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1.Solving Linear Equations

1.1Solving linear equations using multiplication and division (free lessons)

1.2Solving two-step linear equations:

ax + b = c

{x \over a} + b = c

1.3Solving linear equations using distributive property:

a(x + b) = c

1.4Solving linear equations with variables on both sides

1.5Solving literal equations

2.Linear Inequalities

2.1Express linear inequalities graphically and algebraically (free lessons)

2.2Solving one-step linear inequalities

2.3Solving multi-step linear inequalities

3.Factorising Quadratic Equations

3.1Factorise by taking out the greatest common factor (free lessons)

3.2Factorise by grouping

3.3Factorising difference of squares:

x^2 - y^2

3.4Factorising trinomials:

ax^2 + bx + c

3.5Factoring difference of cubes

3.6Factoring sum of cubes

4.Quadratic Functions

4.1Characteristics of quadratic functions (free lessons)

4.2Transformations of quadratic functions

4.3Quadratic function in general form:

y = ax^2 + bx+c

4.4Quadratic function in vertex form: y =

a(x-p)^2 + q

4.5Completing the square

4.6Converting from general to vertex form by completing the square

4.7Shortcut: Vertex formula (free lessons)

4.8Finding the quadratic functions for given parabolas (free lessons)

4.9Applications of quadratic functions

5.Quadratic Equations and Inequalities

5.1Solving quadratic equations by factorising

5.2Solving quadratic equations by completing the square

5.3Using quadratic formula to solve quadratic equations

5.4Nature of roots of quadratic equations: The discriminant

5.5Applications of quadratic equations

5.6Solving quadratic inequalities

6.Introduction to Relations and Functions

6.1Relationship between two variables (free lessons)

6.2Understand relations between x- and y-intercepts

6.3Domain and range of a function

6.4Identifying functions

6.5Function notation (free lessons)

7.Linear Functions

7.1Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

(free lessons)

7.2Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

7.3Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

7.4Gradient intercept form: y = mx + b

7.5General form: Ax + By + C = 0 (free lessons)

7.6Gradient-point form:

y - y_1 = m (x - x_1)

7.7Rate of change

7.8Graphing linear functions using table of values

7.9Graphing linear functions using x- and y-intercepts (free lessons)

7.10Graphing from gradient-intercept form y=mx+b

7.11Graphing linear functions using a single point and gradient

7.12Word problems of graphing linear functions

7.13Parallel and perpendicular lines in linear functions (free lessons)

7.14Applications of linear relations

8.Linear equations (Advanced)

8.1Introduction to linear equations (free lessons)

8.2Introduction to nonlinear equations

8.3Special case of linear equations: Horizontal lines

8.4Special case of linear equations: Vertical lines

8.5Parallel line equation (free lessons)

8.6Perpendicular line equation

8.7Combination of both parallel and perpendicular line equations

8.8Applications of linear equations

9.Solving Simultaneous Equations

9.1Determining number of solutions to linear equations (free lessons)

9.2Solving simultaneous equations by graphing

9.3Solving simultaneous equations by elimination

9.4Solving simultaneous equations by substitution

9.5Money related questions in linear equations (free lessons)

9.6Unknown number related questions in linear equations

9.7Distance and time related questions in linear equations

9.8Rectangular shape related questions in linear equations

10.Imaginary and Complex Numbers

10.1Introduction to imaginary numbers

10.2Complex numbers and complex planes

10.3Adding and subtracting complex numbers

10.4Complex conjugates

10.5Multiplying and dividing complex numbers

10.6Distance and midpoint of complex numbers

10.7Angle and absolute value of complex numbers

10.8Polar form of complex numbers

10.9Operations on complex numbers in polar form

11.Operations of polynomials

11.1What is a polynomial? (free lessons)

11.2Polynomial components

11.3Multiplying monomial by monomial

11.4Multiplying monomial by binomial

11.5Multiplying binomial by binomial (free lessons)

11.6Multiplying polynomial by polynomial

11.7Applications of polynomials

11.8Fundamental theorem of algebra

11.9Pascal's triangle

11.10Binomial theorem

12.Radicals

12.1Operations with radicals (free lessons)

12.2Conversion between entire radicals and mixed radicals

12.3Adding and subtracting radicals (free lessons)

12.4Multiplying radicals

12.5Solving radical equations

13.Radical Functions

13.1Basic radical functions

13.2Transformations of radical functions

13.3Square root of a function

13.4Solving radical equations

14.Rational Expressions

14.1Simplifying rational expressions and restrictions

14.2Adding and subtracting rational expressions (free lessons)

14.3Multiplying rational expressions

14.4Dividing rational expressions

14.5Solving rational equations

14.6Applications of rational equations

14.7Simplifying complex fractions

14.8Partial fraction decomposition

15.Rational Functions

15.1What is a rational function? (free lessons)

15.2Point of discontinuity

15.3Vertical asymptote

15.4Horizontal asymptote

15.5Slant asymptote

15.6Graphs of rational functions

15.7Solving rational equations

15.8Solving rational inequalities

16.Operations of Functions

16.1Function notation (free lessons)

16.2Operations with functions

16.3Adding functions

16.4Subtracting functions

16.5Multiplying functions

16.6Dividing functions

16.7Composite functions (free lessons)

16.8Inverse functions

16.9One to one functions

16.10Difference quotient: applications of functions

17.Transformations of Functions

17.1Transformations of functions: Horizontal translations

17.2Transformations of functions: Vertical translations

17.3Reflection across the y-axis:

y = f(-x)

17.4Reflection across the x-axis:

y = -f(x)

17.5Transformations of functions: Horizontal stretches

17.6Transformations of functions: Vertical stretches

17.7Combining transformations of functions

17.8Even and odd functions

18.Exponential Functions

18.1Exponents: Product rule

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

(free lessons)

18.2Exponents: Division rule

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

18.3Exponents: Power rule

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

(free lessons)

18.4Exponents: Negative exponents

18.5Exponents: Zero exponent:

a^0 = 1

18.6Exponents: Rational exponents

18.7Graphing exponential functions

18.8Graphing transformations of exponential functions

18.9Finding an exponential function given its graph

19.Applications of Exponential Functions

19.1Exponential growth and decay by a factor

19.2Exponential decay: Half-life (free lessons)

19.3Exponential growth and decay by percentage

19.4Finance: Compound interest

19.5Continuous growth and decay

20.Logarithmic Functions

20.1What is a logarithm?

20.2Converting from logarithmic form to exponential form (free lessons)

20.3Evaluating logarithms without a calculator

20.4Common logarithms

20.5Natural log: ln

20.6Evaluating logarithms using change-of-base formula

20.7Converting from exponential form to logarithmic form (free lessons)

20.8Solving exponential equations with logarithms

20.9Product rule of logarithms (free lessons)

20.10Quotient rule of logarithms

20.11Combining product rule and quotient rule in logarithms

20.12Evaluating logarithms using logarithm rules

20.13Solving logarithmic equations

20.14Graphing logarithmic functions

20.15Finding a logarithmic function given its graph

21.Conics

21.1Conics - Parabola

21.2Conics - Ellipse

21.3Conics - Circle

21.4Conics - Hyperbola

22.Introduction to Trigonometry

22.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

22.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

22.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

22.4Combination of SohCahToa questions

22.5Solving expressions using 45-45-90 special right triangles (free lessons)

22.6Solving expressions using 30-60-90 special right triangles

22.7Word problems relating ladder in trigonometry

22.8Word problems relating guy wire in trigonometry

22.9Other word problems relating angles in trigonometry

23.Trigonometry

23.1Angle in standard position

23.2Coterminal angles (free lessons)

23.3Reference angle

23.4Find the exact value of trigonometric ratios

23.5ASTC rule in trigonometry (All Students Take Calculus)

23.6Unit circle (free lessons)

23.7Converting between degrees and radians

23.8Trigonometric ratios of angles in radians

23.9Radian measure and arc length

23.10Law of sines

23.11Law of cosines

23.12Applications of the sine law and cosine law

24.Graphing Trigonometric Functions

24.1Sine graph: y = sin x

24.2Cosine graph: y = cos x

24.3Tangent graph: y = tan x

24.4Cotangent graph: y = cot x

24.5Secant graph: y = sec x

24.6Cosecant graph: y = csc x

24.7Graphing transformations of trigonometric functions

24.8Determining trigonometric functions given their graphs

25.Trigonometric Identities

25.1Quotient identities and reciprocal identities (free lessons)

25.2Pythagorean identities

25.3Sum and difference identities

25.4Cofunction identities

25.5Double-angle identities (free lessons)

26.Sequences

26.1Arithmetic sequences (free lessons)

26.2Geometric sequences

26.3Sigma notation

27.Derivatives

27.1Definition of derivative

27.4Derivative of exponential functions

27.5Product rule

27.6Quotient rule

27.7Derivative of logarithmic functions

28.Probability

28.1Determining probabilities using tree diagrams and tables (free lessons)

28.2Probability of independent events

28.3Applications of probability

28.4Probability with Venn diagrams

29.Statistics

29.1Median and mode

29.3Range and outliers

29.4Application of averages

30.Introduction to Matrices

30.1Notation of matrices

30.2Adding and subtracting matrices

30.3Multiplying a matrix by a scalar

30.4Multiplying a matrix by another matrix

30.5The three types of matrix row operations

30.6Representing a linear system as a matrix

30.7Solving a linear system with matrices using Gaussian elimination

1.Solving Linear Equations

1.1Solving linear equations using multiplication and division (free lessons)

1.2Solving two-step linear equations:

ax + b = c

{x \over a} + b = c

1.3Solving linear equations using distributive property:

a(x + b) = c

1.4Solving linear equations with variables on both sides

1.5Solving literal equations

2.Linear Inequalities

2.1Express linear inequalities graphically and algebraically (free lessons)

2.2Solving one-step linear inequalities

2.3Solving multi-step linear inequalities

3.Factorising Quadratic Equations

3.1Factorise by taking out the greatest common factor (free lessons)

3.2Factorise by grouping

3.3Factorising difference of squares:

x^2 - y^2

3.4Factorising trinomials:

ax^2 + bx + c

3.5Factoring difference of cubes

3.6Factoring sum of cubes

4.Quadratic Functions

4.1Characteristics of quadratic functions (free lessons)

4.2Transformations of quadratic functions

4.3Quadratic function in general form:

y = ax^2 + bx+c

4.4Quadratic function in vertex form: y =

a(x-p)^2 + q

4.5Completing the square

4.6Converting from general to vertex form by completing the square

4.7Shortcut: Vertex formula (free lessons)

4.8Finding the quadratic functions for given parabolas (free lessons)

4.9Applications of quadratic functions

5.Quadratic Equations and Inequalities

5.1Solving quadratic equations by factorising

5.2Solving quadratic equations by completing the square

5.3Using quadratic formula to solve quadratic equations

5.4Nature of roots of quadratic equations: The discriminant

5.5Applications of quadratic equations

5.6Solving quadratic inequalities

6.Introduction to Relations and Functions

6.1Relationship between two variables (free lessons)

6.2Understand relations between x- and y-intercepts

6.3Domain and range of a function

6.4Identifying functions

6.5Function notation (free lessons)

7.Linear Functions

7.1Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

(free lessons)

7.2Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

7.3Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

7.4Gradient intercept form: y = mx + b

7.5General form: Ax + By + C = 0 (free lessons)

7.6Gradient-point form:

y - y_1 = m (x - x_1)

7.7Rate of change

7.8Graphing linear functions using table of values

7.9Graphing linear functions using x- and y-intercepts (free lessons)

7.10Graphing from gradient-intercept form y=mx+b

7.11Graphing linear functions using a single point and gradient

7.12Word problems of graphing linear functions

7.13Parallel and perpendicular lines in linear functions (free lessons)

7.14Applications of linear relations

8.Linear equations (Advanced)

8.1Introduction to linear equations (free lessons)

8.2Introduction to nonlinear equations

8.3Special case of linear equations: Horizontal lines

8.4Special case of linear equations: Vertical lines

8.5Parallel line equation (free lessons)

8.6Perpendicular line equation

8.7Combination of both parallel and perpendicular line equations

8.8Applications of linear equations

9.Solving Simultaneous Equations

9.1Determining number of solutions to linear equations (free lessons)

9.2Solving simultaneous equations by graphing

9.3Solving simultaneous equations by elimination

9.4Solving simultaneous equations by substitution

9.5Money related questions in linear equations (free lessons)

9.6Unknown number related questions in linear equations

9.7Distance and time related questions in linear equations

9.8Rectangular shape related questions in linear equations

10.Imaginary and Complex Numbers

10.1Introduction to imaginary numbers

10.2Complex numbers and complex planes

10.3Adding and subtracting complex numbers

10.4Complex conjugates

10.5Multiplying and dividing complex numbers

10.6Distance and midpoint of complex numbers

10.7Angle and absolute value of complex numbers

10.8Polar form of complex numbers

10.9Operations on complex numbers in polar form

11.Operations of polynomials

11.1What is a polynomial? (free lessons)

11.2Polynomial components

11.3Multiplying monomial by monomial

11.4Multiplying monomial by binomial

11.5Multiplying binomial by binomial (free lessons)

11.6Multiplying polynomial by polynomial

11.7Applications of polynomials

11.8Fundamental theorem of algebra

11.9Pascal's triangle

11.10Binomial theorem

12.Radicals

12.1Operations with radicals (free lessons)

12.2Conversion between entire radicals and mixed radicals

12.3Adding and subtracting radicals (free lessons)

12.4Multiplying radicals

12.5Solving radical equations

13.Radical Functions

13.1Basic radical functions

13.2Transformations of radical functions

13.3Square root of a function

13.4Solving radical equations

14.Rational Expressions

14.1Simplifying rational expressions and restrictions

14.2Adding and subtracting rational expressions (free lessons)

14.3Multiplying rational expressions

14.4Dividing rational expressions

14.5Solving rational equations

14.6Applications of rational equations

14.7Simplifying complex fractions

14.8Partial fraction decomposition

15.Rational Functions

15.1What is a rational function? (free lessons)

15.2Point of discontinuity

15.3Vertical asymptote

15.4Horizontal asymptote

15.5Slant asymptote

15.6Graphs of rational functions

15.7Solving rational equations

15.8Solving rational inequalities

16.Operations of Functions

16.1Function notation (free lessons)

16.2Operations with functions

16.3Adding functions

16.4Subtracting functions

16.5Multiplying functions

16.6Dividing functions

16.7Composite functions (free lessons)

16.8Inverse functions

16.9One to one functions

16.10Difference quotient: applications of functions

17.Transformations of Functions

17.1Transformations of functions: Horizontal translations

17.2Transformations of functions: Vertical translations

17.3Reflection across the y-axis:

y = f(-x)

17.4Reflection across the x-axis:

y = -f(x)

17.5Transformations of functions: Horizontal stretches

17.6Transformations of functions: Vertical stretches

17.7Combining transformations of functions

17.8Even and odd functions

18.Exponential Functions

18.1Exponents: Product rule

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

(free lessons)

18.2Exponents: Division rule

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

18.3Exponents: Power rule

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

(free lessons)

18.4Exponents: Negative exponents

18.5Exponents: Zero exponent:

a^0 = 1

18.6Exponents: Rational exponents

18.7Graphing exponential functions

18.8Graphing transformations of exponential functions

18.9Finding an exponential function given its graph

19.Applications of Exponential Functions

19.1Exponential growth and decay by a factor

19.2Exponential decay: Half-life (free lessons)

19.3Exponential growth and decay by percentage

19.4Finance: Compound interest

19.5Continuous growth and decay

20.Logarithmic Functions

20.1What is a logarithm?

20.2Converting from logarithmic form to exponential form (free lessons)

20.3Evaluating logarithms without a calculator

20.4Common logarithms

20.5Natural log: ln

20.6Evaluating logarithms using change-of-base formula

20.7Converting from exponential form to logarithmic form (free lessons)

20.8Solving exponential equations with logarithms

20.9Product rule of logarithms (free lessons)

20.10Quotient rule of logarithms

20.11Combining product rule and quotient rule in logarithms

20.12Evaluating logarithms using logarithm rules

20.13Solving logarithmic equations

20.14Graphing logarithmic functions

20.15Finding a logarithmic function given its graph

21.Conics

21.1Conics - Parabola

21.2Conics - Ellipse

21.3Conics - Circle

21.4Conics - Hyperbola

22.Introduction to Trigonometry

22.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

22.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

22.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

22.4Combination of SohCahToa questions

22.5Solving expressions using 45-45-90 special right triangles (free lessons)

22.6Solving expressions using 30-60-90 special right triangles

22.7Word problems relating ladder in trigonometry

22.8Word problems relating guy wire in trigonometry

22.9Other word problems relating angles in trigonometry

23.Trigonometry

23.1Angle in standard position

23.2Coterminal angles (free lessons)

23.3Reference angle

23.4Find the exact value of trigonometric ratios

23.5ASTC rule in trigonometry (All Students Take Calculus)

23.6Unit circle (free lessons)

23.7Converting between degrees and radians

23.8Trigonometric ratios of angles in radians

23.9Radian measure and arc length

23.10Law of sines

23.11Law of cosines

23.12Applications of the sine law and cosine law

24.Graphing Trigonometric Functions

24.1Sine graph: y = sin x

24.2Cosine graph: y = cos x

24.3Tangent graph: y = tan x

24.4Cotangent graph: y = cot x

24.5Secant graph: y = sec x

24.6Cosecant graph: y = csc x

24.7Graphing transformations of trigonometric functions

24.8Determining trigonometric functions given their graphs

25.Trigonometric Identities

25.1Quotient identities and reciprocal identities (free lessons)

25.2Pythagorean identities

25.3Sum and difference identities

25.4Cofunction identities

25.5Double-angle identities (free lessons)

26.Sequences

26.1Arithmetic sequences (free lessons)

26.2Geometric sequences

26.3Sigma notation

27.Derivatives

27.1Definition of derivative

27.4Derivative of exponential functions

27.5Product rule

27.6Quotient rule

27.7Derivative of logarithmic functions

28.Probability

28.1Determining probabilities using tree diagrams and tables (free lessons)

28.2Probability of independent events

28.3Applications of probability

28.4Probability with Venn diagrams

29.Statistics

29.1Median and mode

29.3Range and outliers

29.4Application of averages

30.Introduction to Matrices

30.1Notation of matrices

30.2Adding and subtracting matrices

30.3Multiplying a matrix by a scalar

30.4Multiplying a matrix by another matrix

30.5The three types of matrix row operations

30.6Representing a linear system as a matrix

30.7Solving a linear system with matrices using Gaussian elimination

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