# Year 13 Maths Help & Practice

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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##### 1Functions

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

- 1.1Domain and range of a function
##### 2Transformations of Functions

- 2.1Transformations of functions: Horizontal translations
- 2.2Transformations of functions: Vertical translations
- 2.3Reflection across the y-axis:
*y = f(-x)* - 2.4Reflection across the x-axis:
*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

- 2.1Transformations of functions: Horizontal translations
##### 3Quadratic Functions

- 3.1Characteristics of quadratic functions
- 3.2Transformations of quadratic functions
- 3.3Quadratic function in general form:
*y = ax^2 + bx + c* - 3.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 3.5Completing the square
- 3.6Converting from general to vertex form by completing the square
- 3.7Shortcut: Vertex formula
- 3.8Graphing parabolas for given quadratic functions
- 3.9Finding the quadratic functions for given parabolas
- 3.10Applications of quadratic functions

- 3.1Characteristics of quadratic functions
##### 4Quadratic Equations and Inequalities

##### 5Polynomial Functions

- 5.1What is a polynomial function?
- 5.2Polynomial long division
- 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

- 5.1What is a polynomial function?
##### 6Rational Functions

##### 7Exponential Functions

- 7.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 7.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 7.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 7.4Exponents: Negative exponents
- 7.5Exponents: Zero exponent:
*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

- 7.1Exponents: Product rule
##### 8Logarithmic Functions

- 8.1What is a logarithm?
- 8.2Converting from logarithmic form to exponential form
- 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
- 8.8Solving exponential equations with logarithms
- 8.9Product rule of logarithms
- 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

- 8.1What is a logarithm?
##### 9Radical Functions

##### 10Solving Simultaneous Equations

- 10.1Determining number of solutions to linear equations
- 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
- 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

- 10.1Determining number of solutions to linear equations
##### 11Trigonometry

##### 12Bearings

##### 13Trigonometric Ratios and Angle Measure

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

- 13.1Angle in standard position
##### 14Graphing Trigonometric Functions

##### 15Trigonometric Identities

##### 16Parabolas and Circles

##### 17Two-dimensional vectors

##### 18Sequences and Series

##### 19Data Interpretation

##### 20Discrete Probabilities

##### 21Probability

##### 22Permutations and Combinations

##### 23Integration Techniques

##### 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

- 24.1Definition of derivative
##### 25Integration Applications