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A-Level Maths Topics

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video
Surds
Square and square roots
Cubic and cube roots
Evaluating and simplifying radicals
Converting radicals to mixed radicals
Converting radicals to entire radicals
Adding and subtracting radicals
Multiplying and dividing radicals
Rationalize the denominator
video
Laws of Indices
Indices: Product rule (a^x)(a^y) = a^(x+y)
Indices: Division rule (a^x / a^y) = a^(x-y)
Indices: Power rule (a^x)^y = a^(x * y)
Indices: Negative indices
Zero index: a^0 = 1
Rational indices
Combining laws of indices
Solving for indices
Standard form
video
Linear Functions
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Gradient intercept form: y = mx + b
General form: Ax + By + C = 0
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)
Rate of change
Graphing linear functions using table of values
Graphing linear functions using x- and y-intercepts
Graphing from slope-intercept form y=mx+b
Graphing linear functions using a single point and gradient
Word problems of graphing linear functions
Parallel and perpendicular lines in linear functions
Applications of linear relations
video
Factorisation
Factorise by taking out the greatest common factor
Factorise by grouping
Factorise difference of squares: x^2 - y^2
Factorise trinomials
Factorise Difference of Cubes
Factorise Sum of Cubes
video
Quadratic Functions
Introduction to quadratic functions
Transformations of quadratic functions
Quadratic function in general form: y = ax^2 + bx + c
Quadratic function in vertex form: y = a(x-p)^2 + q
Completing the square
Converting from general to vertex form by completing the square
Shortcut: Vertex formula
Graphing quadratic functions: General form VS. Vertex form
Finding the quadratic functions for given parabolas
Applications of quadratic functions
video
Quadratic Equations
Solving quadratic equations by factorising
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
The discriminant: Nature of roots of quadratic equations
Applications of quadratic equations
video
Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Solving quadratic inequalities
Solving absolute value inequalities
video
Simultaneous Equations
Simultaneous linear equations
Simultaneous linear-quadratic equations
Simultaneous quadratic-quadratic equations
video
Operations with Algebraic Fractions
Simplifying algebraic fractions and restrictions
Adding and subtracting algebraic fractions
Multiplying algebraic fractions
Dividing algebraic fractions
Solving algebraic fraction equations
Applications of algebraic fraction equations
Simplifying complex fractions
Partial fraction decomposition
video
Absolute Value Functions
Absolute value functions
Solving absolute value equations
video
Algebraic Division
Polynomial long division
Polynomial synthetic division
Remainder theorem
Factor theorem
video
Functions
Domain and range of a function
Operations with functions
Adding functions
Subtracting functions
Multiplying functions
Dividing functions
Composite functions
Inverse functions
video
Transformations of Functions
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
Combining transformations of functions
video
Reciprocal Functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
video
Rational Functions
What is a rational function?
Point of discontinuity
Vertical asymptote
Horizontal asymptote
Slant asymptote
Graphs of rational functions
Solving rational inequalities
video
Exponentials Functions
Solving exponential equations using laws of indices
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
video
Logarithms
What is a logarithm?
Converting from logarithmic form to exponential form
Evaluating logarithms without a calculator
Common logarithms
Natural log: ln
Evaluating logarithms using change-of-base formula
Converting from exponential form to logarithmic form
Solving exponential equations with logarithms
Product rule of logarithms
Quotient rule of logarithms
Combining product rule and quotient rule in logarithms
Evaluating logarithms using logarithm rules
Solving logarithmic equations
Graphing logarithmic functions
Finding a logarithmic function given its graph
video
Applications of Exponential and Logarithmic Functions
Exponential growth and decay by a factor
Exponential decay: Half-life
Exponential growth and decay by percentage
Finance: Compound interest
Continuous growth and decay
Logarithmic scale: Richter scale (earthquake)
Logarithmic scale: pH scale
Logarithmic scale: dB scale
Finance: Future value and present value
video
Trigonometry
Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h}ho​ )
Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h}ha​ )
Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a}ao​ )
Combination of SohCahToa questions
Solving expressions using 45-45-90 special right triangles
Solving expressions using 30-60-90 special right triangles
Word problems relating ladder in trigonometry
Word problems relating guy wire in trigonometry
Other word problems relating angles in trigonometry
video
Trigonometric Ratios and Angle Measure
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
Unit circle
Converting from exponential form to logarithmic form
Trigonometric ratios of angles in radians
Radian measure and arc length
video
Sine Rule and Cosine Rule
Sine rule
Cosine rule
Sine rule and cosine rule word problems
video
Graphing Trigonometric Functions
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
video
Applications of Trigonometric Functions
Tides and water depth trig problems
Spring (simple harmonic motion) trig problems
video
Trigonometric Identities
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Cofunction identities
Double-angle identities
video
Solving Trigonometric Equations
Solving first degree trigonometric equations
Determining non-permissible values for trig expressions
Solving second degree trigonometric equations
Solving trigonometric equations involving multiple angles
Solving trigonometric equations using pythagorean identities
Solving trigonometric equations using sum and difference identities
Solving trigonometric equations using double-angle identities
video
Circle Theorems
Angles in a circle
Chord properties
Tangent properties
Circle and circumference
Arcs of a circle
Areas and sectors of circles
Inscribed quadrilaterals in circles
Central and inscribed angles in circles
Circles in coordinate plane
video
Sequences and Series
Arithmetic sequences
Arithmetic series
Geometric sequences
Geometric series
Infinite geometric series
Sigma notation
video
Binomial Expansion
Factorial notation
Pascal's triangle
Binomial theorem
video
Vectors
Introduction to vectors
Magnitude of a vector
Direction angle of a vector
Scalar multiplication
Equivalent vectors
Adding and subtracting vectors in component form
Operations on vectors in magnitude and direction form
Unit vector
Word problems on vectors
video
Differentiation
Power rule
Gradient and equation of tangent line
Chain rule
Derivative of trigonometric functions
Derivative of exponential functions
Product rule
Quotient rule
Derivative of inverse trigonometric functions
Derivative of logarithmic functions
Higher order derivatives
Critical number & maximum and minimum values
Curve sketching
video
Integration
Antiderivatives
Fundamental theorem of calculus
Definite integral
Numerical integration
U-Substitution
Integration by parts
Trigonometric substitution
Integration of rational functions by partial fractions
Volumes of solids of revolution - Disc method
Volumes of solids of revolution - Shell method
video
Parametric Equations
Defining curves with parametric equations
Tangent and concavity of parametric equations
video
Differential Equations
Introduction to differential equations
Separable equations
Applications to differential equations
video
Statistics
Median and mode
Mean
Range and outliers
Application of averages
Spread of a data set - standard deviation & variance
video
Data and Graphs
Reading and drawing bar graphs
Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Stem-and-leaf plots
Reading and drawing Venn diagrams
video
Probability
Addition rule for "OR"
Multiplication rule for "AND"
Conditional probability
video
Discrete Probabilities
Histogram, mean, variance & standard deviation
Binomial distribution
Mean and standard deviation of binomial distribution
Poisson distribution
video
Normal Distribution and Confidence Intervals
Introduction to normal distribution
Normal distribution and continuous random variable
Z-scores and random continuous variables
Sampling distributions
Central limit theorem
Confidence levels and critical values
Confidence intervals to estimate population mean
Student's t-distribution
video
Correlation and Regression
Bivariate, scatter plots and correlation
Regression analysis
Equation of the best fit line
video
Hypothesis Testing
Null hypothesis and alternative hypothesis
Proving claims
Confidence levels, significance levels and critical values
Test statistics
Traditional hypothesis testing
P-value hypothesis testing
Mean hypothesis testing with t-distribution
Type 1 and type 2 errors
video
Scalars, Vectors, and Motion
Scalars, vectors, and one dimensional motion
Vector operations in one dimension
Vector operations in two dimensions
Vector components
Solving two dimensional vector problems
Relative velocity
video
Kinematics
Kinematics in a straight line
Position velocity acceleration: Derivative
video
Forces
Newton's first law of motion
Newton's second law of motion
Multiple forces acting on an object
Newton's third law of motion
Friction: Static and kinetic
Forces in two dimensions
Tension and pulley problems
video
Momentum
Momentum and motion
Momentum and impulse
Conservation of momentum in one dimension
Conservation of momentum in two dimensions
Elastic and inelastic collisions
video
Equilibrium
Translational equilibrium
Rotational equilibrium
Static equilibrium problems

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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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