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A-Level Maths (Legacy) topics

We have plenty of free lessons for you to watch

1Surds

1.1Square and square roots (free lessons)
1.2Cubic and cube roots
1.3Evaluating and simplifying surds
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

2Factorisation

2.1Factorise by taking out the greatest common factor (free lessons)
2.2Factorise by grouping
2.3Factorising difference of squares: x2−y2x^2 - y^2
2.4Factorising trinomials
2.5Factoring difference of cubes
2.6Factoring sum of cubes

3Quadratic Functions

3.1Introduction to quadratic functions (free lessons)
3.2Transformations of quadratic functions
3.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
3.4Quadratic function in vertex form: y=a(x−p)2+qy = a(x-p)^2 + q
3.5Completing the square (free lessons)
3.6Converting from general to vertex form by completing the square
3.7Shortcut: Vertex formula (free lessons)
3.8Graphing quadratic functions: General form VS. Vertex form
3.9Finding the quadratic functions for given parabolas (free lessons)
3.10Applications of quadratic functions

4Quadratic Equations

4.1Solving quadratic equations by factorising
4.2Solving quadratic equations by completing the square
4.3Using quadratic formula to solve quadratic equations
4.4The discriminant: Nature of roots of quadratic equations
4.5Applications of quadratic equations

5Inequalities

5.1Express linear inequalities graphically and algebraically (free lessons)
5.2Solving one-step linear inequalities (free lessons)
5.3Solving multi-step linear inequalities (free lessons)
5.4Compound inequalities
5.5Solving quadratic inequalities
5.6Solving absolute value inequalities

6Simultaneous Equations

6.1Simultaneous linear equations
6.2Simultaneous linear-quadratic equations (free lessons)
6.3Simultaneous quadratic-quadratic equations
6.4Solving 3 variable simultaneous equations by substitution
6.5Solving 3 variable simultaneous equations by elimination
6.6Solving 3 variable simultaneous equations with no or infinite solutions
6.7Word problems relating 3 variable simultaneous equations

7Operations with Algebraic Fractions

7.1Simplifying algebraic fractions and restrictions
7.2Adding and subtracting algebraic fractions (free lessons)
7.3Multiplying algebraic fractions
7.4Dividing algebraic fractions
7.5Solving equations with algebraic fractions
7.6Applications of equations with algebraic fractions
7.7Simplifying complex fractions
7.8Partial fraction decomposition

8Algebraic Division

8.1Polynomial long division (free lessons)
8.2Polynomial synthetic division
8.3Remainder theorem
8.4Factor theorem

9Linear Functions

9.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
9.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
9.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
9.4Gradient intercept form: y = mx + b (free lessons)
9.5General form: Ax + By + C = 0 (free lessons)
9.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
9.7Rate of change
9.8Graphing linear functions using table of values
9.9Graphing linear functions using x- and y-intercepts (free lessons)
9.10Graphing from slope-intercept form y=mx+b
9.11Graphing linear functions using a single point and gradient
9.12Word problems of graphing linear functions
9.13Parallel and perpendicular lines in linear functions (free lessons)
9.14Applications of linear relations

10Functions

10.1Function notation (free lessons)
10.2Operations with functions
10.3Adding functions
10.4Subtracting functions
10.5Multiplying functions
10.6Dividing functions
10.7Composite functions (free lessons)
10.8Inverse functions (free lessons)
10.9Domain and range of a function (free lessons)
10.10One to one functions
10.11Difference quotient: applications of functions

11Transformations of Functions

11.1Transformations of functions: Horizontal translations
11.2Transformations of functions: Vertical translations
11.3Reflection across the y-axis: y=f(−x)y = f(-x) (free lessons)
11.4Reflection across the x-axis: y=−f(x)y = -f(x)
11.5Transformations of functions: Horizontal stretches
11.6Transformations of functions: Vertical stretches
11.7Combining transformations of functions

12Reciprocal Functions

12.1Graphing reciprocals of linear functions
12.2Graphing reciprocals of quadratic functions

13Rational Functions

13.1What is a rational function? (free lessons)
13.2Point of discontinuity
13.3Vertical asymptote
13.4Horizontal asymptote
13.5Slant asymptote
13.6Graphs of rational functions
13.7Solving rational inequalities

14Absolute Value Functions

14.1Absolute value functions (free lessons)
14.2Solving absolute value equations

15Laws of Indices

15.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
15.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
15.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
15.4Negative indices
15.5Zero index: a0=1 a^0 = 1
15.6Rational indices

16Exponentials Functions

16.1Solving exponential equations using laws of indices
16.2Graphing exponential functions
16.3Graphing transformations of exponential functions
16.4Finding an exponential function given its graph

17Logarithms

17.1What is a logarithm?
17.2Converting from logarithmic form to exponential form (free lessons)
17.3Evaluating logarithms without a calculator
17.4Common logarithms
17.5Natural log: ln
17.6Evaluating logarithms using change-of-base formula
17.7Converting from exponential form to logarithmic form (free lessons)
17.8Solving exponential equations with logarithms
17.9Product rule of logarithms (free lessons)
17.10Quotient rule of logarithms
17.11Combining product rule and quotient rule in logarithms
17.12Evaluating logarithms using logarithm rules
17.13Solving logarithmic equations (free lessons)
17.14Graphing logarithmic functions
17.15Finding a logarithmic function given its graph

18Trigonometry

18.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} ) (free lessons)
18.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
18.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
18.4Combination of SohCahToa questions (free lessons)
18.5Solving expressions using 45-45-90 special right triangles (free lessons)
18.6Solving expressions using 30-60-90 special right triangles
18.7Word problems relating ladder in trigonometry
18.8Word problems relating guy wire in trigonometry
18.9Other word problems relating angles in trigonometry

19Trigonometric Ratios and Angle Measure

19.1Unit circle (free lessons)
19.2Converting between degrees and radians
19.3Trigonometric ratios of angles in radians
19.4Radian measure and arc length

20Sine Rule and Cosine Rule

20.1Sine rule
20.2Cosine rule
20.3Sine rule and cosine rule word problems

21Bearings

21.1Introduction to bearings
21.2Bearings and direction word problems
21.3Angle of elevation and depression

22Graphing Trigonometric Functions

22.1Sine graph: y = sin x
22.2Cosine graph: y = cos x
22.3Tangent graph: y = tan x
22.4Cotangent graph: y = cot x
22.5Secant graph: y = sec x
22.6Cosecant graph: y = csc x
22.7Graphing transformations of trigonometric functions
22.8Determining trigonometric functions given their graphs

23Trigonometric Identities

23.1Quotient identities and reciprocal identities (free lessons)
23.2Pythagorean identities
23.3Sum and difference identities
23.4Cofunction identities
23.5Double-angle identities (free lessons)

24Solving Trigonometric Equations

24.1Solving first degree trigonometric equations (free lessons)
24.2Determining non-permissible values for trig expressions
24.3Solving second degree trigonometric equations
24.4Solving trigonometric equations involving multiple angles (free lessons)
24.5Solving trigonometric equations using pythagorean identities
24.6Solving trigonometric equations using sum and difference identities
24.7Solving trigonometric equations using double-angle identities

25Inverse Trigonometric Functions

25.1Finding inverse trigonometric function from its graph
25.2Evaluating inverse trigonometric functions
25.3Finding inverse reciprocal trigonometric function from its graph
25.4Finding exact value of inverse reciprocal trig functions

26Circle Theorems

26.1Angles in a circle (free lessons)
26.2Chord properties
26.3Tangent properties
26.4Circles and circumference
26.5Arcs of a circle
26.6Areas and sectors of circles
26.7Inscribed quadrilaterals in circles
26.8Central and inscribed angles in circles
26.9Circles in coordinate plane

27Sequences and Series

27.1Arithmetic sequences (free lessons)
27.2Arithmetic series (free lessons)
27.3Geometric sequences
27.4Geometric series
27.5Infinite geometric series
27.6Sigma notation
27.7Arithmetic mean vs. Geometric mean

28Binomial Expansion

28.1Factorial notation
28.2Pascal's triangle
28.3Binomial theorem

29Differentiation

29.1Power rule
29.2Gradient and equation of tangent line
29.3Chain rule
29.4Derivative of trigonometric functions
29.5Derivative of exponential functions
29.6Product rule
29.7Quotient rule
29.8Derivative of inverse trigonometric functions
29.9Derivative of logarithmic functions
29.10Higher order derivatives
29.11Critical number & maximum and minimum values
29.12Curve sketching

30Integration

30.1Antiderivatives
30.2Definite integral
30.3U-Substitution
30.4Integration by parts
30.5Trigonometric substitution
30.6Integration of rational functions by partial fractions
30.7Volumes of solids of revolution - Disc method
30.8Volumes of solids of revolution - Shell method

31Parametric Equations

31.1Defining curves with parametric equations
31.2Tangent and concavity of parametric equations

32Differential Equations

32.1Introduction to differential equations
32.2Separable equations
32.3Applications to differential equations

33Vectors

33.1Introduction to vectors
33.2Magnitude of a vector
33.3Direction angle of a vector
33.4Scalar multiplication
33.5Equivalent vectors
33.6Adding and subtracting vectors in component form
33.7Operations on vectors in magnitude and direction form
33.8Unit Vector
33.9Word problems on vectors

34Statistics

34.1Median and mode
34.2Mean
34.3Range and outliers
34.4Application of averages
34.5Spread of a data set - standard deviation & variance

35Data and Graphs

35.1Reading and drawing bar graphs
35.2Reading and drawing histograms
35.3Reading and drawing line graphs
35.4Box-and-whisker plots and scatter plots
35.5Reading and drawing Venn diagrams
35.6Stem-and-leaf plots

36Probability

36.1Addition rule for "OR"
36.2Multiplication rule for "AND"
36.3Conditional probability

37Discrete Probabilities

37.1Probability distribution - histogram, mean, variance & standard deviation
37.2Binomial distribution
37.3Mean and standard deviation of binomial distribution
37.4Poisson distribution

38Normal Distribution and Confidence Intervals

38.1Introduction to normal distribution
38.2Normal distribution and continuous random variable
38.3Z-scores and random continuous variables
38.4Sampling distributions
38.5Central limit theorem
38.6Confidence levels and critical values
38.7Confidence intervals to estimate population mean
38.8Student's t-distribution

39Correlation and Regression

39.1Bivariate, scatter plots and correlation
39.2Regression analysis
39.3Equation of the best fit line

40Hypothesis Testing

40.1Null hypothesis and alternative hypothesis
40.2Proving claims
40.3Confidence levels, significance levels and critical values
40.4Test statistics
40.5Traditional hypothesis testing
40.6P-value hypothesis testing
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