Master A-Level Maths Online

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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 Standard form

3. Linear Functions

3.1 Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
3.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
3.3 Gradient equation: m=y2−y1x2−x1m = \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−y1=m(x−x1)y - y_1 = m (x - x_1)
3.7 Rate of change
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 Factor theorem

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 = oh \frac{o}{h} )
19.2 Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
19.3 Use tangent ratio to calculate angles and sides (Tan = oa \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 Unit circle
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 Sine rule
21.2 Cosine rule
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 Sigma notation

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 Unit vector
29.9 Word problems on vectors

30. Differentiation

30.1 Power rule
30.2 Gradient and equation of tangent line
30.3 Chain rule
30.4 Derivative of trigonometric functions
30.5 Derivative of exponential functions
30.6 Product rule
30.7 Quotient rule
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 U-Substitution
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 Mean
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 Proving claims
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

45 Chapters · 280 Topics · 1878 Videos

Is A-Level Maths Hard?

Advanced level maths or "A-Level maths" as its more commonly known, builds upon the topics you would have studied in school, venturing into more complex aspects of mathematics. With that in mind, it's easy to see why so many students fear that A-Level maths may be a bit too difficult for them.

If you've passed GCSE maths, you will be capable of studying A-Level maths. You may find it challenging at times, but with a firm grasp of the basics, you'll find that the problems faced in A-level maths aren't as complicated as they initially seemed.

To assist you in your attempts to conquer A-level maths, StudyPug has a rich collection of video lessons that cover every aspect of the curriculum. Ourvideo tutorials will explore everything you'd expect to find in your exams, and we'll deliver helpful step-by-step examples in plain english, ensuring you learn and retain the necessary information.

Whether you need help with Cosine and Sine rule, integration by parts, circle theorems, or any other topic, our collection of useful revision strategies and proven tips will get you learning in no time at all.

Furthermore, our tutors have worked to ensure that we provide simple solutions to even the trickiest of A-level maths problems. Our online content reflects the same material you'd expect to find in modern textbooks, and our tutorials are suitable guides for all maths exams regardless of the examining body (AQA, Edexcel, MEI, WJEC or OCR).

Don't worry if you're not entirely confident in your maths ability just yet. Our "A-Level maths for dummies" approach to teaching, assumes no prior knowledge and starts from the basics, taking A-Level maths step-by-step. However, if you are relatively confident in your maths abilities, you can skip past the content or fast-forwarded the information you don't need.

What is A-Level Maths Like?

A-Level maths is split into two different programs of study. There is the AS Level maths course, which is a one year course, and the A-Level Maths course, which is a 2 year course that incorporates the AS program as it's first year of content.

Students on both courses will be given a choice as to what modules they study. The modules available are listed below:

  • C1-4 - Core Maths
  • D1 & D2 - Decisions
  • M1 & M2 - Mechanics
  • S1 & S2 - Statistics

All students on either the AS or A-level maths program will be required to study the C1-4 modules. Students on the AS program will then pick one additional module to study (statistics, mechanics, or decisions). A-Level students will be required to pick two.

Popular topics covered on the A-level program are as follows:

  • Binomial expansion
  • Chain rule
  • Surds
  • Geometric series
  • Laws of indices
  • Factor theorem
  • Factorization
  • Parametric equations

How Can I Get an A in A-Level Maths?

To give yourself the best possible chance of securing an A grade in your A-level exams, you'll need to revise on a regular basis, so make time and get yourself into a weekly study routine. Within the routine, you should be reviewing your class notes (which you should be taking!), completing homework, and testing yourself using online worksheets and A-Level maths past papers.

Using past papers will build your confidence and time management ahead of exams. They will also allow you to single out any areas of weakness that needs addressing. Make note of the areas you need to improve upon and visit our site to review our content on the topic. Watch the videos, take notes, resit past papers, and chart your progress. Keep this routine up and you'll soon see improvements in your performance as you strengthen your knowledge across all aspects of A-level maths.

If you're not in a position to subscribe to our services, we do offer a collection of free A-Level Maths lessons across the following subject areas:

  • Converting Radicals to Entire Radicals
  • Distance Formula
  • Graphing Linear Functions Using x- and y-Intercepts
  • Factor by Taking Out the Greatest Common Factor
  • Characteristics of Quadratic Functions
  • And Many More

Finally, during the marking process, examiners will look to see if you've arrived at the solution through an understanding of the problem or if you've just employed simple memorization skills. With this in mind, attempt to show your working out where possible. Taking every step to demonstrate your understanding, could result in additional marks, turning a B grade into an A grade.

What Calculators are Allowed in A-Level Maths?

Each examining board follows the JCQ (Joint Council for Qualifications) regulations when it comes to rulings on acceptable calculators in exams.

The regulations below are taken directly from the JCQ website:

Calculators must be:

  • Of a size suitable for use on the desk
  • Either battery or solar powered
  • Free of lids, cases and covers which have printed instructions or formulas

Calculators must not:

  • Be designed or adapted to offer any of these facilities:
    • translators
    • Symbolic algebra manipulation
    • Symbolic differentiation or integration
    • Communication with other machines or the internet
  • Be borrowed from another candidate during an examination for any reason
  • Have retrievable information stored in them - this includes:
    • Databanks
    • Dictionaries
    • Mathematical formulas
    • Text

Is it Worth Getting my A-Level Maths Paper Remarked?

Understandably, receiving a grade lower than you were expecting can be frustrating. This is made even more frustrating when you need a specific grade for college enrollment or for employment purposes. If this happens to you, you should look into how many marks away from the next grade you were. If its fewer than 5 marks, you may find that it's worth the cost of a remark.

If you want a remark, you'll need to consult with your teacher and see if they also believe you could get a few extra marks. Depending on your examining body and type of remark required, you'll have to pay anywhere between £10 and £57.

AQAEdexcelOCRWJECDeadline
Access to Marked Paper£13.95Free£11.40£11.40Aug 24
Priority Remark£50.30£49.70£56.30£46Aug 24
Full Re-mark£42.25£41.70£45.60£36Sept 21
Clerical Re-check£16.10£11.20£16.40£10Sept 21
Pricing as of 2017

As you can see, it's not a cheap process so please keep in mind that remarking should only be done if you're close to achieving a higher grade. A remark won't change a D grade to an A, but it may just change that failing grade into a pass.

A-Level Maths FAQ

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Full access to step-by-step video lessons, diagnostic assessments, adaptive practice, Photo Search, and progress tracking for A-Level Maths and all other courses.

How quickly will I improve in A-Level Maths?

Most students see better understanding within the first week. With consistent practice, expect measurable improvement in exam scores within 2-4 weeks.

Does this cover my A-Level Maths curriculum?

Yes — our A-Level Maths content covers pure maths, statistics, and mechanics aligned to UK A-Level standards for exam boards including Edexcel, AQA, and OCR.

How does Photo Search work for A-Level Maths?

Snap a photo of your homework problem and StudyPug identifies the topic, then recommends relevant video lessons to help you understand and solve it.

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