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1.Introduction to Relations and Functions

1.1Relationship between two variables (free lessons)

1.2Understand relations between x- and y-intercepts

1.3Domain and range of a function (free lessons)

1.4Identifying functions

1.5Function notation (free lessons)

2.Functions

2.1Function notation (free lessons)

2.2Operations with functions

2.3Adding functions

2.4Subtracting functions

2.5Multiplying functions

2.6Dividing functions

2.7Composite functions (free lessons)

2.8Inverse functions

2.9One to one functions

2.10Difference quotient: applications of functions

3.Transformations of Functions

3.1Transformations of functions: Horizontal translations

3.2Transformations of functions: Vertical translations

3.3Reflection across the y-axis:

y = f(-x)

(free lessons)

3.4Reflection across the x-axis:

y = -f(x)

3.5Transformations of functions: Horizontal stretches

3.6Transformations of functions: Vertical stretches

3.7Combining transformations of functions

3.8Even and odd functions

4.Factorising Polynomial

4.1Factorise by taking out the greatest common factor (free lessons)

4.2Factorise by grouping

4.3Factorising difference of squares:

x^2 - y^2

4.4Factorising trinomials:

ax^2 + bx + c

4.5Factoring difference of cubes

4.6Factoring sum of cubes

5.Quadratic Functions

5.1Characteristics of quadratic functions (free lessons)

5.2Transformations of quadratic functions

5.3Quadratic function in general form:

y = ax^2 + bx+c

5.4Quadratic function in vertex form: y =

a(x-p)^2 + q

5.5Completing the square

5.6Converting from general to vertex form by completing the square

5.7Shortcut: Vertex formula (free lessons)

5.8Finding the quadratic functions for given parabolas (free lessons)

5.9Applications of quadratic functions

6.Polynomial Functions

6.1Solving quadratic equations by factorising

6.2Solving quadratic equations by completing the square

6.3Using quadratic formula to solve quadratic equations

6.4Nature of roots of quadratic equations: The discriminant

6.5Applications of quadratic equations

6.6Solving quadratic inequalities

7.Radicals

7.1Operations with radicals (free lessons)

7.2Conversion between entire radicals and mixed radicals

7.3Adding and subtracting radicals (free lessons)

7.4Multiplying radicals

7.5Solving radical equations

8.Radical Functions

8.1Basic radical functions

8.2Transformations of radical functions

8.3Square root of a function

8.4Solving radical equations

9.Exponents

9.1Product rule of exponents (free lessons)

9.2Quotient rule of exponents

9.3Power of a product rule

9.4Power of a quotient rule

9.5Power of a power rule (free lessons)

9.6Negative exponent rule

9.7Combining the exponent rules

9.8Scientific notation

9.9Convert between radicals and rational exponents (free lessons)

9.10Solving for exponents

10.Rational Functions

10.1What is a rational function? (free lessons)

10.2Point of discontinuity

10.3Vertical asymptote

10.4Horizontal asymptote

10.5Slant asymptote

10.6Graphs of rational functions

10.7Solving rational equations

10.8Solving rational inequalities

11.Exponential Functions

11.1Exponents: Product rule

(a^x)(a^y)=a^{(x+y)}

(free lessons)

11.2Exponents: Division rule

{a^x \over a^y}=a^{(x-y)}

11.3Exponents: Power rule

(a^x)^y = a^{(x\cdot y)}

(free lessons)

11.4Exponents: Negative exponents

11.5Exponents: Zero exponent:

a^0 = 1

11.6Exponents: Rational exponents

11.7Graphing exponential functions

11.8Graphing transformations of exponential functions

11.9Finding an exponential function given its graph

12.Logarithmic Functions

12.1What is a logarithm?

12.2Converting from logarithmic form to exponential form (free lessons)

12.3Evaluating logarithms without a calculator

12.4Common logarithms

12.5Natural log: ln

12.6Evaluating logarithms using change-of-base formula

12.7Converting from exponential form to logarithmic form (free lessons)

12.8Solving exponential equations with logarithms

12.9Product rule of logarithms (free lessons)

12.10Quotient rule of logarithms

12.11Combining product rule and quotient rule in logarithms

12.12Evaluating logarithms using logarithm rules

12.13Solving logarithmic equations (free lessons)

12.14Graphing logarithmic functions

12.15Finding a logarithmic function given its graph

13.Applications of Exponential and Logarithmic Functions

13.1Exponential growth and decay by a factor

13.2Exponential decay: Half-life (free lessons)

13.3Exponential growth and decay by percentage

13.4Finance: Compound interest

13.5Continuous growth and decay

13.6Logarithmic scale: Richter scale (earthquake)

13.7Logarithmic scale: pH scale

13.8Logarithmic scale: dB scale

13.9Finance: Future value and present value

14.Solving Simultaneous Equations

14.1Determining number of solutions to linear equations (free lessons)

14.2Solving simultaneous equations by graphing

14.3Solving simultaneous equations by elimination

14.4Solving simultaneous equations by substitution

14.5Money related questions in linear equations (free lessons)

14.6Unknown number related questions in linear equations

14.7Distance and time related questions in linear equations

14.8Rectangular shape related questions in linear equations

15.Inequalities in Two Variables

15.1Graphing linear inequalities in two variables (free lessons)

15.2Graphing simultaneous linear inequalities (free lessons)

15.3Graphing quadratic inequalities in two variables

15.4Graphing simultaneous quadratic inequalities

15.5Applications of inequalities

15.6What is linear programming?

15.7Linear programming word problems

16.Introduction to Trigonometry

16.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

16.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

16.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

16.4Combination of SohCahToa questions (free lessons)

16.5Solving expressions using 45-45-90 special right triangles (free lessons)

16.6Solving expressions using 30-60-90 special right triangles

16.7Word problems relating ladder in trigonometry

16.8Word problems relating guy wire in trigonometry

16.9Other word problems relating angles in trigonometry

17.Trigonometric Ratios and Angle Measure

17.1Standard angle

17.2Coterminal angles (free lessons)

17.3Reference angles

17.4Find the exact value of trigonometric ratios

17.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)

17.6Unit circle (free lessons)

17.8Cosine rule

17.9Applications of the sine rule and cosine rule

18.Graphing Trigonometric Functions

18.1Sine graph: y = sin x

18.2Cosine graph: y = cos x

18.3Tangent graph: y = tan x

18.4Cotangent graph: y = cot x

18.5Secant graph: y = sec x

18.6Cosecant graph: y = csc x

18.7Graphing transformations of trigonometric functions

18.8Determining trigonometric functions given their graphs

19.Applications of Trigonometric Functions

19.1Ferris wheel trig problems

19.2Tides and water depth trig problems

19.3Spring (simple harmonic motion) trig problems

20.Trigonometric Identities

20.1Quotient identities and reciprocal identities (free lessons)

20.2Pythagorean identities

20.3Sum and difference identities

20.4Cofunction identities

20.5Double-angle identities (free lessons)

21.Conics

21.1Conics - Parabola

21.2Conics - Ellipse

21.3Conics - Circle

21.4Conics - Hyperbola

22.Imaginary and Complex Numbers

22.1Introduction to imaginary numbers

22.2Complex numbers and complex planes

22.3Adding and subtracting complex numbers

22.4Complex conjugates

22.5Multiplying and dividing complex numbers

22.6Distance and midpoint of complex numbers

22.7Angle and absolute value of complex numbers

22.8Polar form of complex numbers

22.9Operations on complex numbers in polar form

23.Vectors

23.1Introduction to vectors

23.2Magnitude of a vector

23.3Direction angle of a vector

23.4Scalar multiplication

23.5Equivalent vectors

23.6Adding and subtracting vectors in component form

23.7Operations on vectors in magnitude and direction form

24.Sequences and Series

24.1Arithmetic sequences (free lessons)

24.2Arithmetic series (free lessons)

24.3Geometric sequences

24.4Geometric series

24.5Infinite geometric series

24.6Sigma notation

24.7Arithmetic mean vs. Geometric mean

25.Permutations and Combinations

25.1Fundamental counting principle

25.2Factorial notation

25.3Path counting problems

25.4Permutation vs. Combination

25.5Permutations

25.6Combinations

25.7Problems involving both permutations and combinations

25.8Pascal's triangle

25.9Binomial theorem

26.Introduction to Probability

26.1Introduction to probability

26.2Organizing outcomes

26.3Probability of independent events

26.4Comparing experimental and theoretical probability

27.Probability

27.1Determining probabilities using tree diagrams and tables (free lessons)

27.2Probability of independent events

27.3Probability with Venn diagrams

28.Derivatives

28.1Definition of derivative

28.3Gradient and equation of tangent line

28.5Derivative of trigonometric functions

28.6Derivative of exponential functions

28.7Product rule

28.8Quotient rule

28.9Implicit differentiation

28.10Derivative of inverse trigonometric functions

28.11Derivative of logarithmic functions

28.12Higher order derivatives

29.Introduction to Matrices

29.1Notation of matrices

29.2Adding and subtracting matrices

29.3Multiplying a matrix by a scalar

29.4Multiplying a matrix by another matrix

29.5The three types of matrix row operations

29.6Representing a linear system as a matrix

29.7Solving a linear system with matrices using Gaussian elimination

30.Properties of Matrices

30.1Zero matrix

30.2Identity matrix

30.3Properties of matrix addition

30.4Properties of matrix scalar multiplication

31.Determinants and Inverses of Matrices

31.1The determinant of a 2 x 2 matrix

31.2The determinant of a 3 x 3 matrix (General & Shortcut Method)

31.3The inverse of a 2 x 2 matrix

31.4The inverse of 3 x 3 matrices with matrix row operations

31.5The inverse of 3 x 3 matrix with determinants and adjugate

31.62 x 2 invertible matrix

31.7Solving linear systems using Cramer's Rule

31.8Solving linear systems using 2 x 2 inverse matrices

32.Transformations with Matrices

32.1Transforming vectors with matrices

32.2Transforming shapes with matrices

32.3Finding the transformation matrix

1.Introduction to Relations and Functions

1.1Relationship between two variables (free lessons)

1.2Understand relations between x- and y-intercepts

1.3Domain and range of a function (free lessons)

1.4Identifying functions

1.5Function notation (free lessons)

2.Functions

2.1Function notation (free lessons)

2.2Operations with functions

2.3Adding functions

2.4Subtracting functions

2.5Multiplying functions

2.6Dividing functions

2.7Composite functions (free lessons)

2.8Inverse functions

2.9One to one functions

2.10Difference quotient: applications of functions

3.Transformations of Functions

3.1Transformations of functions: Horizontal translations

3.2Transformations of functions: Vertical translations

3.3Reflection across the y-axis:

y = f(-x)

(free lessons)

3.4Reflection across the x-axis:

y = -f(x)

3.5Transformations of functions: Horizontal stretches

3.6Transformations of functions: Vertical stretches

3.7Combining transformations of functions

3.8Even and odd functions

4.Factorising Polynomial

4.1Factorise by taking out the greatest common factor (free lessons)

4.2Factorise by grouping

4.3Factorising difference of squares:

x^2 - y^2

4.4Factorising trinomials:

ax^2 + bx + c

4.5Factoring difference of cubes

4.6Factoring sum of cubes

5.Quadratic Functions

5.1Characteristics of quadratic functions (free lessons)

5.2Transformations of quadratic functions

5.3Quadratic function in general form:

y = ax^2 + bx+c

5.4Quadratic function in vertex form: y =

a(x-p)^2 + q

5.5Completing the square

5.6Converting from general to vertex form by completing the square

5.7Shortcut: Vertex formula (free lessons)

5.8Finding the quadratic functions for given parabolas (free lessons)

5.9Applications of quadratic functions

6.Polynomial Functions

6.1Solving quadratic equations by factorising

6.2Solving quadratic equations by completing the square

6.3Using quadratic formula to solve quadratic equations

6.4Nature of roots of quadratic equations: The discriminant

6.5Applications of quadratic equations

6.6Solving quadratic inequalities

7.Radicals

7.1Operations with radicals (free lessons)

7.2Conversion between entire radicals and mixed radicals

7.3Adding and subtracting radicals (free lessons)

7.4Multiplying radicals

7.5Solving radical equations

8.Radical Functions

8.1Basic radical functions

8.2Transformations of radical functions

8.3Square root of a function

8.4Solving radical equations

9.Exponents

9.1Product rule of exponents (free lessons)

9.2Quotient rule of exponents

9.3Power of a product rule

9.4Power of a quotient rule

9.5Power of a power rule (free lessons)

9.6Negative exponent rule

9.7Combining the exponent rules

9.8Scientific notation

9.9Convert between radicals and rational exponents (free lessons)

9.10Solving for exponents

10.Rational Functions

10.1What is a rational function? (free lessons)

10.2Point of discontinuity

10.3Vertical asymptote

10.4Horizontal asymptote

10.5Slant asymptote

10.6Graphs of rational functions

10.7Solving rational equations

10.8Solving rational inequalities

11.Exponential Functions

11.1Exponents: Product rule

(a^x)(a^y)=a^{(x+y)}

(free lessons)

11.2Exponents: Division rule

{a^x \over a^y}=a^{(x-y)}

11.3Exponents: Power rule

(a^x)^y = a^{(x\cdot y)}

(free lessons)

11.4Exponents: Negative exponents

11.5Exponents: Zero exponent:

a^0 = 1

11.6Exponents: Rational exponents

11.7Graphing exponential functions

11.8Graphing transformations of exponential functions

11.9Finding an exponential function given its graph

12.Logarithmic Functions

12.1What is a logarithm?

12.2Converting from logarithmic form to exponential form (free lessons)

12.3Evaluating logarithms without a calculator

12.4Common logarithms

12.5Natural log: ln

12.6Evaluating logarithms using change-of-base formula

12.7Converting from exponential form to logarithmic form (free lessons)

12.8Solving exponential equations with logarithms

12.9Product rule of logarithms (free lessons)

12.10Quotient rule of logarithms

12.11Combining product rule and quotient rule in logarithms

12.12Evaluating logarithms using logarithm rules

12.13Solving logarithmic equations (free lessons)

12.14Graphing logarithmic functions

12.15Finding a logarithmic function given its graph

13.Applications of Exponential and Logarithmic Functions

13.1Exponential growth and decay by a factor

13.2Exponential decay: Half-life (free lessons)

13.3Exponential growth and decay by percentage

13.4Finance: Compound interest

13.5Continuous growth and decay

13.6Logarithmic scale: Richter scale (earthquake)

13.7Logarithmic scale: pH scale

13.8Logarithmic scale: dB scale

13.9Finance: Future value and present value

14.Solving Simultaneous Equations

14.1Determining number of solutions to linear equations (free lessons)

14.2Solving simultaneous equations by graphing

14.3Solving simultaneous equations by elimination

14.4Solving simultaneous equations by substitution

14.5Money related questions in linear equations (free lessons)

14.6Unknown number related questions in linear equations

14.7Distance and time related questions in linear equations

14.8Rectangular shape related questions in linear equations

15.Inequalities in Two Variables

15.1Graphing linear inequalities in two variables (free lessons)

15.2Graphing simultaneous linear inequalities (free lessons)

15.3Graphing quadratic inequalities in two variables

15.4Graphing simultaneous quadratic inequalities

15.5Applications of inequalities

15.6What is linear programming?

15.7Linear programming word problems

16.Introduction to Trigonometry

16.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

16.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

16.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

16.4Combination of SohCahToa questions (free lessons)

16.5Solving expressions using 45-45-90 special right triangles (free lessons)

16.6Solving expressions using 30-60-90 special right triangles

16.7Word problems relating ladder in trigonometry

16.8Word problems relating guy wire in trigonometry

16.9Other word problems relating angles in trigonometry

17.Trigonometric Ratios and Angle Measure

17.1Standard angle

17.2Coterminal angles (free lessons)

17.3Reference angles

17.4Find the exact value of trigonometric ratios

17.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)

17.6Unit circle (free lessons)

17.8Cosine rule

17.9Applications of the sine rule and cosine rule

18.Graphing Trigonometric Functions

18.1Sine graph: y = sin x

18.2Cosine graph: y = cos x

18.3Tangent graph: y = tan x

18.4Cotangent graph: y = cot x

18.5Secant graph: y = sec x

18.6Cosecant graph: y = csc x

18.7Graphing transformations of trigonometric functions

18.8Determining trigonometric functions given their graphs

19.Applications of Trigonometric Functions

19.1Ferris wheel trig problems

19.2Tides and water depth trig problems

19.3Spring (simple harmonic motion) trig problems

20.Trigonometric Identities

20.1Quotient identities and reciprocal identities (free lessons)

20.2Pythagorean identities

20.3Sum and difference identities

20.4Cofunction identities

20.5Double-angle identities (free lessons)

21.Conics

21.1Conics - Parabola

21.2Conics - Ellipse

21.3Conics - Circle

21.4Conics - Hyperbola

22.Imaginary and Complex Numbers

22.1Introduction to imaginary numbers

22.2Complex numbers and complex planes

22.3Adding and subtracting complex numbers

22.4Complex conjugates

22.5Multiplying and dividing complex numbers

22.6Distance and midpoint of complex numbers

22.7Angle and absolute value of complex numbers

22.8Polar form of complex numbers

22.9Operations on complex numbers in polar form

23.Vectors

23.1Introduction to vectors

23.2Magnitude of a vector

23.3Direction angle of a vector

23.4Scalar multiplication

23.5Equivalent vectors

23.6Adding and subtracting vectors in component form

23.7Operations on vectors in magnitude and direction form

24.Sequences and Series

24.1Arithmetic sequences (free lessons)

24.2Arithmetic series (free lessons)

24.3Geometric sequences

24.4Geometric series

24.5Infinite geometric series

24.6Sigma notation

24.7Arithmetic mean vs. Geometric mean

25.Permutations and Combinations

25.1Fundamental counting principle

25.2Factorial notation

25.3Path counting problems

25.4Permutation vs. Combination

25.5Permutations

25.6Combinations

25.7Problems involving both permutations and combinations

25.8Pascal's triangle

25.9Binomial theorem

26.Introduction to Probability

26.1Introduction to probability

26.2Organizing outcomes

26.3Probability of independent events

26.4Comparing experimental and theoretical probability

27.Probability

27.1Determining probabilities using tree diagrams and tables (free lessons)

27.2Probability of independent events

27.3Probability with Venn diagrams

28.Derivatives

28.1Definition of derivative

28.3Gradient and equation of tangent line

28.5Derivative of trigonometric functions

28.6Derivative of exponential functions

28.7Product rule

28.8Quotient rule

28.9Implicit differentiation

28.10Derivative of inverse trigonometric functions

28.11Derivative of logarithmic functions

28.12Higher order derivatives

29.Introduction to Matrices

29.1Notation of matrices

29.2Adding and subtracting matrices

29.3Multiplying a matrix by a scalar

29.4Multiplying a matrix by another matrix

29.5The three types of matrix row operations

29.6Representing a linear system as a matrix

29.7Solving a linear system with matrices using Gaussian elimination

30.Properties of Matrices

30.1Zero matrix

30.2Identity matrix

30.3Properties of matrix addition

30.4Properties of matrix scalar multiplication

31.Determinants and Inverses of Matrices

31.1The determinant of a 2 x 2 matrix

31.2The determinant of a 3 x 3 matrix (General & Shortcut Method)

31.3The inverse of a 2 x 2 matrix

31.4The inverse of 3 x 3 matrices with matrix row operations

31.5The inverse of 3 x 3 matrix with determinants and adjugate

31.62 x 2 invertible matrix

31.7Solving linear systems using Cramer's Rule

31.8Solving linear systems using 2 x 2 inverse matrices

32.Transformations with Matrices

32.1Transforming vectors with matrices

32.2Transforming shapes with matrices

32.3Finding the transformation matrix

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