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1.Surds

1.1Square and square roots (free lessons)

1.2Cubic and cube roots

1.3Evaluating and simplifying radicals

1.4Converting radicals to mixed radicals

1.5Converting radicals to entire radicals (free lessons)

1.6Adding and subtracting surds

1.7Multiplying and dividing surds

1.8Rationalize the denominator

2.Factorisation

2.1Factorise by taking out the greatest common factor (free lessons)

2.2Factorise by grouping

2.3Factorising difference of squares:

x^2 - y^2

2.4Factorising trinomials:

ax^2 + bx + c

2.5Factoring difference of cubes

2.6Factoring sum of cubes

3.Linear Functions

3.1Distance formula:

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

(free lessons)

3.2Midpoint formula:

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

3.3Gradient equation:

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

3.4Gradient intercept form: y = mx + b

3.5General form: Ax + By + C = 0 (free lessons)

3.6Gradient-point form:

y - y_1 = m (x - x_1)

3.7Rate of change

3.8Graphing linear functions using table of values

3.9Graphing linear functions using x- and y-intercepts (free lessons)

3.10Graphing linear functions using various forms

3.11Graphing linear functions using a single point and gradient

3.12Word problems of graphing linear functions

3.13Parallel and perpendicular lines in linear functions (free lessons)

3.14Applications of linear relations

4.Quadratic Functions

4.1Introduction to 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

5.1Solving quadratic equations by factorising

5.2Solving quadratic equations by completing the square

5.3Using quadratic formula to solve quadratic equations

5.4The discriminant: Nature of roots of quadratic equations

5.5Applications of quadratic equations

6.Inequalities

6.1Express linear inequalities graphically and algebraically (free lessons)

6.2Solving one-step linear inequalities

6.3Solving multi-step linear inequalities

6.4Solving quadratic inequalities

7.Simultaneous Equations

7.1Simultaneous linear equations

7.2Simultaneous linear-quadratic equations (free lessons)

7.3Simultaneous quadratic-quadratic equations

7.4Solving 3 variable simultaneous equations by substitution

7.5Solving 3 variable simultaneous equations by elimination

7.6Word problems relating 3 variable simultaneous equations

8.Operations with Algebraic Fractions

8.1Simplifying algebraic fractions and restrictions

8.2Adding and subtracting algebraic fractions (free lessons)

8.3Multiplying algebraic fractions

8.4Dividing algebraic fractions

8.5Solving rational equations

8.6Applications of rational equations

8.7Simplifying complex fractions

8.8Partial fraction decomposition

9.Algebraic Division

9.1Polynomial long division (free lessons)

9.2Polynomial synthetic division

9.3Remainder theorem

9.4Factor theorem

10.Functions

10.1Function notation (free lessons)

10.2Operations with functions

10.3Adding functions

10.4Subtracting functions

10.5Multiplying functions

10.6Dividing functions

11.Transformations of Functions

11.1Transformations of functions: Horizontal translations

11.2Transformations of functions: Vertical translations

11.3Reflection across the y-axis:

y = f(-x)

11.4Reflection across the x-axis:

y = -f(x)

11.5Transformations of functions: Horizontal stretches

11.6Transformations of functions: Vertical stretches

12.Rational Functions

12.1What is a rational function? (free lessons)

12.2Point of discontinuity

12.3Vertical asymptote

12.4Horizontal asymptote

12.5Slant asymptote

12.6Graphs of rational functions

12.7Solving rational equations

12.8Solving rational inequalities

13.Circle Theorems

13.1Angles in a circle (free lessons)

13.2Chord properties

13.3Tangent properties

13.4Circles and circumference

13.5Arcs of a circle

13.6Areas and sectors of circles

13.7Inscribed quadrilaterals in circles

13.8Central and inscribed angles in circles

13.9Circles in coordinate plane

14.Trigonometry

14.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

14.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

14.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

14.4Combination of SohCahToa questions

14.5Solving expressions using 45-45-90 special right triangles (free lessons)

14.6Solving expressions using 30-60-90 special right triangles

14.7Word problems relating ladder in trigonometry

14.8Word problems relating guy wire in trigonometry

14.9Other word problems relating angles in trigonometry

15.Trigonometric Ratios and Angle Measure

15.1Unit circle (free lessons)

15.2Converting between degrees and radians

15.3Trigonometric ratios of angles in radians

15.4Radian measure and arc length

16.Sine Rule and Cosine Rule

16.2Cosine rule

16.3Sine rule and cosine rule word problems

17.Trigonometric Identities and Equations

17.1Pythagorean identities

17.2Solving first degree trigonometric equations (free lessons)

17.3Solving second degree trigonometric equations

18.Graphing Trigonometric Functions

18.1Sine graph: y = sin x

18.2Cosine graph: y = cos x

18.3Tangent graph: y = tan x

19.Laws of Indices

19.1Indices: Product rule

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

(free lessons)

19.2Indices: Division rule

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

19.3Indices: Power rule

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

(free lessons)

19.4Indices: Negative exponents

19.5Indices: Zero exponent:

a^0 = 1

19.6Indices: Rational exponents

20.Exponentials Functions

20.1Solving exponential equations using laws of indices

20.2Graphing exponential functions

20.3Graphing transformations of exponential functions

20.4Finding an exponential function given its graph

21.Logarithms

21.1What is a logarithm?

21.2Converting from logarithmic form to exponential form (free lessons)

21.3Evaluating logarithms without a calculator

21.4Common logarithms

21.5Natural log: ln

21.6Evaluating logarithms using change-of-base formula

21.7Converting from exponential form to logarithmic form (free lessons)

21.8Solving exponential equations with logarithms

21.9Product rule of logarithms (free lessons)

21.10Quotient rule of logarithms

21.11Combining product rule and quotient rule in logarithms

21.12Evaluating logarithms using logarithm rules

21.13Solving logarithmic equations

21.14Graphing logarithmic functions

21.15Finding a logarithmic function given its graph

22.Sequences and Series

22.1Arithmetic sequences (free lessons)

22.2Arithmetic series (free lessons)

22.3Geometric sequences

22.4Geometric series

22.5Infinite geometric series

22.6Sigma notation

22.7Arithmetic mean vs. Geometric mean

23.Binomial Expansion

23.1Factorial notation

23.2Pascal's triangle

23.3Binomial theorem

24.Differentiation

24.2Gradient and equation of tangent line

24.3Higher order derivatives

24.4Critical number & maximum and minimum values

24.5Curve sketching

25.Integration

25.1Antiderivatives

25.2Definite integral

26.Statistics

26.1Median and mode

26.3Range and outliers

26.4Application of averages

26.5Standard deviation & variance

27.Data and Graphs

27.1Reading and drawing histograms

27.2Reading and drawing line graphs

27.3Box-and-whisker plots and scatter plots

27.4Reading and drawing Venn diagrams

27.5Stem-and-leaf plots

28.Probability

28.1Addition rule for "OR"

28.2Multiplication rule for "AND"

28.3Conditional probability

29.Discrete Probabilities

29.1Histogram, mean, variance & standard deviation

29.2Binomial distribution

29.3Mean and standard deviation of binomial distribution

30.Normal Distribution and Confidence Intervals

30.1Introduction to normal distribution

30.2Normal distribution and continuous random variable

30.3Z-scores and random continuous variables

30.4Sampling distributions

30.5Central limit theorem

30.6Confidence levels and critical values

31.Correlation and Regression

31.1Bivariate, scatter plots and correlation

31.2Regression analysis

31.3Equation of the best fit line

1.Surds

1.1Square and square roots (free lessons)

1.2Cubic and cube roots

1.3Evaluating and simplifying radicals

1.4Converting radicals to mixed radicals

1.5Converting radicals to entire radicals (free lessons)

1.6Adding and subtracting surds

1.7Multiplying and dividing surds

1.8Rationalize the denominator

2.Factorisation

2.1Factorise by taking out the greatest common factor (free lessons)

2.2Factorise by grouping

2.3Factorising difference of squares:

x^2 - y^2

2.4Factorising trinomials:

ax^2 + bx + c

2.5Factoring difference of cubes

2.6Factoring sum of cubes

3.Linear Functions

3.1Distance formula:

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

(free lessons)

3.2Midpoint formula:

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

3.3Gradient equation:

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

3.4Gradient intercept form: y = mx + b

3.5General form: Ax + By + C = 0 (free lessons)

3.6Gradient-point form:

y - y_1 = m (x - x_1)

3.7Rate of change

3.8Graphing linear functions using table of values

3.9Graphing linear functions using x- and y-intercepts (free lessons)

3.10Graphing linear functions using various forms

3.11Graphing linear functions using a single point and gradient

3.12Word problems of graphing linear functions

3.13Parallel and perpendicular lines in linear functions (free lessons)

3.14Applications of linear relations

4.Quadratic Functions

4.1Introduction to 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

5.1Solving quadratic equations by factorising

5.2Solving quadratic equations by completing the square

5.3Using quadratic formula to solve quadratic equations

5.4The discriminant: Nature of roots of quadratic equations

5.5Applications of quadratic equations

6.Inequalities

6.1Express linear inequalities graphically and algebraically (free lessons)

6.2Solving one-step linear inequalities

6.3Solving multi-step linear inequalities

6.4Solving quadratic inequalities

7.Simultaneous Equations

7.1Simultaneous linear equations

7.2Simultaneous linear-quadratic equations (free lessons)

7.3Simultaneous quadratic-quadratic equations

7.4Solving 3 variable simultaneous equations by substitution

7.5Solving 3 variable simultaneous equations by elimination

7.6Word problems relating 3 variable simultaneous equations

8.Operations with Algebraic Fractions

8.1Simplifying algebraic fractions and restrictions

8.2Adding and subtracting algebraic fractions (free lessons)

8.3Multiplying algebraic fractions

8.4Dividing algebraic fractions

8.5Solving rational equations

8.6Applications of rational equations

8.7Simplifying complex fractions

8.8Partial fraction decomposition

9.Algebraic Division

9.1Polynomial long division (free lessons)

9.2Polynomial synthetic division

9.3Remainder theorem

9.4Factor theorem

10.Functions

10.1Function notation (free lessons)

10.2Operations with functions

10.3Adding functions

10.4Subtracting functions

10.5Multiplying functions

10.6Dividing functions

11.Transformations of Functions

11.1Transformations of functions: Horizontal translations

11.2Transformations of functions: Vertical translations

11.3Reflection across the y-axis:

y = f(-x)

11.4Reflection across the x-axis:

y = -f(x)

11.5Transformations of functions: Horizontal stretches

11.6Transformations of functions: Vertical stretches

12.Rational Functions

12.1What is a rational function? (free lessons)

12.2Point of discontinuity

12.3Vertical asymptote

12.4Horizontal asymptote

12.5Slant asymptote

12.6Graphs of rational functions

12.7Solving rational equations

12.8Solving rational inequalities

13.Circle Theorems

13.1Angles in a circle (free lessons)

13.2Chord properties

13.3Tangent properties

13.4Circles and circumference

13.5Arcs of a circle

13.6Areas and sectors of circles

13.7Inscribed quadrilaterals in circles

13.8Central and inscribed angles in circles

13.9Circles in coordinate plane

14.Trigonometry

14.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

14.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

14.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

14.4Combination of SohCahToa questions

14.5Solving expressions using 45-45-90 special right triangles (free lessons)

14.6Solving expressions using 30-60-90 special right triangles

14.7Word problems relating ladder in trigonometry

14.8Word problems relating guy wire in trigonometry

14.9Other word problems relating angles in trigonometry

15.Trigonometric Ratios and Angle Measure

15.1Unit circle (free lessons)

15.2Converting between degrees and radians

15.3Trigonometric ratios of angles in radians

15.4Radian measure and arc length

16.Sine Rule and Cosine Rule

16.2Cosine rule

16.3Sine rule and cosine rule word problems

17.Trigonometric Identities and Equations

17.1Pythagorean identities

17.2Solving first degree trigonometric equations (free lessons)

17.3Solving second degree trigonometric equations

18.Graphing Trigonometric Functions

18.1Sine graph: y = sin x

18.2Cosine graph: y = cos x

18.3Tangent graph: y = tan x

19.Laws of Indices

19.1Indices: Product rule

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

(free lessons)

19.2Indices: Division rule

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

19.3Indices: Power rule

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

(free lessons)

19.4Indices: Negative exponents

19.5Indices: Zero exponent:

a^0 = 1

19.6Indices: Rational exponents

20.Exponentials Functions

20.1Solving exponential equations using laws of indices

20.2Graphing exponential functions

20.3Graphing transformations of exponential functions

20.4Finding an exponential function given its graph

21.Logarithms

21.1What is a logarithm?

21.2Converting from logarithmic form to exponential form (free lessons)

21.3Evaluating logarithms without a calculator

21.4Common logarithms

21.5Natural log: ln

21.6Evaluating logarithms using change-of-base formula

21.7Converting from exponential form to logarithmic form (free lessons)

21.8Solving exponential equations with logarithms

21.9Product rule of logarithms (free lessons)

21.10Quotient rule of logarithms

21.11Combining product rule and quotient rule in logarithms

21.12Evaluating logarithms using logarithm rules

21.13Solving logarithmic equations

21.14Graphing logarithmic functions

21.15Finding a logarithmic function given its graph

22.Sequences and Series

22.1Arithmetic sequences (free lessons)

22.2Arithmetic series (free lessons)

22.3Geometric sequences

22.4Geometric series

22.5Infinite geometric series

22.6Sigma notation

22.7Arithmetic mean vs. Geometric mean

23.Binomial Expansion

23.1Factorial notation

23.2Pascal's triangle

23.3Binomial theorem

24.Differentiation

24.2Gradient and equation of tangent line

24.3Higher order derivatives

24.4Critical number & maximum and minimum values

24.5Curve sketching

25.Integration

25.1Antiderivatives

25.2Definite integral

26.Statistics

26.1Median and mode

26.3Range and outliers

26.4Application of averages

26.5Standard deviation & variance

27.Data and Graphs

27.1Reading and drawing histograms

27.2Reading and drawing line graphs

27.3Box-and-whisker plots and scatter plots

27.4Reading and drawing Venn diagrams

27.5Stem-and-leaf plots

28.Probability

28.1Addition rule for "OR"

28.2Multiplication rule for "AND"

28.3Conditional probability

29.Discrete Probabilities

29.1Histogram, mean, variance & standard deviation

29.2Binomial distribution

29.3Mean and standard deviation of binomial distribution

30.Normal Distribution and Confidence Intervals

30.1Introduction to normal distribution

30.2Normal distribution and continuous random variable

30.3Z-scores and random continuous variables

30.4Sampling distributions

30.5Central limit theorem

30.6Confidence levels and critical values

31.Correlation and Regression

31.1Bivariate, scatter plots and correlation

31.2Regression analysis

31.3Equation of the best fit line

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