UK Year 13 Maths made completely easy!

Get better maths marks with our complete Year 13 Maths help. Whether it’s for Upper Sixth form, A Level Maths revision, Core 3 and Core 4 Maths, or Functional skills level 3, we got you all covered!

Just like your class or textbook, our comprehensive help includes topics such as Differentiation, Integration, Quadratic equations, Solving simultaneous equations, Quadratic inequalities, Vectors, Trigonometric identities, and more. StudyPug gives you not just lessons, but tutorials that teach you how to tackle even the hardest A level maths questions with step-by-step solutions – in videos. Then, strengthen your understanding with tons of year 13 maths practice.

All our lessons are taught by experienced A level Maths teachers. Let’s finish your homework in no time, and score an A* in the A-level maths exam.

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Common Questions
My school uses Edexcel as their exam board. Do you cover all A level maths syllabus?

Yes. We cover all topics tested in AS level and A level Maths. Therefore, not only Edexcel, pupils taking the exam with all other exam boards, including AQA, OCR, and WJEC, will find all the topics here too.

I’m looking for help with my A Level Maths revision. Which course should I sign up for?

It doesn’t matter. Your StudyPug subscription gives you unlimited access to all math help across all courses. You can revise all maths help in all courses, including year 12 and year 13 maths. To save your precious study time, you can skip, review and learn any materials anytime based on your needs.

What class should I take after year 13 maths?

You should take this course after you are comfortable with Year 12 Maths. Your follow up course can be Differentiation or Statistics.

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UK Year 13 Maths Topics

We have plenty of free lessons for you to watch

1Functions

1.1Domain and range of a function (free lessons)
1.2Function notation (advanced) (free lessons)
1.3Operations with functions
1.4Adding functions
1.5Subtracting functions
1.6Multiplying functions
1.7Dividing functions
1.8Composite functions (free lessons)
1.9Inequalities of combined functions
1.10Inverse functions (free lessons)
1.11One to one functions
1.12Difference quotient: applications of functions

2Transformations of Functions

2.1Transformations of functions: Horizontal translations
2.2Transformations of functions: Vertical translations
2.3Reflection across the y-axis: y=f(−x)y = f(-x) (free lessons)
2.4Reflection across the x-axis: y=−f(x)y = -f(x)
2.5Transformations of functions: Horizontal stretches
2.6Transformations of functions: Vertical stretches
2.7Combining transformations of functions
2.8Even and odd functions

3Quadratic Functions

3.1Characteristics of 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 (free lessons)
3.6Converting from general to vertex form by completing the square
3.7Shortcut: Vertex formula (free lessons)
3.8Graphing quadratic functions: General form VS. Vertex form
3.9Finding the quadratic functions for given parabolas (free lessons)
3.10Applications of quadratic functions

4Quadratic Equations and Inequalities

4.1Solving quadratic equations by factoring
4.2Solving quadratic equations by completing the square
4.3Using quadratic formula to solve quadratic equations
4.4Nature of roots of quadratic equations: The discriminant
4.5Applications of quadratic equations
4.6Solving quadratic inequalities

5Polynomial Functions

5.1Polynomial functions (free lessons)
5.2Polynomial long division (free lessons)
5.3Polynomial synthetic division
5.4Remainder theorem
5.5Factor theorem
5.6Rational zero theorem
5.7Characteristics of polynomial graphs
5.8Multiplicities of polynomials
5.9Imaginary zeros of polynomials
5.10Determining the equation of a polynomial function
5.11Applications of polynomial functions
5.12Solving polynomial inequalities
5.13Fundamental theorem of algebra
5.14Descartes’ rule of signs

6Rational Functions

6.1What is a rational function? (free lessons)
6.2Point of discontinuity
6.3Vertical asymptote
6.4Horizontal asymptote
6.5Slant asymptote
6.6Graphs of rational functions
6.7Solving rational equations
6.8Solving rational inequalities

7Exponential Functions

7.1Exponents: Product rule (ax)(ay)=a(x+y)(a^x)(a^y)=a^{(x+y)} (free lessons)
7.2Exponents: division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
7.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x \cdot y)} (free lessons)
7.4Exponents: Negative exponents
7.5Exponents: Zero exponent: a0=1 a^0 = 1
7.6Exponents: Rational exponents
7.7Solving exponential equations using exponent rules
7.8Graphing exponential functions
7.9Graphing transformations of exponential functions
7.10Finding an exponential function given its graph

8Logarithmic Functions

8.1What is a logarithm?
8.2Converting from logarithmic form to exponential form (free lessons)
8.3Evaluating logarithms without a calculator
8.4Common logarithms
8.5Natural log: ln
8.6Evaluating logarithms using change-of-base formula
8.7Converting from exponential form to logarithmic form (free lessons)
8.8Solving exponential equations with logarithms
8.9Product rule of logarithms (free lessons)
8.10Quotient rule of logarithms
8.11Combining product rule and quotient rule in logarithms
8.12Evaluating logarithms using logarithm rules
8.13Solving logarithmic equations (free lessons)
8.14Graphing logarithmic functions
8.15Finding a logarithmic function given its graph

9Radical Functions

9.1Basic radical functions
9.2Radical functions and transformations
9.3Square root of a function
9.4Solving radical equations

10Solving Simultaneous Equations

10.1Determining number of solutions to linear equations (free lessons)
10.2Solving systems of linear equations by graphing
10.3Solving systems of linear equations by elimination
10.4Solving systems of linear equations by substitution
10.5Money related questions in linear equations (free lessons)
10.6Unknown number related questions in linear equations
10.7Distance and time related questions in linear equations
10.8Rectangular shape related questions in linear equations

11Trigonometry

11.1Law of sines
11.2Law of cosines
11.3Applications of the sine law and cosine law

12Trigonometric Ratios and Angle Measure

12.1Angle in standard position
12.2Coterminal angles (free lessons)
12.3Reference angle
12.4Find the exact value of trigonometric ratios
12.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
12.6Unit circle (free lessons)
12.7Converting between degrees and radians
12.8Trigonometric ratios of angles in radians
12.9Radian measure and arc length

13Graphing Trigonometric Functions

13.1Sine graph: y = sin x
13.2Cosine graph: y = cos x
13.3Tangent graph: y = tan x
13.4Cotangent graph: y = cot x
13.5Secant graph: y = sec x
13.6Cosecant graph: y = csc x
13.7Graphing transformations of trigonometric functions
13.8Determining trigonometric functions given their graphs

14Trigonometric Identities

14.1Quotient identities and reciprocal identities (free lessons)
14.2Pythagorean identities
14.3Sum and difference identities
14.4Cofunction identities
14.5Double-angle identities (free lessons)

15Parabolas and Circles

15.1Conics - Parabola
15.2Conics - Circle

16Two-dimensional vectors

16.1Introduction to vectors
16.2Magnitude of a vector
16.3Direction angle of a vector
16.4Scalar multiplication of vectors
16.5Equivalent vectors
16.6Adding and subtracting vectors in component form
16.7Operations on vectors in magnitude and direction form

17Sequences and Series

17.1Arithmetic sequences (free lessons)
17.2Arithmetic series (free lessons)
17.3Geometric sequences
17.4Geometric series
17.5Infinite geometric series
17.6Sigma notation
17.7Arithmetic mean vs. Geometric mean

18Data Interpretation

18.1Center of a data set: mean, median, mode
18.2Spread of a data set - standard deviation & variance
18.3Measures of relative standing - z-score, quartiles, percentiles
18.4Bivariate, scatter plots and correlation
18.5Regression analysis
18.6Equation of the best fit line

19Discrete Probabilities

19.1Probability distribution - histogram, mean, variance & standard deviation
19.2Binomial distribution
19.3Mean and standard deviation of binomial distribution
19.4Poisson distribution
19.5Geometric distribution
19.6Negative binomial distribution

20Probability

20.1Addition rule for "OR"
20.2Multiplication rule for "AND"
20.3Conditional probability
20.4Probability involving permutations and combinations
20.5Law of total probability
20.6Bayes' rule

21Permutations and Combinations

21.1Fundamental counting principle
21.2Factorial notation
21.3Path counting problems
21.4Permutation vs. Combination
21.5Permutations
21.6Combinations
21.7Problems involving both permutations and combinations
21.8Pascal's triangle
21.9Binomial theorem

22Integration Techniques

22.1U-Substitution
22.2Integration by parts
22.3Integration using trigonometric identities
22.4Trigonometric substitution
22.5Integration of rational functions by partial fractions
22.6Improper integrals

23Derivatives

23.1Definition of derivative
23.2Power rule
23.3Slope and equation of tangent line
23.4Chain rule
23.5Derivative of trigonometric functions
23.6Derivative of exponential functions
23.7Product rule
23.8Quotient rule
23.9Implicit differentiation
23.10Derivative of inverse trigonometric functions
23.11Derivative of logarithmic functions
23.12Higher order derivatives
23.13Tangent and concavity of parametric equations

24Integration Applications

24.1Areas between curves
24.2Volumes of solid with known cross-sections
24.3Volumes of solids of revolution - Disc method
24.4Volumes of solid of revolution - Shell method
24.5Average value of a function
24.6Arc length
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