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AS-Level Maths Topics

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1. Set Theory

1.1

1.2

Set builder notation

1.3

Intersection and union of 2 sets

1.4

Intersection and union of 3 sets

2. Number System

2.1

Understanding the number systems

2.2

Prime factorization

2.3

Greatest Common Factors (GCF)

2.4

Least Common Multiple (LCM)

2.5

Rational vs. Irrational numbers

2.6

Converting repeating decimals to fractions

3. Surds

3.1

Square and square roots

3.2

Cubic and cube roots

3.3

Evaluating and simplifying radicals

3.4

Converting radicals to mixed radicals

3.5

Converting radicals to entire radicals

3.6

Adding and subtracting radicals

3.7

Multiplying and dividing radicals

3.8

Rationalize the denominator

4. Laws of Indices

4.1

Indices: Product rule (a^x)(a^y) = a^(x+y)

4.2

Indices: Division rule (a^x / a^y) = a^(x-y)

4.3

Indices: Power rule (a^x)^y = a^(x * y)

4.4

Indices: Negative indices

4.5

Zero index: a^0 = 1

4.6

Rational indices

4.7

Combining laws of indices

4.8

Solving for indices

4.9

5. Linear Functions

5.1

Distance formula:

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

5.2

Midpoint formula:

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

5.3

Gradient equation:

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

5.4

Gradient intercept form: y = mx + b

5.5

General form: Ax + By + C = 0

5.6

Gradient-point form:

y - y_1 = m (x - x_1)

5.7

5.8

Graphing linear functions using table of values

5.9

Graphing linear functions using x- and y-intercepts

5.10

Graphing from slope-intercept form y=mx+b

5.11

Graphing linear functions using a single point and gradient

5.12

Word problems of graphing linear functions

5.13

Parallel and perpendicular lines in linear functions

5.14

Applications of linear relations

6. Quadratic Functions

6.1

Introduction to quadratic functions

6.2

Transformations of quadratic functions

6.3

Quadratic function in general form: y = ax^2 + bx + c

6.4

Quadratic function in vertex form: y = a(x-p)^2 + q

6.5

Completing the square

6.6

Converting from general to vertex form by completing the square

6.7

Shortcut: Vertex formula

6.8

Graphing quadratic functions: General form VS. Vertex form

6.9

Finding the quadratic functions for given parabolas

6.10

Applications of quadratic functions

7. Quadratic Equations

7.1

Solving quadratic equations by factorising

7.2

Solving quadratic equations by completing the square

7.3

Using quadratic formula to solve quadratic equations

7.4

The discriminant: Nature of roots of quadratic equations

7.5

Applications of quadratic equations

8. Simultaneous Equations

8.1

Simultaneous linear equations

8.2

Simultaneous linear-quadratic equations

8.3

Simultaneous quadratic-quadratic equations

9. Inequalities

9.1

Express linear inequalities graphically and algebraically

9.2

Solving one-step linear inequalities

9.3

Solving multi-step linear inequalities

9.4

Solving quadratic inequalities

10. Factorisation

10.1

Factorise by taking out the greatest common factor

10.2

Factorise by grouping

10.3

Factorise difference of squares: x^2 - y^2

10.4

Factorise trinomials

10.5

Factorise difference of cubes

10.6

Factorise sum of cubes

11. Operations with Algebraic Fractions

11.1

Simplifying algebraic fractions and restrictions

11.2

Adding and subtracting algebraic fractions

11.3

Multiplying algebraic fractions

11.4

Dividing algebraic fractions

11.5

Solving algebraic fraction equations

11.6

Applications of algebraic fraction equations

11.7

Simplifying complex fractions

11.8

Partial fraction decomposition

12. Functions

12.1

Function notation

12.2

Operations with functions

12.3

Adding functions

12.4

Subtracting functions

12.5

Multiplying functions

12.6

Dividing functions

12.7

Composite functions

12.8

Inequalities of combined functions

12.9

Inverse functions

12.10

One to one functions

12.11

Difference quotient: applications of functions

13. Transformations of Functions

13.1

Transformations of functions: Horizontal translations

13.2

Transformations of functions: Vertical translations

13.3

Reflection across the y-axis: y = f(-x)

13.4

Reflection across the x-axis: y = -f(x)

13.5

Transformations of functions: Horizontal stretches

13.6

Transformations of functions: Vertical stretches

13.7

Combining transformations of functions

14. Algebraic Division

14.1

Polynomial long division

14.2

Polynomial synthetic division

14.3

Remainder theorem

14.4

15. Reciprocal Functions

15.1

Graphing reciprocals of linear functions

15.2

Graphing reciprocals of quadratic functions

16. Rational Functions

16.1

What is a rational function?

16.2

Point of discontinuity

16.3

Vertical asymptote

16.4

Horizontal asymptote

16.5

Slant asymptote

16.6

Graphs of rational functions

16.7

Solving rational inequalities

17. Circle Theorems

17.1

Angles in a circle

17.2

Chord properties

17.3

Tangent properties

17.4

Circle and circumference

17.5

Arcs of a circle

17.6

Areas and sectors of circles

17.7

Inscribed quadrilaterlas in circles

17.8

Central and inscribed angles in circles

18. Binomial Expansion

18.1

Factorial notation

18.2

Pascal's triangle

18.3

Binomial theorem

19. Trigonometry

19.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

19.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

19.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

19.4

Combination of SohCahToa questions

19.5

Solving expressions using 45-45-90 special right triangles

19.6

Solving expressions using 30-60-90 special right triangles

19.7

Word problems relating ladder in trigonometry

19.8

Word problems relating guy wire in trigonometry

19.9

Other word problems relating angles in trigonometry

20. Trigonometric Ratios and Angle Measure

20.1

20.2

Converting between degrees and radians

20.3

Trigonometric ratios of angles in radians

20.4

Radian measure and arc length

21. Sine Rule and Cosine Rule

21.1

21.2

21.3

Sine rule and cosine rule word problems

22. Trigonometric Identities and Equations

22.1

Pythagorean identities

22.2

Solving first degree trigonometric equations

22.3

Solving second degree trigonometric equations

23. Graphing Trigonometric Functions

23.1

Sine graph: y = sin x

23.2

Cosine graph: y = cos x

23.3

Tangent graph: y = tan x

23.4

Graphing transformations of trigonometric functions

24. Exponentials Functions

24.1

Solving exponential equations using laws of indices

24.2

Graphing exponential functions

24.3

Graphing transformations of exponential functions

24.4

Finding an exponential function given its graph

25. Logarithms

25.1

What is a logarithm?

25.2

Converting from logarithmic form to exponential form

25.3

Evaluating logarithms without a calculator

25.4

Common logarithms

25.5

Natural log: ln

25.6

Evaluating logarithms using change-of-base formula

25.7

Converting from exponential form to logarithmic form

25.8

Solving exponential equations with logarithms

25.9

Product rule of logarithms

25.10

Quotient rule of logarithms

25.11

Combining product rule and quotient rule in logarithms

25.12

Evaluating logarithms using logarithm rules

25.13

Solving logarithmic equations

26. Growth and Decay

26.1

Exponential growth and decay by a factor

26.2

Exponential growth and decay by percentage

26.3

Finance: Compound interest

26.4

Finance: Future value and present value

27. Differentiation

27.1

Definition of derivative

27.2

27.3

Gradient and equation of tangent line

27.4

Higher order derivatives

27.5

Critical number & maximum and minimum values

28. Integration

28.1

Antiderivatives

28.2

Definite integral

28.3

Fundamental theorem of calculus

28.4

Indefinite integral

29. Vectors

29.1

Introduction to vectors

29.2

Magnitude of a vector

29.3

Direction angle of a vector

29.4

Scalar multiplication

29.5

Equivalent vectors

29.6

Adding and subtracting vectors in component form

29.7

Operations on vectors in magnitude and direction form

29.8

29.9

Word problems on vectors

30. Statistics

30.1

Sampling methods

30.2

Median and mode

30.3

30.4

Range and outliers

30.5

Application of averages

30.6

Standard deviation and variance

30.7

Quartiles, Percentile, and Outliers

31. Data and Graphs

31.1

Reading and drawing bar graphs

31.2

Reading and drawing histograms

31.3

Reading and drawing line graphs

31.4

Box-and-whisker plots and scatter plots

31.5

Stem-and-leaf plots

31.6

Reading and drawing Venn diagrams

31.7

Frequency distribution and histograms

32. Correlation and Regression

32.1

Bivariate, scatter plots, and correlation

32.2

Regression analysis

32.3

Equation of the best fit line

33. Probability

33.1

Determining probabilities using tree diagrams and tables

33.2

Probability of independent and combined events

33.3

Probability with Venn diagrams

33.4

Addition rule for

33.5

Binomial distribution

34. Hypothesis Testing

34.1

Null hypothesis and alternative hypothesis

34.2

34.3

Confidence levels, significance levels, and critical values

34.4

Test statistics

34.5

Traditional hypothesis testing

34.6

P-value hypothesis testing

34.7

Type 1 and type 2 errors

35. Scalars, Vectors, and Motion

35.1

Scalars, vectors, and one dimensional motion

35.2

Vector operations in one dimension

35.3

Vector operations in two dimensions

36. Kinematics

36.1

Kinematics in a straight line

36.2

Position velocity acceleration: Derivative

37. Forces

37.1

Newton's first law of motion

37.2

Newton's second law of motion

37.3

Multiple forces acting on an object

37.4

Newton's third law of motion

37.5

Friction: Static and kinetic

38. Momentum

38.1

Momentum and motion

38.2

Momentum and impulse

38.3

Conservation of momentum in one dimension

38Chapters

223Topics

1620Videos

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