Grade 12‎ > ‎

MHF4U

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

Quadratics: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_ineq/v/quadratic-inequalities-visual-explanation


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


https://www.khanacademy.org/math/algebra2/polynomial_and_rational/asymptotes-graphing-rational/v/another-rational-function-graph-example


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


https://www.khanacademy.org/math/algebra2/rational-expressions/solving-rational-equations/v/solving-rational-equations-1


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:

https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/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

https://www.khanacademy.org/math/trigonometry/trig-function-graphs/modeling-periodic-functions/v/modeling-temperature-fluxtuations


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

https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_basics/v/fancier-logarithm-expressions

 

8.4 Laws of logarithms

http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U18_L2_T2_text_final.html

 

8.5 Solving Exponential Equations

http://www.purplemath.com/modules/solvexpo2.htm

 

https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_basics/v/exponential-equation

 

8.6 Solving Logarithmic Equations

https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/logarithmic-equations/v/solving-logarithmic-equations

 

8.7 Solving Problems with Exponential and Logarithmic Functions

http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U18_L4_T2_text_final.html

 

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

https://www.khanacademy.org/math/algebra/algebra-functions/eval-function-expressions/v/product-of-functions

 

9.4 Quotients of Functions

https://www.khanacademy.org/math/algebra/algebra-functions/eval-function-expressions/v/quotient-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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