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've 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.

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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.

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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 (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+qa(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 parabolas for given quadratic functions
3.9Finding the quadratic functions for given parabolas (free lessons)
3.10Applications of quadratic functions

4Quadratic 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

5Polynomial 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
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 equations with algebraic fractions
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
9.2Transformations of radical functions
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 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

11Trigonometry

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

12Bearings

12.1Introduction to bearings
12.2Bearings and direction word problems
12.3Angle of elevation and depression

13Trigonometric Ratios and Angle Measure

13.1Angle in standard position
13.2Coterminal angles (free lessons)
13.3Reference angle
13.4Find the exact value of trigonometric ratios
13.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
13.6Unit circle (free lessons)
13.7Converting between degrees and radians
13.8Trigonometric ratios of angles in radians
13.9Radian measure and arc length

14Graphing Trigonometric Functions

14.1Sine graph: y = sin x
14.2Cosine graph: y = cos x
14.3Tangent graph: y = tan x
14.4Cotangent graph: y = cot x
14.5Secant graph: y = sec x
14.6Cosecant graph: y = csc x
14.7Graphing transformations of trigonometric functions
14.8Determining trigonometric functions given their graphs

15Trigonometric Identities

15.1Quotient identities and reciprocal identities (free lessons)
15.2Pythagorean identities
15.3Sum and difference identities
15.4Cofunction identities
15.5Double-angle identities (free lessons)

16Parabolas and Circles

16.1Conics - Parabola
16.2Conics - Circle

17Two-dimensional vectors

17.1Introduction to vectors
17.2Magnitude of a vector
17.3Direction angle of a vector
17.4Scalar multiplication
17.5Equivalent vectors
17.6Adding and subtracting vectors in component form
17.7Operations on vectors in magnitude and direction form
17.8Unit Vector
17.9Word problems on vectors

18Sequences and Series

18.1Arithmetic sequences (free lessons)
18.2Arithmetic series (free lessons)
18.3Geometric sequences
18.4Geometric series
18.5Infinite geometric series
18.6Sigma notation
18.7Arithmetic mean vs. Geometric mean

19Data Interpretation

19.1Center of a data set: mean, median, mode
19.2Spread of a data set - standard deviation & variance
19.3Measures of relative standing - z-score, quartiles, percentiles
19.4Bivariate, scatter plots and correlation
19.5Regression analysis
19.6Equation of the best fit line

20Discrete Probabilities

20.1Probability distribution - histogram, mean, variance & standard deviation
20.2Binomial distribution
20.3Mean and standard deviation of binomial distribution
20.4Poisson distribution
20.5Geometric distribution
20.6Negative binomial distribution

21Probability

21.1Addition rule for "OR"
21.2Multiplication rule for "AND"
21.3Conditional probability
21.4Probability with permutations and combinations
21.5Law of total probability
21.6Bayes' rule

22Permutations and Combinations

22.1Fundamental counting principle
22.2Factorial notation
22.3Path counting problems
22.4Permutation vs. Combination
22.5Permutations
22.6Combinations
22.7Problems involving both permutations and combinations
22.8Pascal's triangle
22.9Binomial theorem

23Integration Techniques

23.1U-Substitution
23.2Integration by parts
23.3Integration using trigonometric identities
23.4Trigonometric substitution
23.5Integration of rational functions by partial fractions
23.6Improper integrals

24Derivatives

24.1Definition of derivative
24.2Power rule
24.3Slope and equation of tangent line
24.4Chain rule
24.5Derivative of trigonometric functions
24.6Derivative of exponential functions
24.7Product rule
24.8Quotient rule
24.9Implicit differentiation
24.10Derivative of inverse trigonometric functions
24.11Derivative of logarithmic functions
24.12Higher order derivatives
24.13Tangent and concavity of parametric equations

25Integration Applications

25.1Areas between curves
25.2Volumes of solids with known cross-sections
25.3Volumes of solids of revolution - Disc method
25.4Volumes of solids of revolution - Shell method
25.5Average value of a function
25.6Arc length
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