutions to equations

29Same thing to both sides of equations

30Representing a relationship with an equation

31Dividing both sides of an equation

32Onestep equations intuition

33Onestep addition & subtraction equations

34Onestep addition equation

35Onestep addition & subtraction equations: fractions & decimals

36Onestep division equations

37Onestep multiplication equations

38Onestep multiplication & division equations: fractions & decimals

39Intro to twostep equations

40Twostep equations intuition

41Worked example: twostep equations

42Describing steps when solving equations

43Twostep equation word problem: computers

44Twostep equation word problem: garden

45Twostep equation word problem: oranges

46Why we do the same thing to both sides: Variable on both sides

47Intro to equations with variables on both sides

48Equations with variables on both sides: 207x=6x6

49Equation with variables on both sides: fractions

50Equation with the variable in the denominator

51Figuring out missing algebraic step

52Equations with parentheses

53Number of solutions to equations

54Worked example: number of solutions to equations

55Creating an equation with no solutions

56Creating an equation with infinitely many solutions

57Sums of consecutive integers

58Sum of integers challenge

59Linear equation word problem: saline

60Linear equation word problem: sugary drinks

61Linear equations with unknown coefficients

62Linear equations 1

63Linear equations 2

64Linear equations 3

65Linear equations 4

66Averages

67Taking percentages

68Growing by a percentage

69More percent problems

70Solving an equation for a variable

71Testing solutions to inequalities

72Plotting inequalities

73Plotting an inequality example

74Inequalities word problems

75Onestep inequalities examples

76Onestep inequalities: 5c ≤ 15

77Onestep inequality involving addition

78Onestep inequality word problem

79Inequalities using addition and subtraction

80Solving and graphing linear inequalities

81Twostep inequalities

82Twostep inequality word problem: apples

83Twostep inequality word problem: R&B

84Inequalities with variables on both sides

85Inequalities with variables on both sides (with parentheses)

86Multistep inequalities

87Compound inequalities: OR

88Compound inequalities: AND

89A compound inequality with no solution

90Double inequalities

91Compound inequalities examples
Linear equations, functions, & graphs

92Twovariable linear equations intro

93Solutions to 2variable equations

94Worked example: solutions to 2variable equations

95Completing solutions to 2variable equations

96Solutions to 2variable equations: substitution (old)

97Solutions to 2variable equations: graphical (old)

98Intro to intercepts

99xintercept of a line

100Intercepts from an equation

101Intercepts from a table

102Graphing using intercepts (old)

103Intro to slope

104Positive & negative slope

105Worked example: slope from graph

106Worked example: slope from two points

107Slope (more examples)

108Slope of a horizontal line

109Horizontal & vertical lines

110Intro to slopeintercept form

111Worked examples: slopeintercept intro

112Graph from slopeintercept equation

113Slopeintercept equation from graph

114Slopeintercept equation from slope & point

115Slopeintercept equation from two points

116Slopeintercept form problems

117Slopeintercept equation from slope & point (old)

118Slopeintercept equation from slope & point: fractions (old)

119Finding y intercept given slope & point (old)

120Intro to pointslope form

121Pointslope & slopeintercept equations

122Intro to linear equation standard form

123Graphing a linear equation: 5x+2y=20

124Converting from slopeintercept to standard form

125Slope from equation

126Writing linear equations in all forms

127Linear equations word problems: earnings

128Linear equations word problems: volcano

129Linear graphs word problems

130Linear graphs word problem: cats

131Linear equations word problem: marbles

132Linear equations word problem: file transfer

133Comparing linear functions: equation vs. graph

134Comparing linear functions: same rate of change

135Comparing linear functions: faster rate of change

136Comparing linear functions word problem: climb

137Comparing linear functions word problem: walk

138Comparing linear functions word problem: work

139Linear functions word problem: fuel

140Linear functions word problem: pool

141Linear functions word problem: iceberg

142Linear functions word problem: paint

143Linear models word problem: book

144Linear models word problem: marbles

145Comparing linear rates example
Sequences

146Sequences intro

147Intro to arithmetic sequences

148Extending arithmetic sequences

149Using arithmetic sequences formulas

150Worked example: using recursive formula for arithmetic sequence

151Recursive formulas for arithmetic sequences

152Explicit formulas for arithmetic sequences

153Arithmetic sequence problem

154Converting recursive & explicit forms of arithmetic sequences

155Intro to geometric sequences

156Extending geometric sequences

157Using explicit formulas of geometric sequences

158Using recursive formulas of geometric sequences

159Explicit & recursive formulas for geometric sequences

160Converting recursive & explicit forms of geometric sequences

161Sequences word problems

162Evaluating sequences in recursive form
System of equations

163Systems of equations: trolls, tolls (1 of 2)

164Systems of equations: trolls, tolls (2 of 2)

165Systems of equations with elimination: King's cupcakes

166Systems of equations with elimination: potato chips

167Systems of equations with substitution: potato chips

168Systems of equations number of solutions: fruit prices (1 of 2)

169Systems of equations number of solutions: fruit prices (2 of 2)

170Systems of equations: trolls, tolls (1 of 2)

171Testing a solution to a system of equations

172Systems of equations: trolls, tolls (2 of 2)

173Systems of equations with graphing: y=7/5x5 & y=3/5x1

174Systems of equations with graphing: exact & approximate solutions

175Systems of equations with elimination: King's cupcakes

176Systems of equations with elimination: x4y=18 & x+3y=11

177Systems of equations with elimination: potato chips

178Systems of equations with elimination (and manipulation)

179Why can we subtract one equation from the other in a system of equations?

180Worked example: equivalent systems of equations

181Worked example: nonequivalent systems of equations

182Solving systems of equations by elimination (old)

183Systems of equations with substitution: potato chips

184Systems of equations with substitution: 3x4y=2 & y=2x5

185Solving linear systems by substitution (old)

186Manipulating expressions using structure

187Manipulating expressions using structure (example 2)

188Systems of equations number of solutions: fruit prices (1 of 2)

189Systems of equations number of solutions: fruit prices (2 of 2)

190Solutions to systems of equations: consistent vs. inconsistent

191Solutions to systems of equations: dependent vs. independent

192Number of solutions to a system of equations

193Number of solutions to a system of equations graphically

194Number of solutions to a system of equations algebraically

195How many solutions does a system of linear equations have if there are at least two?

196Age word problem: Imran

197Age word problem: Ben & William

198Age word problem: Arman & Diya

199System of equations word problem: walk & ride

200System of equations word problem: no solution

201System of equations word problem: infinite solutions

202Systems of equations with elimination: TV & DVD

203Systems of equations with elimination: apples and oranges

204Systems of equations with substitution: coins

205Systems of equations with elimination: coffee and croissants

206Interpreting equations graphically

207Interpreting equations graphically (example 2)

208Solving equations graphically (1 of 2)

209Solving equations graphically (2 of 2)

210Intro to linear systems with 3 variables

211Solving linear systems with 3 variables

212Solving linear systems with 3 variables: no solution

2133variable linear system word problem
Twovariable inequalities

214Testing solutions to inequalities

215Testing solutions to systems of inequalities

216Constraining solutions of twovariable inequalities

217Constraining solutions of systems of inequalities

218Intro to graphing twovariable inequalities

219Graphing twovariable inequalities

220Twovariable inequalities from their graphs

221Intro to graphing systems of inequalities

222Graphing systems of inequalities

223Graphing twovariable inequalities (old)

224Writing twovariable inequalities word problem

225Interpreting twovariable inequalities word problem

226Solving twovariable inequalities word problem

227Graphs of twovariable inequalities word problem

228Modeling with systems of inequalities

229Writing systems of inequalities word problem

230Solving systems of inequalities word problem

231Graphs of systems of inequalities word problem

232Analyzing structure with linear inequalities: fruits

233Analyzing structure with linear inequalities: balls
Functions

234What is a function?

235Worked example: Evaluating functions from equation

236Worked example: Evaluating functions from graph

237Worked example: evaluating expressions with function notation

238Worked example: matching an input to a function's output (equation)

239Worked example: matching an input to a function's output (graph)

240Worked example: two inputs with the same output (graph)

241Equations vs. functions

242Obtaining a function from an equation

243Function notation word problem: bank

244Function notation word problem: beach

245Intervals and interval notation

246What is the domain of a function?

247What is the range of a function?

248Worked example: domain and range from graph

249Domain of a radical function

250Worked example: domain of algebraic functions

251Worked example: determining domain word problem (real numbers)

252Worked example: determining domain word problem (positive integers)

253Worked example: determining domain word problem (all integers)

254Recognizing functions from graph

255Does a vertical line represent a function?

256Recognizing functions from table

257Recognizing functions from verbal description

258Recognizing functions from verbal description word problem

259Introduction to piecewise functions

260Worked example: evaluating piecewise functions

261Worked example: graphing piecewise functions

262Worked example: domain & range of step function

263Worked example: domain & range of piecewise linear functions

264Introduction to minimum and maximum points

265Worked example: absolute and relative extrema

266Increasing, decreasing, positive or negative intervals

267Worked example: positive & negative intervals

268Graph interpretation word problem: temperature

269Graph interpretation word problem: basketball

270Introduction to average rate of change

271Worked example: average rate of change from graph

272Worked example: average rate of change from table

273Worked example: average rate of change from equation

274Average rate of change word problem: table

275Average rate of change word problem: graph

276Average rate of change word problem: equation

277Adding functions

278Subtracting functions

279Multiplying functions

280Dividing functions

281Intro to composing functions

282Evaluating composite functions

283Evaluating composite functions: using tables

284Evaluating composite functions: using graphs

285Evaluating composite functions: using graphs

286Finding composite functions

287Evaluating composite functions (advanced)

288Shifting functions examples

289Graphing shifted functions

290Identifying function transformations

291Identifying horizontal squash from graph

292Reflecting & compressing functions

293Modeling with function combination

294Modeling with composite functions

295Modeling with composite functions: skydiving

296Intro to inverse functions

297Inputs & outputs of inverse functions

298Graphing the inverse of a linear function

299Finding inverse functions: linear

300Finding inverse functions: quadratic

301Finding inverse functions: quadratic (example 2)

302Finding inverse functions: radical

303Finding inverses of rational functions

304Verifying inverse functions by composition

305Verifying inverse functions by composition: not inverse

306Determining if a function is invertible

307Restricting domains of functions to make them invertible

308Domain of advanced functions

309Domain and range of quadratic functions

310Graphs of nonlinear piecewise functions

311Symmetry of algebraic models

312End behavior of algebraic models

313Periodicity of algebraic models

314Comparing functions: xintercepts

315Comparing functions: shared features

316Comparing maximum points of quadratic functions

317New operator definitions 1

318New operator definitions 2
Absolute value equations, functions, & inequalities

319Shifting absolute value graphs

320Scaling & reflecting absolute value functions: equation

321Scaling & reflecting absolute value functions: graph

322Graphing absolute value functions

323Intro to absolute value equations and graphs

324Worked example: absolute value equations with one solution

325Worked example: absolute value equations with no solution

326Intro to absolute value inequalities

327Solving absolute value inequalities 1

328Solving absolute value inequalities 2

329Solving absolute value inequalities: fractions

330Solving absolute value inequalities: no solution

331Absolute value inequalities word problem
Quadratic equations & functions

332Parabolas intro

333Zero product property

334Graphing quadratics in factored form

335Quadratic word problems (factored form)

336Solving quadratics by taking square roots

337Solving quadratics by taking square roots examples

338Solving quadratics by taking square roots: with steps

339Quadratics by taking square roots: strategy

340Solving quadratics by taking square roots: challenge

341Vertex form introduction

342Graphing quadratics: vertex form

343Quadratic word problems (vertex form)

344Solving quadratics by factoring

345Solving quadratics by factoring: leading coefficient ≠ 1

346Solving quadratics using structure

347Quadratic equations word problem: triangle dimensions

348Quadratic equations word problem: box dimensions

349Solving quadratic equations by factoring (old)

350Completing the square

351Worked example: Completing the square (intro)

352Worked example: Rewriting expressions by completing the square

353Worked example: Rewriting & solving equations by completing the square

354Worked example: completing the square (leading coefficient ≠ 1)

355Solving quadratics by completing the square: no solution

356The quadratic formula

357Using the quadratic formula

358Worked example: quadratic formula

359Worked example: quadratic formula (example 2)

360Worked example: quadratic formula (negative coefficients)

361Using the quadratic formula: number of solutions

362Proof of the quadratic formula

363Finding the vertex of a parabola in standard form

364Graphing quadratics: standard form

365Quadratic word problem: ball

366Forms & features of quadratic functions

367Worked examples: Forms & features of quadratic functions

368Vertex & axis of symmetry of a parabola

369Finding features of quadratic functions

370Comparing features of quadratic functions

371Comparing maximum points of quadratic functions

372Intro to parabola transformations

373Shifting parabolas

374Scaling & reflecting parabolas

375Quadratic systems: graphical solution

376Quadratic system with no solutions

377Quadratic systems: both variables are squared

378Quadratic systems: a line and a circle

379Quadratic inequalities

380Quadratic inequalities (example 2)

381Quadratic inequalities: graphical approach
Polynomial expressions, equations, & functions

382Polynomials intro

383The parts of polynomial expressions

384Evaluating polynomials

385Simplifying polynomials

386Adding polynomials

387Subtracting polynomials

388Polynomial subtraction

389Adding & subtracting multiple polynomials

390Adding polynomials (old)

391Adding polynomials: two variables (intro)

392Subtracting polynomials: two variables (intro)

393Subtracting polynomials: two variables

394Finding an error in polynomial subtraction

395Polynomials review

396Multiplying monomials

397Multiplying monomials to find area: two variables

398Multiplying monomials to find area

399Multiplying monomials challenge

400Multiplying monomials by polynomials: area model

401Multiplying monomials by polynomials

402Multiplying monomials by polynomials challenge

403Multiplying binomials: area model

404Multiplying binomials intro

405Multiplying binomials

406Multiplying binomials by polynomials

407Multiplying binomials by polynomials: area model

408Multiplying binomials by polynomials challenge

409Multiplying binomials by polynomials (old)

410Multiplying binomials with radicals (old)

411Polynomial multiplication word problem

412Polynomial word problem: rectangle and circle area

413Polynomial word problem: total value of bills

414Polynomial word problem: area of a window

415Intro to factors & divisibility

416Which monomial factorization is correct?

417Worked example: finding the missing monomial factor

418Worked example: finding missing monomial side in area model

419Greatest common factor of monomials

420Factoring with the distributive property

421Taking common factor from binomial

422Taking common factor from trinomial

423Taking common factor: area model

424Factoring polynomials: common binomial factor

425Factoring polynomials: common factor (old)

426Factoring polynomials: common factor (old)

427Worked example: evaluating expressions using structure

428Worked example: evaluating expressions using structure (more examples)

429Factoring quadratics as (x+a)(x+b)

430Factoring quadratics as (x+a)(x+b) (example 2)

431More examples of factoring quadratics as (x+a)(x+b)

432Intro to grouping

433Factoring quadratics by grouping

434Factoring quadratics: common factor + grouping

435Factoring quadratics: negative common factor + grouping

436Factoring twovariable quadratics

437Factoring twovariable quadratics: rearranging

438Factoring twovariable quadratics: grouping

439Factoring quadratics with common factor (old)

440Difference of squares intro

441Factoring difference of squares: leading coefficient ≠ 1

442Factoring difference of squares: analyzing factorization

443Factoring difference of squares: missing values

444Factoring difference of squares: shared factors

445Perfect square factorization intro

446Factoring perfect squares

447Identifying perfect square form

448Factoring higherdegree polynomials: Common factor

449Factoring perfect squares: negative common factor

450Factoring perfect squares: negative common factor

451Factoring perfect squares: missing values

452Factoring perfect squares: shared factors

453Strategy in factoring quadratics (part 1 of 2)

454Strategy in factoring quadratics (part 2 of 2)

455Factoring using the perfect square pattern

456Factoring using the difference of squares pattern

457Factoring difference of squares: two variables (example 2)

458Dividing polynomials: long divisionIntro to long division of polynomials

459Dividing polynomials: long division

460Intro to polynomial synthetic division

461Dividing polynomials: synthetic division

462Why synthetic division works

463Divide polynomials by x (with remainders)

464Divide polynomials by monomials (with remainders)

465Dividing polynomials with remainders

466Intro to the Polynomial Remainder Theorem

467Remainder theorem: finding remainder from equation

468Remainder theorem: checking factors

469Remainder theorem: finding coefficients

470Proof of the Polynomial Remainder Theorem

471Intro to the Binomial Theorem

472Pascal's triangle and binomial expansion

473Expanding binomials

474Expanding binomials w/o Pascal's triangle

475Binomial expansion & combinatorics

476Pascal's triangle & combinatorics

477Binomial expansion & combinatorics (old)

478Factoring higherdegree polynomials

479Factoring sum of cubes

480Factoring difference of cubes

481Analyzing polynomial identities

482Complex numbers & sum of squares factorization

483Factoring sum of squares

484Solving quadratic equations: complex roots

485The Fundamental theorem of Algebra

486Quadratics & the Fundamental Theorem of Algebra

487Number of possible real roots of a polynomial

488Finding zeros of polynomials (1 of 2)

489Finding zeros of polynomials (2 of 2)

490Finding zeros of polynomials (example 2)

491Zeros of polynomials & their graphs

492Zeros of polynomials & their graphs

493Intro to end behavior of polynomials

494End behavior of functions & their graphs

495Function symmetry introduction

496Even and odd functions: Graphs

497Even/odd functions & numbers

498Even & odd polynomials
Exponential & logarithmic functions

499Multiplying & dividing powers (integer exponents)

500Powers of products & quotients (integer exponents)

501Intro to square roots

502Understanding square roots

503Intro to cube roots

504Square root of decimal

5055th roots

506Intro to rational exponents

507Rewriting roots as rational exponents

508Exponential equation with rational answer

509Rewriting quotient of powers (rational exponents)

510Rewriting mixed radical and exponential expressions

511Evaluating fractional exponents

512Evaluating fractional exponents: negative unitfraction

513Evaluating fractional exponents: fractional base

514Evaluating quotient of fractional exponents

515Evaluating mixed radicals and exponents

516Simplifying square roots

517Simplifying square roots (variables)

518Simplifying squareroot expressions

519Simplifying square roots

520Simplifying square roots (variables)

521Simplifying squareroot expressions

522Simplifying higherindex roots

523Simplifying cube root expressions

524Simplifying cube root expressions (two variables)

525Simplifying higherindex root expressions

526Simplifying squareroot expressions: no variables

527Simplifying square roots of fractions

528Simplifying rational exponent expressions: mixed exponents and radicals

529Simplifying squareroot expressions: no variables (advanced)

530Simplifying squareroot expressions: no variables (advanced)

531Intro to rationalizing the denominator

532Worked example: rationalizing the denominator

533Simplifying radical expressions (addition)

534Simplifying radical expressions (subtraction)

535Simplifying radical expressions: two variables

536Simplifying radical expressions: three variables

537Simplifying hairy expression with fractional exponents

538Intro to exponential functions

539Exponential vs. linear growth

540Exponential vs. linear models: verbal

541Exponential vs. linear models: table

542Exponential expressions word problems (numerical)

543Initial value & common ratio of exponential functions

544Exponential expressions word problems (algebraic)

545Interpreting exponential expression word problem

546Exponential function graph

547Graphs of exponential growth

548Exponential vs. linear growth over time

549Exponential decay intro

550Graphing exponential growth & decay

551Exponential growth & decay word problems

552Writing exponential functions

553Writing exponential functions from tables

554Writing exponential functions from graphs

555Analyzing tables of exponential functions

556Analyzing graphs of exponential functions

557Analyzing graphs of exponential functions: negative initial value

558Modeling with basic exponential functions word problem

559Rewriting exponential expressions as A⋅Bᵗ

560Equivalent forms of exponential expressions

561Solving exponential equations using exponent properties

562Solving exponential equations using exponent properties (advanced)

563Exponential growth & decay word problems

564Interpreting change in exponential models

565Interpreting time in exponential models

566Constructing exponential models

567Constructing exponential models: half life

568Constructing exponential models: percent change

569Constructing exponential models (old example)

570Interpreting change in exponential models: with manipulation

571Interpreting change in exponential models: changing units

572Structure in exponential expression

573Linear vs. exponential growth: from data

574Linear vs. exponential growth: from data (example 2)

575Comparing growth of exponential & quadratic models

576Intro to logarithms

577Evaluating logarithms (advanced)

578Relationship between exponentials & logarithms

579Relationship between exponentials & logarithms: graphs

580Relationship between exponentials & logarithms: tables

581𝑒 and compound interest

582𝑒 as a limit

583Evaluating natural logarithm with calculator

584Intro to logarithm properties (1 of 2)

585Intro to logarithm properties (2 of 2)

586Using the logarithmic product rule

587Using the logarithmic power rule

588Using the properties of logarithms: multiple steps

589Proof of the logarithm product rule

590Proof of the logarithm quotient and power rules

591Evaluating logarithms: change of base rule

592Using the logarithm change of base rule

593Proof of the logarithm change of base rule

594Proof of the logarithm change of base rule

595Logarithmic equations: variable in the argument

596Logarithmic equations: variable in the base

597Solving exponential equations using logarithms: base10

598Solving exponential equations using logarithms: base2

599Exponential model word problem: medication dissolve

600Exponential model word problem: bacteria growth

601Transforming exponential graphs

602Transforming exponential graphs (example 2)

603Graphing exponential functions

604Exponential function graph

605Graphs of exponential functions (old example)

606Graphical relationship between 2ˣ and log₂(x)

607Shape of a logarithmic parent graph

608Graphs of logarithmic functions

609Vertical asymptote of natural log

610Logarithmic scale (with Vi Hart)

611Logarithmic scale

612Richter scale

613Benford's law (with Vi Hart, 1 of 2)

614Benford's law (with Vi Hart, 2 of 2)
Radical equations & functions

615Intro to squareroot equations & extraneous solutions

616Solving squareroot equations: one solution

617Solving squareroot equations: two solutions

618Solving squareroot equations: no solution

619Squareroot equations intro

620Equation that has a specific extraneous solution

621Solving cuberoot equations

622Domain of a radical function

623Transforming the squareroot function

624Graphs of squareroot functions

625Squareroot functions & their graphs
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