# UK Year 12 Maths Help & Practice!

We've got you covered with our complete help for Year 12 maths, whether it's for Lower Sixth form, AS-Level Maths, Core 1 and Core 2 Maths, or Functional skills level 3.

Aligned with your class or textbook, you will get year 12 maths help on topics like Trigonometric identities, Derivatives, Integrals, Solving simultaneous equations, Factorising quadratic equations, Sequences and series, and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest algebra problems. Then, strengthen your understanding with tons of Algebra 2 practice.

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##### 1Linear Equations

- 1.1Introduction to linear equations
- 1.2Introduction to nonlinear equations
- 1.3Special case of linear equations: Horizontal lines
- 1.4Special case of linear equations: Vertical lines
- 1.5Parallel line equation
- 1.6Perpendicular line equation
- 1.7Combination of both parallel and perpendicular line equations
- 1.8Applications of linear equations

- 1.1Introduction to linear equations
##### 2Linear Inequalities

##### 3Inequalities in Two Variables

##### 4Introduction to Relations and Functions

##### 5Linear Functions

- 5.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 5.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 5.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 5.4Gradient intercept form: y = mx + b
- 5.5General form: Ax + By + C = 0
- 5.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 5.7Rate of change
- 5.8Graphing linear functions using table of values
- 5.9Graphing linear functions using x- and y-intercepts
- 5.10Graphing from gradient-intercept form y=mx+b
- 5.11Graphing linear functions using a single point and gradient
- 5.12Word problems of graphing linear functions
- 5.13Parallel and perpendicular lines in linear functions
- 5.14Applications of linear relations

- 5.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 6Absolute Value Functions

##### 7Solving Simultaneous Equations

- 7.1Determining number of solutions to linear equations
- 7.2Solving simultaneous equations by graphing
- 7.3Solving simultaneous equations by elimination
- 7.4Solving simultaneous equations by substitution
- 7.5Money related questions in linear equations
- 7.6Unknown number related questions in linear equations
- 7.7Distance and time related questions in linear equations
- 7.8Rectangular shape related questions in linear equations
- 7.9Simultaneous linear-quadratic equations

- 7.1Determining number of solutions to linear equations
##### 8Factorising Polynomial Expressions

- 8.1Common factors of polynomials
- 8.2Factorising polynomials by grouping
- 8.3Solving polynomials with the unknown "b" from
*x^2 + bx + c* - 8.4Solving polynomials with the unknown "c" from
*x^2 + bx + c* - 8.5Factorising polynomials:
*x^2 + bx + c* - 8.6Applications of polynomials:
*x^2 + bx + c* - 8.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$
- 8.8Factorising polynomials: $ax^2 + bx + c$
- 8.9Factorising perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 8.10Find the difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 8.11Evaluating polynomials
- 8.12Using algebra tiles to factorise polynomials
- 8.13Solving polynomial equations
- 8.14Word problems of polynomials

- 8.1Common factors of polynomials
##### 9Quadratic Functions

- 9.1Characteristics of quadratic functions
- 9.2Transformations of quadratic functions
- 9.3Quadratic function in general form:
*y = ax^2 + bx + c* - 9.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 9.5Completing the square
- 9.6Converting from general to vertex form by completing the square
- 9.7Shortcut: Vertex formula
- 9.8Graphing parabolas for given quadratic functions
- 9.9Finding the quadratic functions for given parabolas
- 9.10Applications of quadratic functions

- 9.1Characteristics of quadratic functions
##### 10Quadratic Equations and Inequalities

##### 11Polynomial Functions

- 11.1What is a polynomial function?
- 11.2Polynomial long division
- 11.3Polynomial synthetic division
- 11.4Remainder theorem
- 11.5Factor theorem
- 11.6Rational zero theorem
- 11.7Characteristics of polynomial graphs
- 11.8Multiplicities of polynomials
- 11.9Imaginary zeros of polynomials
- 11.10Determining the equation of a polynomial function
- 11.11Applications of polynomial functions
- 11.12Solving polynomial inequalities
- 11.13Solving polynomial equations by iteration
- 11.14Fundamental theorem of algebra
- 11.15Descartes' rule of signs

- 11.1What is a polynomial function?
##### 12Surds

##### 13Laws of indices

##### 14Algebraic Fractions

- 14.1Simplifying algebraic fractions and restrictions
- 14.2Adding and subtracting algebraic fractions
- 14.3Multiplying algebraic fractions
- 14.4Dividing algebraic fractions
- 14.5Solving equations with algebraic fractions
- 14.6Applications of equations with algebraic fractions
- 14.7Simplifying complex fractions
- 14.8Partial fraction decomposition

- 14.1Simplifying algebraic fractions and restrictions
##### 15Functions

- 15.1Function notation
- 15.2Operations with functions
- 15.3Adding functions
- 15.4Subtracting functions
- 15.5Multiplying functions
- 15.6Dividing functions
- 15.7Composite functions
- 15.8Inequalities of combined functions
- 15.9Inverse functions
- 15.10One to one functions
- 15.11Difference quotient: applications of functions

- 15.1Function notation
##### 16Transformations of Functions

- 16.1Transformations of functions: Horizontal translations
- 16.2Transformations of functions: Vertical translations
- 16.3Reflection across the y-axis:
*y = f(-x)* - 16.4Reflection across the x-axis:
*y = -f(x)* - 16.5Transformations of functions: Horizontal stretches
- 16.6Transformations of functions: Vertical stretches
- 16.7Combining transformations of functions
- 16.8Even and odd functions

- 16.1Transformations of functions: Horizontal translations
##### 17Reciprocal functions

##### 18Exponential Functions

- 18.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 18.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 18.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 18.4Exponents: Negative exponents
- 18.5Exponents: Zero exponent:
*a^0 = 1* - 18.6Exponents: Rational exponents
- 18.7Solving exponential equations using exponent rules
- 18.8Graphing exponential functions
- 18.9Graphing transformations of exponential functions
- 18.10Finding an exponential function given its graph

- 18.1Exponents: Product rule
##### 19Logarithmic Functions

- 19.1What is a logarithm?
- 19.2Converting from logarithmic form to exponential form
- 19.3Evaluating logarithms without a calculator
- 19.4Common logarithms
- 19.5Natural log: ln
- 19.6Evaluating logarithms using change-of-base formula
- 19.7Converting from exponential form to logarithmic form
- 19.8Solving exponential equations with logarithms
- 19.9Product rule of logarithms
- 19.10Quotient rule of logarithms
- 19.11Combining product rule and quotient rule in logarithms
- 19.12Evaluating logarithms using logarithm rules
- 19.13Solving logarithmic equations
- 19.14Graphing logarithmic functions
- 19.15Finding a logarithmic function given its graph

- 19.1What is a logarithm?
##### 20Applications of Exponential and Logarithmic Functions

- 20.1Exponential growth and decay by a factor
- 20.2Exponential decay: Half-life
- 20.3Exponential growth and decay by percentage
- 20.4Finance: Compound interest
- 20.5Continuous growth and decay
- 20.6Logarithmic scale: Richter scale (earthquake)
- 20.7Logarithmic scale: pH scale
- 20.8Logarithmic scale: dB scale
- 20.9Finance: Future value and present value

- 20.1Exponential growth and decay by a factor
##### 21Circles and Parabolas

##### 22Introduction to Trigonometry

- 22.1Use sine ratio to calculate angles and side (Sin = $\frac{o}{h}$ )
- 22.2Use cosine ratio to calculate angles and side (Cos = $\frac{a}{h}$ )
- 22.3Use tangent ratio to calculate angles and side (Tan = $\frac{o}{a}$ )
- 22.4Combination of SohCahToa questions
- 22.5Solving expressions using 45-45-90 special right triangles
- 22.6Solving expressions using 30-60-90 special right triangles
- 22.7Word problems relating ladder in trigonometry
- 22.8Word problems relating guy wire in trigonometry
- 22.9Other word problems relating angles in trigonometry

- 22.1Use sine ratio to calculate angles and side (Sin = $\frac{o}{h}$ )
##### 23Trigonometry

- 23.1Angle in standard position
- 23.2Coterminal angles
- 23.3Reference angle
- 23.4Find the exact value of trigonometric ratios
- 23.5ASTC rule in trigonometry (All Students Take Calculus)
- 23.6Unit circle
- 23.7Converting between degrees and radians
- 23.8Trigonometric ratios of angles in radians
- 23.9Radian measure and arc length

- 23.1Angle in standard position
##### 24Sine Rule and Cosine Rule

##### 25Bearings

##### 26Graphing Trigonometric Functions

##### 27Trigonometric Identities

##### 28Sequences and Series

##### 29Set Theory

##### 30Probability

##### 31Permutations and Combinations

##### 32Statistics

##### 33Data and Graphs

##### 34Parametric Equations and Polar Coordinates

##### 35Limits

- 35.1Finding limits from graphs
- 35.2Continuity
- 35.3Finding limits algebraically - direct substitution
- 35.4Finding limits algebraically - when direct substitution is not possible
- 35.5Infinite limits - vertical asymptotes
- 35.6Limits at infinity - horizontal asymptotes
- 35.7Intermediate value theorem
- 35.8Squeeze theorem

- 35.1Finding limits from graphs
##### 36Differentiation

- 36.1Definition of derivative
- 36.2Power rule
- 36.3Slope and equation of tangent line
- 36.4Chain rule
- 36.5Derivative of trigonometric functions
- 36.6Derivative of exponential functions
- 36.7Product rule
- 36.8Quotient rule
- 36.9Implicit differentiation
- 36.10Derivative of inverse trigonometric functions
- 36.11Derivative of logarithmic functions
- 36.12Higher order derivatives
- 36.13Critical number & maximum and minimum values

- 36.1Definition of derivative
##### 37Integration

##### 38Integration Applications