A-Level Maths Help & Practice!

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Aligning with all exam boards' A level maths specifications, our comprehensive help includes all materials you need for the exam, 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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  1. 1Surds
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    1. 1.1Square and square roots
    2. 1.2Cubic and cube roots
    3. 1.3Evaluating and simplifying radicals
    4. 1.4Converting radicals to mixed radicals
    5. 1.5Converting radicals to entire radicals
    6. 1.6Adding and subtracting radicals
    7. 1.7Multiplying and dividing radicals
    8. 1.8Rationalize the denominator
  2. 2Laws of Indices
    1. 2.1Indices: Product rule (a^x)(a^y) = a^(x+y)
    2. 2.2Indices: Division rule (a^x / a^y) = a^(x-y)
    3. 2.3Indices: Power rule (a^x)^y = a^(x * y)
    4. 2.4Indices: Negative indices
    5. 2.5Zero index: a^0 = 1
    6. 2.6Rational indices
    7. 2.7Combining laws of indices
    8. 2.8Solving for indices
    9. 2.9Standard form
  3. 3Linear Functions
    1. 3.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
    2. 3.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
    3. 3.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
    4. 3.4Gradient intercept form: y = mx + b
    5. 3.5General form: Ax + By + C = 0
    6. 3.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
    7. 3.7Rate of change
    8. 3.8Graphing linear functions using table of values
    9. 3.9Graphing linear functions using x- and y-intercepts
    10. 3.10Graphing from slope-intercept form y=mx+b
    11. 3.11Graphing linear functions using a single point and gradient
    12. 3.12Word problems of graphing linear functions
    13. 3.13Parallel and perpendicular lines in linear functions
    14. 3.14Applications of linear relations
  4. 4Factorisation
    1. 4.1Factorise by taking out the greatest common factor
    2. 4.2Factorise by grouping
    3. 4.3Factorise difference of squares: x^2 - y^2
    4. 4.4Factorise trinomials
    5. 4.5Factorise Difference of Cubes
    6. 4.6Factorise Sum of Cubes
  5. 5Quadratic Functions
    1. 5.1Introduction to quadratic functions
    2. 5.2Transformations of quadratic functions
    3. 5.3Quadratic function in general form: y = ax^2 + bx + c
    4. 5.4Quadratic function in vertex form: y = a(x-p)^2 + q
    5. 5.5Completing the square
    6. 5.6Converting from general to vertex form by completing the square
    7. 5.7Shortcut: Vertex formula
    8. 5.8Graphing quadratic functions: General form VS. Vertex form
    9. 5.9Finding the quadratic functions for given parabolas
    10. 5.10Applications of quadratic functions
  6. 6Quadratic Equations
    1. 6.1Solving quadratic equations by factorising
    2. 6.2Solving quadratic equations by completing the square
    3. 6.3Using quadratic formula to solve quadratic equations
    4. 6.4The discriminant: Nature of roots of quadratic equations
    5. 6.5Applications of quadratic equations
  7. 7Inequalities
    1. 7.1Express linear inequalities graphically and algebraically
    2. 7.2Solving one-step linear inequalities
    3. 7.3Solving multi-step linear inequalities
    4. 7.4Solving quadratic inequalities
    5. 7.5Solving absolute value inequalities
  8. 8Simultaneous Equations
    1. 8.1Simultaneous linear equations
    2. 8.2Simultaneous linear-quadratic equations
    3. 8.3Simultaneous quadratic-quadratic equations
  9. 9Operations with Algebraic Fractions
    1. 9.1Simplifying algebraic fractions and restrictions
    2. 9.2Adding and subtracting algebraic fractions
    3. 9.3Multiplying algebraic fractions
    4. 9.4Dividing algebraic fractions
    5. 9.5Solving algebraic fraction equations
    6. 9.6Applications of algebraic fraction equations
    7. 9.7Simplifying complex fractions
    8. 9.8Partial fraction decomposition
  10. 10Absolute Value Functions
    1. 10.1Absolute value functions
    2. 10.2Solving absolute value equations
  11. 11Algebraic Division
    1. 11.1Polynomial long division
    2. 11.2Polynomial synthetic division
    3. 11.3Remainder theorem
    4. 11.4Factor theorem
  12. 12Functions
    1. 12.1Domain and range of a function
    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. 12.8Inverse 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. 14Reciprocal Functions
    1. 14.1Graphing reciprocals of linear functions
    2. 14.2Graphing reciprocals of quadratic functions
  15. 15Rational Functions
    1. 15.1What is a rational function?
    2. 15.2Point of discontinuity
    3. 15.3Vertical asymptote
    4. 15.4Horizontal asymptote
    5. 15.5Slant asymptote
    6. 15.6Graphs of rational functions
    7. 15.7Solving rational inequalities
  16. 16Exponentials Functions
    1. 16.1Solving exponential equations using laws of indices
    2. 16.2Graphing exponential functions
    3. 16.3Graphing transformations of exponential functions
    4. 16.4Finding an exponential function given its graph
  17. 17Logarithms
    1. 17.1What is a logarithm?
    2. 17.2Converting from logarithmic form to exponential form
    3. 17.3Evaluating logarithms without a calculator
    4. 17.4Common logarithms
    5. 17.5Natural log: ln
    6. 17.6Evaluating logarithms using change-of-base formula
    7. 17.7Converting from exponential form to logarithmic form
    8. 17.8Solving exponential equations with logarithms
    9. 17.9Product rule of logarithms
    10. 17.10Quotient rule of logarithms
    11. 17.11Combining product rule and quotient rule in logarithms
    12. 17.12Evaluating logarithms using logarithm rules
    13. 17.13Solving logarithmic equations
    14. 17.14Graphing logarithmic functions
    15. 17.15Finding a logarithmic function given its graph
  18. 18Applications of Exponential and Logarithmic Functions
    1. 18.1Exponential growth and decay by a factor
    2. 18.2Exponential decay: Half-life
    3. 18.3Exponential growth and decay by percentage
    4. 18.4Finance: Compound interest
    5. 18.5Continuous growth and decay
    6. 18.6Logarithmic scale: Richter scale (earthquake)
    7. 18.7Logarithmic scale: pH scale
    8. 18.8Logarithmic scale: dB scale
    9. 18.9Finance: Future value and present value
  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. 20.1Find the exact value of trigonometric ratios
    2. 20.2ASTC rule in trigonometry (All Students Take Calculus)
    3. 20.3Unit circle
    4. 20.4Converting from exponential form to logarithmic form
    5. 20.5Trigonometric ratios of angles in radians
    6. 20.6Radian 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. 22Graphing Trigonometric Functions
    1. 22.1Sine graph: y = sin x
    2. 22.2Cosine graph: y = cos x
    3. 22.3Tangent graph: y = tan x
    4. 22.4Cotangent graph: y = cot x
    5. 22.5Secant graph: y = sec x
    6. 22.6Cosecant graph: y = csc x
    7. 22.7Graphing transformations of trigonometric functions
    8. 22.8Determining trigonometric functions given their graphs
  23. 23Applications of Trigonometric Functions
    1. 23.1Tides and water depth trig problems
    2. 23.2Spring (simple harmonic motion) trig problems
  24. 24Trigonometric Identities
    1. 24.1Quotient identities and reciprocal identities
    2. 24.2Pythagorean identities
    3. 24.3Sum and difference identities
    4. 24.4Cofunction identities
    5. 24.5Double-angle identities
  25. 25Solving Trigonometric Equations
    1. 25.1Solving first degree trigonometric equations
    2. 25.2Determining non-permissible values for trig expressions
    3. 25.3Solving second degree trigonometric equations
    4. 25.4Solving trigonometric equations involving multiple angles
    5. 25.5Solving trigonometric equations using pythagorean identities
    6. 25.6Solving trigonometric equations using sum and difference identities
    7. 25.7Solving trigonometric equations using double-angle identities
  26. 26Circle Theorems
    1. 26.1Angles in a circle
    2. 26.2Chord properties
    3. 26.3Tangent properties
    4. 26.4Circle and circumference
    5. 26.5Arcs of a circle
    6. 26.6Areas and sectors of circles
    7. 26.7Inscribed quadrilaterals in circles
    8. 26.8Central and inscribed angles in circles
    9. 26.9Circles in coordinate plane
  27. 27Sequences and Series
    1. 27.1Arithmetic sequences
    2. 27.2Arithmetic series
    3. 27.3Geometric sequences
    4. 27.4Geometric series
    5. 27.5Infinite geometric series
    6. 27.6Sigma notation
  28. 28Binomial Expansion
    1. 28.1Factorial notation
    2. 28.2Pascal's triangle
    3. 28.3Binomial theorem
  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. 30Differentiation
    1. 30.1Power rule
    2. 30.2Gradient and equation of tangent line
    3. 30.3Chain rule
    4. 30.4Derivative of trigonometric functions
    5. 30.5Derivative of exponential functions
    6. 30.6Product rule
    7. 30.7Quotient rule
    8. 30.8Derivative of inverse trigonometric functions
    9. 30.9Derivative of logarithmic functions
    10. 30.10Higher order derivatives
    11. 30.11Critical number & maximum and minimum values
    12. 30.12Curve sketching
  31. 31Integration
    1. 31.1Antiderivatives
    2. 31.2Fundamental theorem of calculus
    3. 31.3Definite integral
    4. 31.4Numerical integration
    5. 31.5U-Substitution
    6. 31.6Integration by parts
    7. 31.7Trigonometric substitution
    8. 31.8Integration of rational functions by partial fractions
    9. 31.9Volumes of solids of revolution - Disc method
    10. 31.10Volumes of solids of revolution - Shell method
  32. 32Parametric Equations
    1. 32.1Defining curves with parametric equations
    2. 32.2Tangent and concavity of parametric equations
  33. 33Differential Equations
    1. 33.1Introduction to differential equations
    2. 33.2Separable equations
    3. 33.3Applications to differential equations
  34. 34Statistics
    1. 34.1Median and mode
    2. 34.2Mean
    3. 34.3Range and outliers
    4. 34.4Application of averages
    5. 34.5Spread of a data set - standard deviation & variance
  35. 35Data and Graphs
    1. 35.1Reading and drawing bar graphs
    2. 35.2Reading and drawing histograms
    3. 35.3Reading and drawing line graphs
    4. 35.4Box-and-whisker plots and scatter plots
    5. 35.5Stem-and-leaf plots
    6. 35.6Reading and drawing Venn diagrams
  36. 36Probability
    1. 36.1Addition rule for "OR"
    2. 36.2Multiplication rule for "AND"
    3. 36.3Conditional probability
  37. 37Discrete Probabilities
    1. 37.1Histogram, mean, variance & standard deviation
    2. 37.2Binomial distribution
    3. 37.3Mean and standard deviation of binomial distribution
    4. 37.4Poisson distribution
  38. 38Normal Distribution and Confidence Intervals
    1. 38.1Introduction to normal distribution
    2. 38.2Normal distribution and continuous random variable
    3. 38.3Z-scores and random continuous variables
    4. 38.4Sampling distributions
    5. 38.5Central limit theorem
    6. 38.6Confidence levels and critical values
    7. 38.7Confidence intervals to estimate population mean
    8. 38.8Student's t-distribution
  39. 39Correlation and Regression
    1. 39.1Bivariate, scatter plots and correlation
    2. 39.2Regression analysis
    3. 39.3Equation of the best fit line
  40. 40Hypothesis Testing
    1. 40.1Null hypothesis and alternative hypothesis
    2. 40.2Proving claims
    3. 40.3Confidence levels, significance levels and critical values
    4. 40.4Test statistics
    5. 40.5Traditional hypothesis testing
    6. 40.6P-value hypothesis testing
    7. 40.7Mean hypothesis testing with t-distribution
    8. 40.8Type 1 and type 2 errors
  41. 41Scalars, Vectors, and Motion
    1. 41.1Scalars, vectors, and one dimensional motion
    2. 41.2Vector operations in one dimension
    3. 41.3Vector operations in two dimensions
    4. 41.4Vector components
    5. 41.5Solving two dimensional vector problems
    6. 41.6Relative velocity
  42. 42Kinematics
    1. 42.1Kinematics in a straight line
    2. 42.2Position velocity acceleration: Derivative
  43. 43Forces
    1. 43.1Newton's first law of motion
    2. 43.2Newton's second law of motion
    3. 43.3Multiple forces acting on an object
    4. 43.4Newton's third law of motion
    5. 43.5Friction: Static and kinetic
    6. 43.6Forces in two dimensions
    7. 43.7Tension and pulley problems
  44. 44Momentum
    1. 44.1Momentum and motion
    2. 44.2Momentum and impulse
    3. 44.3Conservation of momentum in one dimension
    4. 44.4Conservation of momentum in two dimensions
    5. 44.5Elastic and inelastic collisions
  45. 45Equilibrium
    1. 45.1Translational equilibrium
    2. 45.2Rotational equilibrium
    3. 45.3Static equilibrium problems
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Description

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.

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