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Aligning with all exam boards’ A level maths specifications, our comprehensive help includes all materials in Core 1, Core 2, Core 3 and Core 4 maths such as Derivatives, Integration, Factorisation, Solving simultaneous equations, Trigonometry, Vectors, Circle theorems, and more. Learn the concepts with our online video tutorials that show you step-by-step solutions to even the hardest a level maths questions. Then, reinforce your understanding with tons of a level maths practice.

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Common Questions
My school uses Edexcel as our exam board. Which school board do you follow?

We follow a level maths syllabus of All school boards. We have all topics tested in A level Maths exam. Therefore, not only Edexcel, pupils taking the exam with all other exam boards, including AQA, OCR, and WJEC, will find all the help you need here too.

I’m taking Statistics 1 (S1) and Statistics 1 (S2) too. Can StudyPug help?

Most certainly! You will find the statistics topics also covered in our A-level maths course. If you want to learn more about statistics, check out our Statistics course.

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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)
5.4Solving quadratic inequalities
5.5Solving 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

12Rational 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 inequalities

13Absolute Value Functions

13.1Absolute value functions (free lessons)
13.2Solving absolute value equations

14Laws of Indices

14.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
14.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
14.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
14.4Negative indices
14.5Zero index: a0=1 a^0 = 1
14.6Rational indices

15Exponentials Functions

15.1Solving exponential equations using laws of indices
15.2Graphing exponential functions
15.3Graphing transformations of exponential functions
15.4Finding an exponential function given its graph

16Logarithms

16.1What is a logarithm?
16.2Converting from logarithmic form to exponential form (free lessons)
16.3Evaluating logarithms without a calculator
16.4Common logarithms
16.5Natural log: ln
16.6Evaluating logarithms using change-of-base formula
16.7Converting from exponential form to logarithmic form (free lessons)
16.8Solving exponential equations with logarithms
16.9Product rule of logarithms (free lessons)
16.10Quotient rule of logarithms
16.11Combining product rule and quotient rule in logarithms
16.12Evaluating logarithms using logarithm rules
16.13Solving logarithmic equations (free lessons)
16.14Graphing logarithmic functions
16.15Finding a logarithmic function given its graph

17Trigonometry

17.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
17.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
17.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
17.4Combination of SohCahToa questions (free lessons)
17.5Solving expressions using 45-45-90 special right triangles (free lessons)
17.6Solving expressions using 30-60-90 special right triangles
17.7Word problems relating ladder in trigonometry
17.8Word problems relating guy wire in trigonometry
17.9Other word problems relating angles in trigonometry

18Trigonometric Ratios and Angle Measure

18.1Unit circle (free lessons)
18.2Converting between degrees and radians
18.3Trigonometric ratios of angles in radians
18.4Radian measure and arc length

19Sine Rule and Cosine Rule

19.1Sine rule
19.2Cosine rule
19.3Sine rule and cosine rule word problems

20Graphing Trigonometric Functions

20.1Sine graph: y = sin x
20.2Cosine graph: y = cos x
20.3Tangent graph: y = tan x
20.4Cotangent graph: y = cot x
20.5Secant graph: y = sec x
20.6Cosecant graph: y = csc x
20.7Graphing transformations of trigonometric functions
20.8Determining trigonometric functions given their graphs

21Trigonometric Identities

21.1Quotient identities and reciprocal identities (free lessons)
21.2Pythagorean identities
21.3Sum and difference identities
21.4Cofunction identities
21.5Double-angle identities (free lessons)

22Solving Trigonometric Equations

22.1Solving first degree trigonometric equations (free lessons)
22.2Determining non-permissible values for trig expressions
22.3Solving second degree trigonometric equations
22.4Solving trigonometric equations involving multiple angles (free lessons)
22.5Solving trigonometric equations using pythagorean identities
22.6Solving trigonometric equations using sum and difference identities
22.7Solving trigonometric equations using double-angle identities

23Inverse Trigonometric Functions

23.1Finding inverse trigonometric function from its graph
23.2Evaluating inverse trigonometric functions
23.3Finding inverse reciprocal trigonometric function from its graph
23.4Finding exact value of inverse reciprocal trig functions

24Circle Theorems

24.1Angles in a circle (free lessons)
24.2Chord properties
24.3Tangent properties
24.4Circles and circumference
24.5Arcs of a circle
24.6Areas and sectors of circles
24.7Inscribed quadrilaterals in circles
24.8Central and inscribed angles in circles
24.9Circles in coordinate plane

25Sequences and Series

25.1Arithmetic sequences (free lessons)
25.2Arithmetic series (free lessons)
25.3Geometric sequences
25.4Geometric series
25.5Infinite geometric series
25.6Sigma notation
25.7Arithmetic mean vs. Geometric mean

26Binomial Expansion

26.1Factorial notation
26.2Pascal's triangle
26.3Binomial theorem

27Differentiation

27.1Power rule
27.2Gradient and equation of tangent line
27.3Chain rule
27.4Derivative of trigonometric functions
27.5Derivative of exponential functions
27.6Product rule
27.7Quotient rule
27.8Derivative of inverse trigonometric functions
27.9Derivative of logarithmic functions
27.10Higher order derivatives
27.11Critical number & maximum and minimum values
27.12Curve sketching

28Integration

28.1Antiderivatives
28.2Definite integral
28.3U-Substitution
28.4Integration by parts
28.5Trigonometric substitution
28.6Integration of rational functions by partial fractions
28.7Volumes of solids of revolution - Disc method
28.8Volumes of solids of revolution - Shell method

29Parametric Equations

29.1Defining curves with parametric equations
29.2Tangent and concavity of parametric equations

30Differential Equations

30.1Introduction to differential equations
30.2Separable equations
30.3Applications to differential equations

31Vectors

31.1Introduction to vectors
31.2Magnitude of a vector
31.3Direction angle of a vector
31.4Scalar multiplication
31.5Equivalent vectors
31.6Adding and subtracting vectors in component form
31.7Operations on vectors in magnitude and direction form

32Statistics

32.1Median and mode
32.2Mean
32.3Range and outliers
32.4Application of averages
32.5Spread of a data set - standard deviation & variance

33Data and Graphs

33.1Reading and drawing histograms
33.2Reading and drawing line graphs
33.3Box-and-whisker plots and scatter plots
33.4Reading and drawing Venn diagrams
33.5Stem-and-leaf plots

34Probability

34.1Addition rule for "OR"
34.2Multiplication rule for "AND"
34.3Conditional probability

35Discrete Probabilities

35.1Probability distribution - histogram, mean, variance & standard deviation
35.2Binomial distribution
35.3Mean and standard deviation of binomial distribution
35.4Poisson distribution

36Normal Distribution and Confidence Intervals

36.1Introduction to normal distribution
36.2Normal distribution and continuous random variable
36.3Z-scores and random continuous variables
36.4Sampling distributions
36.5Central limit theorem
36.6Confidence levels and critical values
36.7Confidence intervals to estimate population mean
36.8Student's t-distribution

37Correlation and Regression

37.1Bivariate, scatter plots and correlation
37.2Regression analysis
37.3Equation of the best fit line

38Hypothesis Testing

38.1Null hypothesis and alternative hypothesis
38.2Proving claims
38.3Confidence levels, significance levels and critical values
38.4Test statistics
38.5Traditional hypothesis testing
38.6P-value hypothesis testing
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