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 Derivatives, 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 ACE GCE.

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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?

A prerequisite for this course is Year 12 Maths, and after you mastered year 13 maths, your follow up course should be Calculus 1 or Statistics.

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It’s hard to find a good A level maths review site with hard maths questions that makes sense. A lot of them are either too easy, or are so hard it’s discouraging. It also doesn’t help when they don’t provide answers. StudyPug has been great in helping me review material, and I think it’s a new way to study maths.

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Hazel Sanford

As a tutor that covers maths for year 1 and A-level maths, I’m always on the lookout for good math revision problems. StudyPug is the best that I’ve seen! Perfect for teaching my students.

Kendall W.

Last year, I was very stressed with maths. I wasn’t coping very well since my teacher didn’t have time to help me out with the chapters I had troubles understanding (to be fair, I had quite a few questions). This year, for my senior year, I started it off with a subscription to StudyPug. I finally feel like I have maths support. We have our A level maths this year, but I’m not super worried. I’ve been acing my math tests at school!

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UK Year 13 Maths Topics

We have plenty of free lessons for you to watch

1.Functions

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

2.Transformations 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)
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

3.Quadratic 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+qa(x-p)^2 + q
3.5Completing the square
3.6Converting from general to vertex form by completing the square
3.7Shortcut: Vertex formula (free lessons)
3.8Finding the quadratic functions for given parabolas (free lessons)
3.9Applications of quadratic functions

4.Quadratic Equations and Inequalities

4.1Solving quadratic equations by factorising
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

5.Polynomial Functions

5.1What is a polynomial function? (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

6.Rational 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

7.Exponential 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
7.7Graphing exponential functions
7.8Graphing transformations of exponential functions
7.9Finding an exponential function given its graph

8.Logarithmic 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
8.14Graphing logarithmic functions
8.15Finding a logarithmic function given its graph

9.Radical Functions

9.1Basic radical functions
9.2Transformations of radical functions
9.3Square root of a function
9.4Solving radical equations

10.Solving Simultaneous Equations

10.1Determining number of solutions to linear equations (free lessons)
10.2Solving simultaneous equations by graphing
10.3Solving simultaneous equations by elimination
10.4Solving simultaneous 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

11.Trigonometry

11.1Sine rule
11.2Cosine rule
11.3Applications of the sine rule and cosine rule

12.Trigonometric 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)
12.6Unit circle (free lessons)
12.7Converting between degrees and radians
12.8Trigonometric ratios of angles in radians
12.9Radian measure and arc length

13.Graphing 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

14.Trigonometric 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)

15.Parabolas and Circles

15.1Conics - Parabola
15.2Conics - Circle

16.Two-dimensional vectors

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

17.Sequences 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

18.Data 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

19.Discrete Probabilites

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

20.Probability

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

21.Permutations 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

22.Integration 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

23.Derivatives

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

24.Integration Applications

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