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A-Level Maths Topics

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1. Surds

1.1

Square and square roots

1.2

Cubic and cube roots

1.3

Evaluating and simplifying radicals

1.4

Converting radicals to mixed radicals

1.5

Converting radicals to entire radicals

1.6

Adding and subtracting radicals

1.7

Multiplying and dividing radicals

1.8

Rationalize the denominator

2. Laws of Indices

2.1

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

2.2

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

2.3

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

2.4

Indices: Negative indices

2.5

Zero index: a^0 = 1

2.6

Rational indices

2.7

Combining laws of indices

2.8

Solving for indices

2.9

3. Linear Functions

3.1

Distance formula:

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

3.2

Midpoint formula:

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

3.3

Gradient equation:

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

3.4

Gradient intercept form: y = mx + b

3.5

General form: Ax + By + C = 0

3.6

Gradient-point form:

y - y_1 = m (x - x_1)

3.7

3.8

Graphing linear functions using table of values

3.9

Graphing linear functions using x- and y-intercepts

3.10

Graphing from slope-intercept form y=mx+b

3.11

Graphing linear functions using a single point and gradient

3.12

Word problems of graphing linear functions

3.13

Parallel and perpendicular lines in linear functions

3.14

Applications of linear relations

4. Factorisation

4.1

Factorise by taking out the greatest common factor

4.2

Factorise by grouping

4.3

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

4.4

Factorise trinomials

4.5

Factorise Difference of Cubes

4.6

Factorise Sum of Cubes

5. Quadratic Functions

5.1

Introduction to quadratic functions

5.2

Transformations of quadratic functions

5.3

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

5.4

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

5.5

Completing the square

5.6

Converting from general to vertex form by completing the square

5.7

Shortcut: Vertex formula

5.8

Graphing quadratic functions: General form VS. Vertex form

5.9

Finding the quadratic functions for given parabolas

5.10

Applications of quadratic functions

6. Quadratic Equations

6.1

Solving quadratic equations by factorising

6.2

Solving quadratic equations by completing the square

6.3

Using quadratic formula to solve quadratic equations

6.4

The discriminant: Nature of roots of quadratic equations

6.5

Applications of quadratic equations

7. Inequalities

7.1

Express linear inequalities graphically and algebraically

7.2

Solving one-step linear inequalities

7.3

Solving multi-step linear inequalities

7.4

Solving quadratic inequalities

7.5

Solving absolute value inequalities

8. Simultaneous Equations

8.1

Simultaneous linear equations

8.2

Simultaneous linear-quadratic equations

8.3

Simultaneous quadratic-quadratic equations

9. Operations with Algebraic Fractions

9.1

Simplifying algebraic fractions and restrictions

9.2

Adding and subtracting algebraic fractions

9.3

Multiplying algebraic fractions

9.4

Dividing algebraic fractions

9.5

Solving algebraic fraction equations

9.6

Applications of algebraic fraction equations

9.7

Simplifying complex fractions

9.8

Partial fraction decomposition

10. Absolute Value Functions

10.1

Absolute value functions

10.2

Solving absolute value equations

11. Algebraic Division

11.1

Polynomial long division

11.2

Polynomial synthetic division

11.3

Remainder theorem

11.4

12. Functions

12.1

Domain and range of a function

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

Inverse 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. Reciprocal Functions

14.1

Graphing reciprocals of linear functions

14.2

Graphing reciprocals of quadratic functions

15. Rational Functions

15.1

What is a rational function?

15.2

Point of discontinuity

15.3

Vertical asymptote

15.4

Horizontal asymptote

15.5

Slant asymptote

15.6

Graphs of rational functions

15.7

Solving rational inequalities

16. Exponentials Functions

16.1

Solving exponential equations using laws of indices

16.2

Graphing exponential functions

16.3

Graphing transformations of exponential functions

16.4

Finding an exponential function given its graph

17. Logarithms

17.1

What is a logarithm?

17.2

Converting from logarithmic form to exponential form

17.3

Evaluating logarithms without a calculator

17.4

Common logarithms

17.5

Natural log: ln

17.6

Evaluating logarithms using change-of-base formula

17.7

Converting from exponential form to logarithmic form

17.8

Solving exponential equations with logarithms

17.9

Product rule of logarithms

17.10

Quotient rule of logarithms

17.11

Combining product rule and quotient rule in logarithms

17.12

Evaluating logarithms using logarithm rules

17.13

Solving logarithmic equations

17.14

Graphing logarithmic functions

17.15

Finding a logarithmic function given its graph

18. Applications of Exponential and Logarithmic Functions

18.1

Exponential growth and decay by a factor

18.2

Exponential decay: Half-life

18.3

Exponential growth and decay by percentage

18.4

Finance: Compound interest

18.5

Continuous growth and decay

18.6

Logarithmic scale: Richter scale (earthquake)

18.7

Logarithmic scale: pH scale

18.8

Logarithmic scale: dB scale

18.9

Finance: Future value and present value

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

Find the exact value of trigonometric ratios

20.2

ASTC rule in trigonometry (All Students Take Calculus)

20.3

20.4

Converting from exponential form to logarithmic form

20.5

Trigonometric ratios of angles in radians

20.6

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. Graphing Trigonometric Functions

22.1

Sine graph: y = sin x

22.2

Cosine graph: y = cos x

22.3

Tangent graph: y = tan x

22.4

Cotangent graph: y = cot x

22.5

Secant graph: y = sec x

22.6

Cosecant graph: y = csc x

22.7

Graphing transformations of trigonometric functions

22.8

Determining trigonometric functions given their graphs

23. Applications of Trigonometric Functions

23.1

Tides and water depth trig problems

23.2

Spring (simple harmonic motion) trig problems

24. Trigonometric Identities

24.1

Quotient identities and reciprocal identities

24.2

Pythagorean identities

24.3

Sum and difference identities

24.4

Cofunction identities

24.5

Double-angle identities

25. Solving Trigonometric Equations

25.1

Solving first degree trigonometric equations

25.2

Determining non-permissible values for trig expressions

25.3

Solving second degree trigonometric equations

25.4

Solving trigonometric equations involving multiple angles

25.5

Solving trigonometric equations using pythagorean identities

25.6

Solving trigonometric equations using sum and difference identities

25.7

Solving trigonometric equations using double-angle identities

26. Circle Theorems

26.1

Angles in a circle

26.2

Chord properties

26.3

Tangent properties

26.4

Circle and circumference

26.5

Arcs of a circle

26.6

Areas and sectors of circles

26.7

Inscribed quadrilaterals in circles

26.8

Central and inscribed angles in circles

26.9

Circles in coordinate plane

27. Sequences and Series

27.1

Arithmetic sequences

27.2

Arithmetic series

27.3

Geometric sequences

27.4

Geometric series

27.5

Infinite geometric series

27.6

28. Binomial Expansion

28.1

Factorial notation

28.2

Pascal's triangle

28.3

Binomial theorem

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. Differentiation

30.1

30.2

Gradient and equation of tangent line

30.3

30.4

Derivative of trigonometric functions

30.5

Derivative of exponential functions

30.6

30.7

30.8

Derivative of inverse trigonometric functions

30.9

Derivative of logarithmic functions

30.10

Higher order derivatives

30.11

Critical number & maximum and minimum values

30.12

Curve sketching

31. Integration

31.1

Antiderivatives

31.2

Fundamental theorem of calculus

31.3

Definite integral

31.4

Numerical integration

31.5

31.6

Integration by parts

31.7

Trigonometric substitution

31.8

Integration of rational functions by partial fractions

31.9

Volumes of solids of revolution - Disc method

31.10

Volumes of solids of revolution - Shell method

32. Parametric Equations

32.1

Defining curves with parametric equations

32.2

Tangent and concavity of parametric equations

33. Differential Equations

33.1

Introduction to differential equations

33.2

Separable equations

33.3

Applications to differential equations

34. Statistics

34.1

Median and mode

34.2

34.3

Range and outliers

34.4

Application of averages

34.5

Spread of a data set - standard deviation & variance

35. Data and Graphs

35.1

Reading and drawing bar graphs

35.2

Reading and drawing histograms

35.3

Reading and drawing line graphs

35.4

Box-and-whisker plots and scatter plots

35.5

Stem-and-leaf plots

35.6

Reading and drawing Venn diagrams

36. Probability

36.1

Addition rule for "OR"

36.2

Multiplication rule for "AND"

36.3

Conditional probability

37. Discrete Probabilities

37.1

Histogram, mean, variance & standard deviation

37.2

Binomial distribution

37.3

Mean and standard deviation of binomial distribution

37.4

Poisson distribution

38. Normal Distribution and Confidence Intervals

38.1

Introduction to normal distribution

38.2

Normal distribution and continuous random variable

38.3

Z-scores and random continuous variables

38.4

Sampling distributions

38.5

Central limit theorem

38.6

Confidence levels and critical values

38.7

Confidence intervals to estimate population mean

38.8

Student's t-distribution

39. Correlation and Regression

39.1

Bivariate, scatter plots and correlation

39.2

Regression analysis

39.3

Equation of the best fit line

40. Hypothesis Testing

40.1

Null hypothesis and alternative hypothesis

40.2

40.3

Confidence levels, significance levels and critical values

40.4

Test statistics

40.5

Traditional hypothesis testing

40.6

P-value hypothesis testing

40.7

Mean hypothesis testing with t-distribution

40.8

Type 1 and type 2 errors

41. Scalars, Vectors, and Motion

41.1

Scalars, vectors, and one dimensional motion

41.2

Vector operations in one dimension

41.3

Vector operations in two dimensions

41.4

Vector components

41.5

Solving two dimensional vector problems

41.6

Relative velocity

42. Kinematics

42.1

Kinematics in a straight line

42.2

Position velocity acceleration: Derivative

43. Forces

43.1

Newton's first law of motion

43.2

Newton's second law of motion

43.3

Multiple forces acting on an object

43.4

Newton's third law of motion

43.5

Friction: Static and kinetic

43.6

Forces in two dimensions

43.7

Tension and pulley problems

44. Momentum

44.1

Momentum and motion

44.2

Momentum and impulse

44.3

Conservation of momentum in one dimension

44.4

Conservation of momentum in two dimensions

44.5

Elastic and inelastic collisions

45. Equilibrium

45.1

Translational equilibrium

45.2

Rotational equilibrium

45.3

Static equilibrium problems

45Chapters

280Topics

1881Videos

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