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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  1. 1Linear Equations
    1. 1.1Introduction to linear equations
    2. 1.2Introduction to nonlinear equations
    3. 1.3Special case of linear equations: Horizontal lines
    4. 1.4Special case of linear equations: Vertical lines
    5. 1.5Parallel line equation
    6. 1.6Perpendicular line equation
    7. 1.7Combination of both parallel and perpendicular line equations
    8. 1.8Applications of linear equations
  2. 2Linear Inequalities
    1. 2.1Express linear inequalities graphically and algebraically
    2. 2.2Solving one-step linear inequalities
    3. 2.3Solving multi-step linear inequalities
    4. 2.4Compound inequalities
  3. 3Inequalities in Two Variables
    1. 3.1Graphing linear inequalities in two variables
    2. 3.2Graphing simultaneous linear inequalities
    3. 3.3Graphing quadratic inequalities in two variables
    4. 3.4Graphing simultaneous quadratic inequalities
    5. 3.5Applications of inequalities
    6. 3.6What is linear programming?
    7. 3.7Linear programming word problems
  4. 4Introduction to Relations and Functions
    1. 4.1Relationship between two variables
    2. 4.2Understand relations between x- and y-intercepts
    3. 4.3Domain and range of a function
    4. 4.4Identifying functions
    5. 4.5Function notation
  5. 5Linear Functions
    1. 5.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
    2. 5.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
    3. 5.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
    4. 5.4Gradient intercept form: y = mx + b
    5. 5.5General form: Ax + By + C = 0
    6. 5.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
    7. 5.7Rate of change
    8. 5.8Graphing linear functions using table of values
    9. 5.9Graphing linear functions using x- and y-intercepts
    10. 5.10Graphing from gradient-intercept form y=mx+b
    11. 5.11Graphing linear functions using a single point and gradient
    12. 5.12Word problems of graphing linear functions
    13. 5.13Parallel and perpendicular lines in linear functions
    14. 5.14Applications of linear relations
  6. 6Absolute Value Functions
    1. 6.1Absolute value functions
    2. 6.2Solving absolute value equations
    3. 6.3Solving absolute value inequalities
  7. 7Solving Simultaneous Equations
    1. 7.1Determining number of solutions to linear equations
    2. 7.2Solving simultaneous equations by graphing
    3. 7.3Solving simultaneous equations by elimination
    4. 7.4Solving simultaneous equations by substitution
    5. 7.5Money related questions in linear equations
    6. 7.6Unknown number related questions in linear equations
    7. 7.7Distance and time related questions in linear equations
    8. 7.8Rectangular shape related questions in linear equations
    9. 7.9Simultaneous linear-quadratic equations
  8. 8Factorising Polynomial Expressions
    1. 8.1Common factors of polynomials
    2. 8.2Factorising polynomials by grouping
    3. 8.3Solving polynomials with the unknown "b" from x^2 + bx + c
    4. 8.4Solving polynomials with the unknown "c" from x^2 + bx + c
    5. 8.5Factorising polynomials: x^2 + bx + c
    6. 8.6Applications of polynomials: x^2 + bx + c
    7. 8.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
    8. 8.8Factorising polynomials: ax2+bx+cax^2 + bx + c
    9. 8.9Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
    10. 8.10Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
    11. 8.11Evaluating polynomials
    12. 8.12Using algebra tiles to factorise polynomials
    13. 8.13Solving polynomial equations
    14. 8.14Word problems of polynomials
  9. 9Quadratic Functions
    1. 9.1Characteristics of quadratic functions
    2. 9.2Transformations of quadratic functions
    3. 9.3Quadratic function in general form: y = ax^2 + bx + c
    4. 9.4Quadratic function in vertex form: y = a(x-p)^2 + q
    5. 9.5Completing the square
    6. 9.6Converting from general to vertex form by completing the square
    7. 9.7Shortcut: Vertex formula
    8. 9.8Graphing parabolas for given quadratic functions
    9. 9.9Finding the quadratic functions for given parabolas
    10. 9.10Applications of quadratic functions
  10. 10Quadratic Equations and Inequalities
    1. 10.1Solving quadratic equations by factoring
    2. 10.2Solving quadratic equations by completing the square
    3. 10.3Using quadratic formula to solve quadratic equations
    4. 10.4Nature of roots of quadratic equations: The discriminant
    5. 10.5Applications of quadratic equations
    6. 10.6Solving quadratic inequalities
  11. 11Polynomial Functions
    1. 11.1What is a polynomial function?
    2. 11.2Polynomial long division
    3. 11.3Polynomial synthetic division
    4. 11.4Remainder theorem
    5. 11.5Factor theorem
    6. 11.6Rational zero theorem
    7. 11.7Characteristics of polynomial graphs
    8. 11.8Multiplicities of polynomials
    9. 11.9Imaginary zeros of polynomials
    10. 11.10Determining the equation of a polynomial function
    11. 11.11Applications of polynomial functions
    12. 11.12Solving polynomial inequalities
    13. 11.13Solving polynomial equations by iteration
    14. 11.14Fundamental theorem of algebra
    15. 11.15Descartes' rule of signs
  12. 12Surds
    1. 12.1Operations with surds
    2. 12.2Conversion between entire radicals and mixed surds
    3. 12.3Adding and subtracting surds
    4. 12.4Multiplying surds
    5. 12.5Solving surd equations
  13. 13Laws of indices
    1. 13.1Product rule of exponents
    2. 13.2Quotient rule of exponents
    3. 13.3Power of a product rule
    4. 13.4Power of a quotient rule
    5. 13.5Power of a power rule
    6. 13.6Negative exponent rule
    7. 13.7Combining the exponent rules
    8. 13.8Standard form
    9. 13.9Convert between radicals and rational exponents
    10. 13.10Solving for exponents
  14. 14Algebraic Fractions
    1. 14.1Simplifying algebraic fractions and restrictions
    2. 14.2Adding and subtracting algebraic fractions
    3. 14.3Multiplying algebraic fractions
    4. 14.4Dividing algebraic fractions
    5. 14.5Solving equations with algebraic fractions
    6. 14.6Applications of equations with algebraic fractions
    7. 14.7Simplifying complex fractions
    8. 14.8Partial fraction decomposition
  15. 15Functions
    1. 15.1Function notation
    2. 15.2Operations with functions
    3. 15.3Adding functions
    4. 15.4Subtracting functions
    5. 15.5Multiplying functions
    6. 15.6Dividing functions
    7. 15.7Composite functions
    8. 15.8Inequalities of combined functions
    9. 15.9Inverse functions
    10. 15.10One to one functions
    11. 15.11Difference quotient: applications of functions
  16. 16Transformations of Functions
    1. 16.1Transformations of functions: Horizontal translations
    2. 16.2Transformations of functions: Vertical translations
    3. 16.3Reflection across the y-axis: y = f(-x)
    4. 16.4Reflection across the x-axis: y = -f(x)
    5. 16.5Transformations of functions: Horizontal stretches
    6. 16.6Transformations of functions: Vertical stretches
    7. 16.7Combining transformations of functions
    8. 16.8Even and odd functions
  17. 17Reciprocal functions
    1. 17.1Graphing reciprocals of linear functions
    2. 17.2Graphing reciprocals of quadratic functions
  18. 18Exponential Functions
    1. 18.1Exponents: Product rule (a^x)(a^y) = a^(x+y)
    2. 18.2Exponents: Division rule (a^x / a^y) = a^(x-y)
    3. 18.3Exponents: Power rule (a^x)^y = a^(x * y)
    4. 18.4Exponents: Negative exponents
    5. 18.5Exponents: Zero exponent: a^0 = 1
    6. 18.6Exponents: Rational exponents
    7. 18.7Solving exponential equations using exponent rules
    8. 18.8Graphing exponential functions
    9. 18.9Graphing transformations of exponential functions
    10. 18.10Finding an exponential function given its graph
  19. 19Logarithmic Functions
    1. 19.1What is a logarithm?
    2. 19.2Converting from logarithmic form to exponential form
    3. 19.3Evaluating logarithms without a calculator
    4. 19.4Common logarithms
    5. 19.5Natural log: ln
    6. 19.6Evaluating logarithms using change-of-base formula
    7. 19.7Converting from exponential form to logarithmic form
    8. 19.8Solving exponential equations with logarithms
    9. 19.9Product rule of logarithms
    10. 19.10Quotient rule of logarithms
    11. 19.11Combining product rule and quotient rule in logarithms
    12. 19.12Evaluating logarithms using logarithm rules
    13. 19.13Solving logarithmic equations
    14. 19.14Graphing logarithmic functions
    15. 19.15Finding a logarithmic function given its graph
  20. 20Applications of Exponential and Logarithmic Functions
    1. 20.1Exponential growth and decay by a factor
    2. 20.2Exponential decay: Half-life
    3. 20.3Exponential growth and decay by percentage
    4. 20.4Finance: Compound interest
    5. 20.5Continuous growth and decay
    6. 20.6Logarithmic scale: Richter scale (earthquake)
    7. 20.7Logarithmic scale: pH scale
    8. 20.8Logarithmic scale: dB scale
    9. 20.9Finance: Future value and present value
  21. 21Circles and Parabolas
    1. 21.1Angles in a circle
    2. 21.2Chord properties
    3. 21.3Tangent properties
    4. 21.4Circles and circumference
    5. 21.5Arcs of a circle
    6. 21.6Areas and sectors of circles
    7. 21.7Inscribed quadrilaterlas in circles
    8. 21.8Central and inscribed angles in circles
    9. 21.9Circles in coordinate plane
    10. 21.10Parabola
  22. 22Introduction to Trigonometry
    1. 22.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} )
    2. 22.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
    3. 22.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
    4. 22.4Combination of SohCahToa questions
    5. 22.5Solving expressions using 45-45-90 special right triangles
    6. 22.6Solving expressions using 30-60-90 special right triangles
    7. 22.7Word problems relating ladder in trigonometry
    8. 22.8Word problems relating guy wire in trigonometry
    9. 22.9Other word problems relating angles in trigonometry
  23. 23Trigonometry
    1. 23.1Angle in standard position
    2. 23.2Coterminal angles
    3. 23.3Reference angle
    4. 23.4Find the exact value of trigonometric ratios
    5. 23.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 23.6Unit circle
    7. 23.7Converting between degrees and radians
    8. 23.8Trigonometric ratios of angles in radians
    9. 23.9Radian measure and arc length
  24. 24Sine Rule and Cosine Rule
    1. 24.1Sine rule
    2. 24.2Cosine rule
    3. 24.3Applications of the sine rule and cosine rule
  25. 25Bearings
    1. 25.1Introduction to bearings
    2. 25.2Bearings and direction word problems
    3. 25.3Angle of elevation and depression
  26. 26Graphing Trigonometric Functions
    1. 26.1Sine graph: y = sin x
    2. 26.2Cosine graph: y = cos x
    3. 26.3Tangent graph: y = tan x
    4. 26.4Cotangent graph: y = cot x
    5. 26.5Secant graph: y = sec x
    6. 26.6Cosecant graph: y = csc x
    7. 26.7Graphing transformations of trigonometric functions
    8. 26.8Determining trigonometric functions given their graphs
  27. 27Trigonometric Identities
    1. 27.1Quotient identities and reciprocal identities
    2. 27.2Pythagorean identities
    3. 27.3Sum and difference identities
    4. 27.4Cofunction identities
    5. 27.5Double-angle identities
  28. 28Sequences and Series
    1. 28.1Arithmetic sequences
    2. 28.2Arithmetic series
    3. 28.3Geometric sequences
    4. 28.4Geometric series
    5. 28.5Infinite geometric series
    6. 28.6Sigma notation
    7. 28.7Arithmetic mean vs. Geometric mean
  29. 29Set Theory
    1. 29.1Set notation
    2. 29.2Set builder notation
    3. 29.3Intersection and union of 2 sets
    4. 29.4Intersection and union of 3 sets
  30. 30Probability
    1. 30.1Determining probabilities using tree diagrams and tables
    2. 30.2Probability of independent events
    3. 30.3Finding probabilities using two-way frequency tables
    4. 30.4Probability with Venn diagrams
  31. 31Permutations and Combinations
    1. 31.1Fundamental counting principle
    2. 31.2Factorial notation
    3. 31.3Path counting problems
    4. 31.4Permutation vs. Combination
    5. 31.5Permutations
    6. 31.6Combinations
    7. 31.7Problems involving both permutations and combinations
    8. 31.8Pascal's triangle
    9. 31.9Binomial theorem
  32. 32Statistics
    1. 32.1Median and mode
    2. 32.2Mean
    3. 32.3Range and outliers
    4. 32.4Application of averages
    5. 32.5Influencing factors in data collection
    6. 32.6Data collection
  33. 33Data and Graphs
    1. 33.1Reading and drawing bar graphs
    2. 33.2Reading and drawing histograms
    3. 33.3Reading and drawing line graphs
    4. 33.4Box-and-whisker plots and scatter plots
    5. 33.5Stem-and-leaf plots
    6. 33.6Reading and drawing Venn diagrams
  34. 34Parametric Equations and Polar Coordinates
    1. 34.1Defining curves with parametric equations
    2. 34.2Polar coordinates
  35. 35Limits
    1. 35.1Finding limits from graphs
    2. 35.2Continuity
    3. 35.3Finding limits algebraically - direct substitution
    4. 35.4Finding limits algebraically - when direct substitution is not possible
    5. 35.5Infinite limits - vertical asymptotes
    6. 35.6Limits at infinity - horizontal asymptotes
    7. 35.7Intermediate value theorem
    8. 35.8Squeeze theorem
  36. 36Differentiation
    1. 36.1Definition of derivative
    2. 36.2Power rule
    3. 36.3Slope and equation of tangent line
    4. 36.4Chain rule
    5. 36.5Derivative of trigonometric functions
    6. 36.6Derivative of exponential functions
    7. 36.7Product rule
    8. 36.8Quotient rule
    9. 36.9Implicit differentiation
    10. 36.10Derivative of inverse trigonometric functions
    11. 36.11Derivative of logarithmic functions
    12. 36.12Higher order derivatives
    13. 36.13Critical number & maximum and minimum values
  37. 37Integration
    1. 37.1Antiderivatives
    2. 37.2Riemann sum
    3. 37.3Definite integral
    4. 37.4Fundamental theorem of calculus
  38. 38Integration Applications
    1. 38.1Areas between curves
    2. 38.2Volumes of solids with known cross-sections
    3. 38.3Volumes of solids of revolution - Disc method
    4. 38.4Volumes of solids of revolution - Shell method
    5. 38.5Average value of a function
    6. 38.6Arc length

How Can I Pass A Year 12 Maths Exam?

To help you obtain a passing grade in your year 12 maths exam, you should be doing maths revision on a regular basis. Try and take the time to get yourself into a weekly study routine that involves reviewing your class notes (which if you're not taking, you should be!), working on homework assignments, and testing your knowledge via online maths aids like worksheets and past year 12 maths exam papers.

Use these past papers to build your confidence and improve your time management ahead of your actual exams. Assess how long it takes for you to answer questions and see how long you should realistic spend on each section. If a section proves to be too difficult, skip it and come back to it later. It's more important to get through the paper, answering as many questions as possible, so don't waste time on one problem.

Using these past papers, you can also single out any topics that are giving you trouble. By Highlighting these weaker areas, you will able able to build much more effective revision strategies.

Once you know where you need to improve, use StudyPug for some additional year 12 maths help. You can find the lesson you need help with via the easy to use search function and from there, we'll help you tackle the problems by introducing step-by-step examples that work to build your understanding.

Our year 12 maths tutors will cover all the complicated A level maths questions and we've made sure that our content reflects the current Year 12 maths curriculum and the A level maths syllabus. You'll also have access to your very own study planner that you can use to track your progress and keep you moving towards your goals.

Once you're comfortable using our videos to study maths, try sitting additional past papers and attempt more worksheets to chart your progress. You'll soon see improvements in your performance and you'll be in a much better position to pass your upcoming exams.

Finally, when you're actually in your exam, please keep in mind that the external markers will be looking for proof that you understood the problem. They want to see that you knew how to solve the problems beyond memorizing formulae and other tools. Where possible, show your working out! This will show them your thought process and your mathematical reasoning abilities. In doing so, you may earn additional marks and receive a bump in your final grade.

Should I Try to Take an A-level Exam Early?

If you feel confident enough to take the test ahead of time, you can, but please be aware that it's not necessarily something that will help you in your university applications. The UCAS points you earn will still count towards your overall UCAS score, but keep in mind that universities are looking for more than just UCAS points.

The Russell Group, an association of United Kingdom-based universities, founded in 1994, had this to say in regards to taking A-levels early and how it may impact your university applications.

Some universities or their individual subject departments may want to see that you have taken a number of Advanced level qualifications all at the same time; for example, they may want to see three A-levels taken in Year 13.

This can be because they want to know that you can comfortably manage a workload of this size… Admissions policies may therefore differ in relation to A-levels taken early, and whether these are included in offers made or not.

For example, some courses that typically make a conditional offer of AAB may take account of an A-level A grade achieved at the end of Year 12 and, as a result, make a conditional offer of AB for A-levels taken in Year 13. Others may still make a conditional offer of AAB on subjects taken at the end of Year 13 and will not include the A-level already taken in their conditional offer.

What Units Will I Study in A-Level Maths?

Choosing to study A level maths will not only benefit your university applications, but a qualification in A-Level maths, will help you in your future career too. It demonstrates to potential employers that you have the ability to apply analytical thinking, finding logical solutions to solve a variety of problems.

We're not suggesting that employers are specifically looking for a candidate that can solve maths equations or knows how to calculate angels (unless it's an architectural role), but they'll certainly see the value in the various transferable skills that are associated with solving those problems.

Once you've decided to study A/AS-level maths, you'll need to narrow down that actual units you'd like to cover throughout the program. Within A-Level mathematics, there are two different programs of study.

Firstly, there's AS Level maths, this is a one year course that will cover 2 core maths units plus one additional unit from either mechanics, decisions, or statistics. If you decide to study a full 2 year A-level course, you'll cover all 4 core maths units plus two additional units.

With this in mind, you should select the optional units that will benefit you best in your future university applications and career. For example, if you're looking to enter into engineering, you may want to consider studying mechanics.

To give you an idea of what to expect, here is a breakdown of topics you'll likely cover in the three optional units (not a complete list).


  • Statistical models
  • Summarising data
  • Probability
  • Correlation and Regression
  • Discrete Random Variables
  • Continuous Random Variables
  • Continuous Distributions
  • Hypothesis tests
  • Combinations of random variables


  • Vectors
  • Kinematics
  • Dynamics
  • Statics
  • Moments
  • Centres of mass
  • Work and energy
  • Collisions
  • Statics of rigid bodies


  • Algorithms
  • Algorithms on graphs
  • Route inspection
  • Critical path analysis
  • Linear programming
  • Matchings
  • Flows in a network
  • I'm revising for A-level maths. Will I have access to both Year 12 and Year 13 maths help?

    Of course. Your StudyPug membership gives you unlimited access to all math help across all courses. 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 12 maths?

    The course you would take before year 12 maths is Year 11 Maths. Then, your follow up course should be Year 13 Maths.

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