Some Online Resources for Extra Help Unit 1 Review and Properties of Functions
What is a function, domain and range http://www.purplemath.com/modules/fcns2.htm
12 basic functions https://teacher.ocps.net/jean.adams/media/15pcf.pdf
Odd and Even functions http://www.mathsisfun.com/algebra/functions-odd-even.html
Inverse relations: http://www.purplemath.com/modules/invrsfcn3.htm
Unit 2: Rates of Change 2.1 Average Rate of Change: https://www.youtube.com/watch?v=YpYSEXAxMJ0 2.2 Finding the Instantaneous Rate of Change From a Table: https://www.youtube.com/watch?v=Srq77uwSC8A From an equation (difference quotient): https://www.youtube.com/watch?v=IePCHjMeFkE 2.3 Finding the Instantaneous Rate of Change from a graph http://youtu.be/oDrxCR4s9BE?t=3m18s 2.5 Finding maximum and minimum values with the derivative http://www.themathpage.com/acalc/max.htm Unit 3: Polynomial Functions, Polynomial equations and inequalities: 3.1 Exploring polynomials What is a Polynomial? http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-polynomial-2009-1.pdf Using Finite Differences https://www.youtube.com/watch?v=Vp-PyKOf9NI 3.2 Characteristics of polynomials, 3.3 Multiplicities of zeroes http://www.purplemath.com/modules/polyends.htm (5 pages, comprehensive) 3.4 Transformations of cubics and quartics https://www.youtube.com/watch?v=P8cz-YqWaMw 3.5 division of functions long division: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/dividing_polynomials/v/polynomial-division synthetic division: http://www.purplemath.com/modules/synthdiv.htm 3.6 factoring polynomials The Remainder and Factor Theorems: http://www.mathsisfun.com/algebra/polynomials-remainder-factor.html 3.7 Solving Higher Degree Polynomials: synthetic method: https://www.youtube.com/watch?v=V4SwG-SPCn0 3.8 Solving linear inequalities http://www.purplemath.com/modules/ineqlin3.htm 3.9 Solving Polynomial Inequalities Using a table: https://www.youtube.com/watch?v=idBbsanc8BQ 3.10 Rates of change in polynomial functions see rates of change section Unit 4: Rational functions: 4.1 Graphing Reciprocal Functions https://www.youtube.com/watch?v=xRcPMktBHDw 4.2 Introduction to Rational Functions 4.3 Graphs of Rational Functions Graphing: https://www.youtube.com/watch?v=b-CydtdDYD8 Finding asymptotes: https://www.youtube.com/watch?v=f4s7POhnEGU 4.4 Rational Equations Solving rational equations: http://www.purplemath.com/modules/solvrtnl.htm 4.5 Rational Inequalities Rational inequalities: https://www.youtube.com/watch?v=Dd-dwlUqkZM (he uses testing points, using a table is often easier) 4.6 Rates of Change in Rational Functions See Rates of Change Unit Unit 5: Trigonometric functions: 5.1 Introduction to radians: 5.2 Radian measure on the Cartesian plane and special triangles https://www.youtube.com/watch?v=nh__OEPKXnY 5.3 Graphing the primary trigonometric functions http://www.purplemath.com/modules/triggrph.htm 5.4 Transformations of trigonometric functions: Sine function: https://www.desmos.com/calculator/absl7xylcv All 6 basic functions: http://illuminations.nctm.org/Activity.aspx?id=3589 5.5 Graphs of the reciprocal trigonometric functions: Graphing: http://www.purplemath.com/modules/triggrph3.htm Arithmetic series review: https://www.youtube.com/watch?v=6W4AiQbRrCk 5.6 Modelling with Trigonometric Functions 5.7 Rates of Change in Trigonometric Functions See Rates of Change Unit Unit 6: Logarithmic Functions: Unit 7: Trigonometric Identities:
7.1 Equivalent trigonometric functions https://www.desmos.com/calculator/segceek8zw
7.2 Compound angle formulas http://www.projectalevel.co.uk/as_a2_maths/compound_angle_formulae
7.3 Double Angle Formulas http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-doubleangle-2009-1.pdf
7.4 Proving Trig Identities http://www.purplemath.com/modules/proving.htm
7.5 and 7.6 SolvingTrig Equations http://www.purplemath.com/modules/solvtrig.htm Unit 8: Combined Functions:
8.1 Introduction to Logarithms https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_basics/v/logarithms
8.2 Transformations of logarithmic functions https://www.youtube.com/watch?v=gfbfLplz3us
8.3 Simplifying Logarithms
8.4 Laws of logarithms
8.5 Solving Exponential Equations http://www.purplemath.com/modules/solvexpo2.htm
8.6 Solving Logarithmic Equations
8.7 Solving Problems with Exponential and Logarithmic Functions
8.8 Rate of Change in Logarithmic Functions See rate of change unit. Note that we can only approximate an IROC for logarithms and exponentials at this time.
Unit 9: Combining Functions
9.1 Exploring function combinations https://www.desmos.com/calculator/eqw4vvbwzl
9.2 Sums and Differences of Functions https://learnzillion.com/lessons/4007-combining-functions-by-adding-and-subtracting
9.3 Product of functions
9.4 Quotients of Functions
9.5 Composition of Functions https://www.youtube.com/watch?v=PCHkzAxiJwU
9.6 Solving Function Equalities and 9.7 Modelling With Functions These sections use skills developed over the entire course, hence there are no easy resources available. |
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