AS-Level Maths Help & Practice

Get better marks with our comprehensive AS level Maths help ? whether it's for Edexcel (Pearson), AQA, OCR or WJEC. Our AS Maths tutors have you all covered!

Keeping with the specifications of all the exam boards, our thorough help for the exam includes topics such as Trigonometry, Factorisation, Quadratic functions, Exponential functions, Logarithms, Calculus, Statistics, and a lot more. Learn the concepts with our online video tutorials that show you step-by-step solutions to even the hardest maths problems. Then, strengthen your understanding with tons of as maths practice.

All our lessons are taught by experienced AS Maths teachers. Let's finish your revision in no time, and ACE that maths exam.

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  1. 1Set Theory
    1. 1.1Set notation
    2. 1.2Set builder notation
    3. 1.3Intersection and union of 2 sets
    4. 1.4Intersection and union of 3 sets
  2. 2Number System
    1. 2.1Understanding the number systems
    2. 2.2Prime factorization
    3. 2.3Greatest Common Factors (GCF)
    4. 2.4Least Common Multiple (LCM)
    5. 2.5Rational vs. Irrational numbers
    6. 2.6Converting repeating decimals to fractions
  3. 3Surds
    1. 3.1Square and square roots
    2. 3.2Cubic and cube roots
    3. 3.3Evaluating and simplifying radicals
    4. 3.4Converting radicals to mixed radicals
    5. 3.5Converting radicals to entire radicals
    6. 3.6Adding and subtracting radicals
    7. 3.7Multiplying and dividing radicals
    8. 3.8Rationalize the denominator
  4. 4Laws of Indices
    1. 4.1Indices: Product rule (a^x)(a^y) = a^(x+y)
    2. 4.2Indices: Division rule (a^x / a^y) = a^(x-y)
    3. 4.3Indices: Power rule (a^x)^y = a^(x * y)
    4. 4.4Indices: Negative indices
    5. 4.5Zero index: a^0 = 1
    6. 4.6Rational indices
    7. 4.7Combining laws of indices
    8. 4.8Solving for indices
    9. 4.9Standard form
  5. 5Linear Functions
    1. 5.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
    2. 5.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
    3. 5.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
    4. 5.4Gradient intercept form: y = mx + b
    5. 5.5General form: Ax + By + C = 0
    6. 5.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
    7. 5.7Rate of change
    8. 5.8Graphing linear functions using table of values
    9. 5.9Graphing linear functions using x- and y-intercepts
    10. 5.10Graphing from slope-intercept form y=mx+b
    11. 5.11Graphing linear functions using a single point and gradient
    12. 5.12Word problems of graphing linear functions
    13. 5.13Parallel and perpendicular lines in linear functions
    14. 5.14Applications of linear relations
  6. 6Quadratic Functions
    1. 6.1Introduction to quadratic functions
    2. 6.2Transformations of quadratic functions
    3. 6.3Quadratic function in general form: y = ax^2 + bx + c
    4. 6.4Quadratic function in vertex form: y = a(x-p)^2 + q
    5. 6.5Completing the square
    6. 6.6Converting from general to vertex form by completing the square
    7. 6.7Shortcut: Vertex formula
    8. 6.8Graphing quadratic functions: General form VS. Vertex form
    9. 6.9Finding the quadratic functions for given parabolas
    10. 6.10Applications of quadratic functions
  7. 7Quadratic Equations
    1. 7.1Solving quadratic equations by factorising
    2. 7.2Solving quadratic equations by completing the square
    3. 7.3Using quadratic formula to solve quadratic equations
    4. 7.4The discriminant: Nature of roots of quadratic equations
    5. 7.5Applications of quadratic equations
  8. 8Simultaneous Equations
    1. 8.1Simultaneous linear equations
    2. 8.2Simultaneous linear-quadratic equations
    3. 8.3Simultaneous quadratic-quadratic equations
  9. 9Inequalities
    1. 9.1Express linear inequalities graphically and algebraically
    2. 9.2Solving one-step linear inequalities
    3. 9.3Solving multi-step linear inequalities
    4. 9.4Solving quadratic inequalities
  10. 10Factorisation
    1. 10.1Factorise by taking out the greatest common factor
    2. 10.2Factorise by grouping
    3. 10.3Factorise difference of squares: x^2 - y^2
    4. 10.4Factorise trinomials
    5. 10.5Factorise difference of cubes
    6. 10.6Factorise sum of cubes
  11. 11Operations with Algebraic Fractions
    1. 11.1Simplifying algebraic fractions and restrictions
    2. 11.2Adding and subtracting algebraic fractions
    3. 11.3Multiplying algebraic fractions
    4. 11.4Dividing algebraic fractions
    5. 11.5Solving algebraic fraction equations
    6. 11.6Applications of algebraic fraction equations
    7. 11.7Simplifying complex fractions
    8. 11.8Partial fraction decomposition
  12. 12Functions
    1. 12.1Function notation
    2. 12.2Operations with functions
    3. 12.3Adding functions
    4. 12.4Subtracting functions
    5. 12.5Multiplying functions
    6. 12.6Dividing functions
    7. 12.7Composite functions
    8. 12.8Inequalities of combined functions
    9. 12.9Inverse functions
    10. 12.10One to one functions
    11. 12.11Difference quotient: applications of functions
  13. 13Transformations of Functions
    1. 13.1Transformations of functions: Horizontal translations
    2. 13.2Transformations of functions: Vertical translations
    3. 13.3Reflection across the y-axis: y = f(-x)
    4. 13.4Reflection across the x-axis: y = -f(x)
    5. 13.5Transformations of functions: Horizontal stretches
    6. 13.6Transformations of functions: Vertical stretches
    7. 13.7Combining transformations of functions
  14. 14Algebraic Division
    1. 14.1Polynomial long division
    2. 14.2Polynomial synthetic division
    3. 14.3Remainder theorem
    4. 14.4Factor theorem
  15. 15Reciprocal Functions
    1. 15.1Graphing reciprocals of linear functions
    2. 15.2Graphing reciprocals of quadratic functions
  16. 16Rational Functions
    1. 16.1What is a rational function?
    2. 16.2Point of discontinuity
    3. 16.3Vertical asymptote
    4. 16.4Horizontal asymptote
    5. 16.5Slant asymptote
    6. 16.6Graphs of rational functions
    7. 16.7Solving rational inequalities
  17. 17Circle Theorems
    1. 17.1Angles in a circle
    2. 17.2Chord properties
    3. 17.3Tangent properties
    4. 17.4Circle and circumference
    5. 17.5Arcs of a circle
    6. 17.6Areas and sectors of circles
    7. 17.7Inscribed quadrilaterlas in circles
    8. 17.8Central and inscribed angles in circles
  18. 18Binomial Expansion
    1. 18.1Factorial notation
    2. 18.2Pascal's triangle
    3. 18.3Binomial theorem
  19. 19Trigonometry
    1. 19.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
    2. 19.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
    3. 19.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
    4. 19.4Combination of SohCahToa questions
    5. 19.5Solving expressions using 45-45-90 special right triangles
    6. 19.6Solving expressions using 30-60-90 special right triangles
    7. 19.7Word problems relating ladder in trigonometry
    8. 19.8Word problems relating guy wire in trigonometry
    9. 19.9Other word problems relating angles in trigonometry
  20. 20Trigonometric Ratios and Angle Measure
    1. 20.1Unit circle
    2. 20.2Converting between degrees and radians
    3. 20.3Trigonometric ratios of angles in radians
    4. 20.4Radian measure and arc length
  21. 21Sine Rule and Cosine Rule
    1. 21.1Sine rule
    2. 21.2Cosine rule
    3. 21.3Sine rule and cosine rule word problems
  22. 22Trigonometric Identities and Equations
    1. 22.1Pythagorean identities
    2. 22.2Solving first degree trigonometric equations
    3. 22.3Solving second degree trigonometric equations
  23. 23Graphing Trigonometric Functions
    1. 23.1Sine graph: y = sin x
    2. 23.2Cosine graph: y = cos x
    3. 23.3Tangent graph: y = tan x
    4. 23.4Graphing transformations of trigonometric functions
  24. 24Exponentials Functions
    1. 24.1Solving exponential equations using laws of indices
    2. 24.2Graphing exponential functions
    3. 24.3Graphing transformations of exponential functions
    4. 24.4Finding an exponential function given its graph
  25. 25Logarithms
    1. 25.1What is a logarithm?
    2. 25.2Converting from logarithmic form to exponential form
    3. 25.3Evaluating logarithms without a calculator
    4. 25.4Common logarithms
    5. 25.5Natural log: ln
    6. 25.6Evaluating logarithms using change-of-base formula
    7. 25.7Converting from exponential form to logarithmic form
    8. 25.8Solving exponential equations with logarithms
    9. 25.9Product rule of logarithms
    10. 25.10Quotient rule of logarithms
    11. 25.11Combining product rule and quotient rule in logarithms
    12. 25.12Evaluating logarithms using logarithm rules
    13. 25.13Solving logarithmic equations
  26. 26Growth and Decay
    1. 26.1Exponential growth and decay by a factor
    2. 26.2Exponential growth and decay by percentage
    3. 26.3Finance: Compound interest
    4. 26.4Finance: Future value and present value
  27. 27Differentiation
    1. 27.1Definition of derivative
    2. 27.2Power rule
    3. 27.3Gradient and equation of tangent line
    4. 27.4Higher order derivatives
    5. 27.5Critical number & maximum and minimum values
  28. 28Integration
    1. 28.1Antiderivatives
    2. 28.2Definite integral
    3. 28.3Fundamental theorem of calculus
    4. 28.4Indefinite integral
  29. 29Vectors
    1. 29.1Introduction to vectors
    2. 29.2Magnitude of a vector
    3. 29.3Direction angle of a vector
    4. 29.4Scalar multiplication
    5. 29.5Equivalent vectors
    6. 29.6Adding and subtracting vectors in component form
    7. 29.7Operations on vectors in magnitude and direction form
    8. 29.8Unit vector
    9. 29.9Word problems on vectors
  30. 30Statistics
    1. 30.1Sampling methods
    2. 30.2Median and mode
    3. 30.3Mean
    4. 30.4Range and outliers
    5. 30.5Application of averages
    6. 30.6Standard deviation and variance
    7. 30.7Quartiles, Percentile, and Outliers
  31. 31Data and Graphs
    1. 31.1Reading and drawing bar graphs
    2. 31.2Reading and drawing histograms
    3. 31.3Reading and drawing line graphs
    4. 31.4Box-and-whisker plots and scatter plots
    5. 31.5Stem-and-leaf plots
    6. 31.6Reading and drawing Venn diagrams
    7. 31.7Frequency distribution and histograms
  32. 32Correlation and Regression
    1. 32.1Bivariate, scatter plots, and correlation
    2. 32.2Regression analysis
    3. 32.3Equation of the best fit line
  33. 33Probability
    1. 33.1Determining probabilities using tree diagrams and tables
    2. 33.2Probability of independent and combined events
    3. 33.3Probability with Venn diagrams
    4. 33.4Addition rule for "OR"
    5. 33.5Binomial distribution
  34. 34Hypothesis Testing
    1. 34.1Null hypothesis and alternative hypothesis
    2. 34.2Proving claims
    3. 34.3Confidence levels, significance levels, and critical values
    4. 34.4Test statistics
    5. 34.5Traditional hypothesis testing
    6. 34.6P-value hypothesis testing
    7. 34.7Type 1 and type 2 errors
  35. 35Scalars, Vectors, and Motion
    1. 35.1Scalars, vectors, and one dimensional motion
    2. 35.2Vector operations in one dimension
    3. 35.3Vector operations in two dimensions
  36. 36Kinematics
    1. 36.1Kinematics in a straight line
    2. 36.2Position velocity acceleration: Derivative
  37. 37Forces
    1. 37.1Newton's first law of motion
    2. 37.2Newton's second law of motion
    3. 37.3Multiple forces acting on an object
    4. 37.4Newton's third law of motion
    5. 37.5Friction: Static and kinetic
  38. 38Momentum
    1. 38.1Momentum and motion
    2. 38.2Momentum and impulse
    3. 38.3Conservation of momentum in one dimension

Is AS level Maths Hard?

As the name suggests, advanced subsidiary (AS) level maths, expands beyond the basic concepts of maths and into more complex or "advanced" areas of mathematics. If the thought of this seems a little daunting to you, you're not alone. There are many students across the UK that are put off by the complex sounding maths problems and terms like simultaneous equations, algebraic expressions, and more.

From the outside looking in, AS level maths can seem like a hard course of study, but if you have a firm grasp of the basics and you paid attention in secondary school maths, you should be well equipped to tackle even the trickiest of problems within this course.

Even if you struggled in year 10 or year 11 maths, you could still earn a good grade within AS level maths. All it would take is some organization, studying and an effective revision tool like StudyPug.

Our platform has a vast collection of video tutorials and revision guides for each topic of AS level maths. Our content will walk you through all the relevant topics that are bound to come up during your course of study, providing AS level maths step-by-step with videos on the following:

  • Simultaneous Equations
  • Differentiation
  • Circle Theorems
  • Operations with Surds
  • Law of Indices
  • Binomial Expansion
  • And more.

If you want to familiarize yourself with the topics you studied in secondary school before you take on an A level course, we have an extensive collection of materials for revision in trigonometry, statistics, integration vectors, and all other topic studied across the GCSE curriculum.

Our AS level Maths tutoring service will show you easy to understand solutions to even the hardest AS level maths questions. Furthermore, the information that we deliver, reflects everything you'd expect to find in modern maths textbooks and covers the content most likely to appear on your AQA, Edexcel, MEI, WJEC or OCR maths exams.

We understand that each student will have their own unique learning style and not every student will come to us at the same skill level. That's why we offer an "AS level maths for dummies" approach that starts with the basics and assumes no prior knowledge. The beauty of our on-demand video service is in is flexibility. You don't need to sit through lessons you already know. You can skip them entirely or simply fast-forward to the section you need.

If you join StudyPug today as a subscriber, you'll have direct access to all of our GCSE and AS level maths help, giving you unprecedented access to a wealth of quality videos and resources that can supplement your studies and help you find your way to the right maths solutions.

What is AS level Maths Like?

A level maths is separated into two variants. An AS Level maths course is one year long, whereas the A level Maths course, is a 2 year program with the AS acting as its first year.

Within the structure of the course, students are given a choice as to what modules they study. The modules are as follows:

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

Regardless of whether you're studying AS or A level maths, you will be required to study the C1-4 modules. AS students then pick one further module to study (statistics, mechanics, or decisions) and A level students, will pick two.

As an example, has drafted what a typical AS student studying statistics might encounter on their course (see below).

  1. Laws of indices
  2. Integration and differentiation of xn
  3. Integration gives areas under curves
  4. Laws of logarithms (log(ab)=log(a)+log(b) etc)
  5. Solution of quadratic equations
  6. Linear and quadratic graphs
  7. Simple use of sin, cos and tan functions and graphs, including
    1. cos2(x)+sin2(x)=1
    2. Radians
    3. Sin rule
  8. Expanding brackets and geometric series.
  9. Basic ideas of statistics: Mean, standard deviation, variance, outliers
  10. Various methods of plotting data and linear regression.
  11. The shape of the normal distribution and use of tables

How to Get an A in AS Level Maths?

To stand a chance of getting an A grade in your AS level exams, you'll need to be prepared to get yourself into a good study routine, which should include homework, worksheets, and AS level maths past papers. Using these past papers to sit mock exams, you will be better prepared for you actual tests, and it could help with your confidence and time management. Work within the time limits for each paper and review your performance to single out any areas of weakness.

If you get a few questions wrong within a specific topic, revisit the whole topic on StudyPug and review your class notes. Our content is broken down into individual topics, so you'll be able to find the videos that are relevant to you with ease. Watch the videos, resit mock papers, and chart your progress. Eventually, you'll see an improvement in your scores, and by addressing your weaker areas, you'll be better prepared for whatever arises in your end of year exam.

When the examiners are marking papers, they're not just looking for the right answers. Examiners are looking to see if you arrived at the solution through an understanding of the problem or via simple memorization. This is why its key to always show you working out! Even if its a simple question don't just answer it and move on, show how you arrived at the solution. There's always the potential to receive extra marks for showing your thought process, and that could mean the difference between a B and an A grade.

How to Revise for AS level Maths

When it comes to maths revision, as mentioned above, you should highlight your areas of weakness so that you know what to focus on. Once you know the topics of AS level maths you need to work on, you can visit StudyPug to find video tutorials that cover each topic with handy step-by-step examples.

You, much like many of students, may find that revising via our video format is a lot more engaging and easier to follow than the traditional textbook revision methods. To help get you started, we're offering a collection of free AS Level Maths lessons across the following subject areas:

  • Understanding the Number Systems
  • Least Common Multiple (LCM)
  • Converting Radicals to Entire Radicals
  • Slope Intercept Form: y = mx + b
  • Graphing Linear Functions Using x- and y- Intercepts
  • And Many More

Think of StudyPug as your own personal AS level maths tutor that's available 24/7.

What Calculators are Allowed in AS level Maths?

All examining boards will follow the regulations of the JCQ (Joint Council for Qualifications) with regards to calculators in exams.

The regulations are as follows:

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 AS Level Maths Paper Remarked?

If you don't receive the marks you were expecting, having your paper remarked could help. Firstly, you'll need to consult with your teacher and see if they also expected a higher score from your test paper (based on previous tests and in-class performance). Accessing the papers may be free for the school, but it can cost anywhere from £11 - £15, depending on the exam board.

There will also be an additional cost for the actual remarking and this will vary between exam boards and the nature of the remark (please see below).

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

It's not a cheap process and in most cases, remarking will only add a few extra marks, it won't change a D grade to an A. With that in mind, check how far away you are from the next possible grade, if you're 2-3 marks away, it may be worth the cost of a remark, specially it its the difference between a failing and passing grade.

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