A-Level Maths made completely easy!

Get an A with our complete A level Maths help. Whether it’s for Edexcel (Pearson), AQA, OCR or WJEC, our A level maths tutors got you all covered!

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.

I am doing a level maths revision, but I want to revise some of the basic maths first. Which course should I sign up for?

It doesn’t matter. Your StudyPug subscription gives you unlimited access to all maths help across all courses. You can review all maths help in all courses, including GCSE maths, year 11 and year 12 maths. To save your precious study time, you can skip, review and learn any materials anytime based on your needs.

A-Level Maths Topics

We have plenty of free lessons for you to watch

1.Surds

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

2.Factorisation

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

3.Quadratic 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
3.6Converting from general to vertex form by completing the square
3.7Shortcut: Vertex formula (free lessons)
3.8Finding the quadratic functions for given parabolas (free lessons)
3.9Applications of quadratic functions

4.Quadratic 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

5.Inequalities

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

6.Simultaneous 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 (no solution, infinite solutions)
6.7Word problems relating 3 variable simultaneous equations

7.Operations 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

8.Algebraic Division

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

9.Linear 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

10.Functions

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
10.9Domain and range of a function (free lessons)
10.10One to one functions
10.11Difference quotient: applications of 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)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

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 equations with algebraic fractions
12.8Solving rational inequalities

13.Absolute Value Functions

13.1Absolute value functions (free lessons)
13.2Solving absolute value equations
13.3Solving absolute value inequalities

14.Laws 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)
14.4Indices: Negative exponents
14.5Indices: Zero exponent: a0=1 a^0 = 1
14.6Indices: Rational exponents

15.Exponentials 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

16.Logarithms

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

17.Trigonometry

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

18.Trigonometric 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

19.Sine Rule and Cosine Rule

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

20.Graphing 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

21.Trigonometric 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)

22.Solving 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

23.Inverse Trigonometric Functions

23.1Evaluating inverse trigonometric functions
23.2Finding inverse reciprocal trigonometric function from its graph
23.3Inverse reciprocal trigonometric function: finding the exact value

24.Circle 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

25.Sequences 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

26.Binomial Expansion

26.1Factorial notation
26.2Pascal's triangle
26.3Binomial theorem

27.Differentiation

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

28.Integration

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

29.Parametric Equations

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

30.Differential Equations

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

31.Vectors

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

32.Statistics

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

33.Data 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

34.Probability

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

35.Discrete Probabilities

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

36.Normal 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

37.Correlation and Regression

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

38.Hypothesis 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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