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Year 12 Maths Topics

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video
Linear Equations
Introduction to linear equations
Introduction to nonlinear equations
Special case of linear equations: Horizontal lines
Special case of linear equations: Vertical lines
Parallel line equation
Perpendicular line equation
Combination of both parallel and perpendicular line equations
Applications of linear equations
video
Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Compound inequalities
video
Inequalities in Two Variables
Graphing linear inequalities in two variables
Graphing simultaneous linear inequalities
Graphing quadratic inequalities in two variables
Graphing simultaneous quadratic inequalities
Applications of inequalities
What is linear programming?
Linear programming word problems
video
Introduction to Relations and Functions
Relationship between two variables
Understand relations between x- and y-intercepts
Domain and range of a function
Identifying functions
Function notation
video
Linear Functions
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Gradient intercept form: y = mx + b
General form: Ax + By + C = 0
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)
Rate of change
Graphing linear functions using table of values
Graphing linear functions using x- and y-intercepts
Graphing from gradient-intercept form y=mx+b
Graphing linear functions using a single point and gradient
Word problems of graphing linear functions
Parallel and perpendicular lines in linear functions
Applications of linear relations
video
Absolute Value Functions
Absolute value functions
Solving absolute value equations
Solving absolute value inequalities
video
Solving Simultaneous Equations
Determining number of solutions to linear equations
Solving simultaneous equations by graphing
Solving simultaneous equations by elimination
Solving simultaneous equations by substitution
Money related questions in linear equations
Unknown number related questions in linear equations
Distance and time related questions in linear equations
Rectangular shape related questions in linear equations
Simultaneous linear-quadratic equations
video
Factorising Polynomial Expressions
Common factors of polynomials
Factorising polynomials by grouping
Solving polynomials with the unknown "b" from x^2 + bx + c
Solving polynomials with the unknown "c" from x^2 + bx + c
Factorising polynomials: x^2 + bx + c
Applications of polynomials: x^2 + bx + c
Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + cax2+bx+c
Factorising polynomials: ax2+bx+cax^2 + bx + cax2+bx+c
Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
Evaluating polynomials
Using algebra tiles to factorise polynomials
Solving polynomial equations
Word problems of polynomials
video
Quadratic Functions
Characteristics of quadratic functions
Transformations of quadratic functions
Quadratic function in general form: y = ax^2 + bx + c
Quadratic function in vertex form: y = a(x-p)^2 + q
Completing the square
Converting from general to vertex form by completing the square
Shortcut: Vertex formula
Graphing parabolas for given quadratic functions
Finding the quadratic functions for given parabolas
Applications of quadratic functions
video
Quadratic Equations and Inequalities
Solving quadratic equations by factoring
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
Nature of roots of quadratic equations: The discriminant
Applications of quadratic equations
Solving quadratic inequalities
video
Polynomial Functions
What is a polynomial function?
Polynomial long division
Polynomial synthetic division
Remainder theorem
Factor theorem
Rational zero theorem
Characteristics of polynomial graphs
Multiplicities of polynomials
Imaginary zeros of polynomials
Determining the equation of a polynomial function
Applications of polynomial functions
Solving polynomial inequalities
Solving polynomial equations by iteration
Fundamental theorem of algebra
Descartes' rule of signs
video
Surds
Operations with surds
Conversion between entire radicals and mixed surds
Adding and subtracting surds
Multiplying surds
Solving surd equations
video
Laws of indices
Product rule of exponents
Quotient rule of exponents
Power of a product rule
Power of a quotient rule
Power of a power rule
Negative exponent rule
Combining the exponent rules
Standard form
Convert between radicals and rational exponents
Solving for exponents
video
Algebraic Fractions
Simplifying algebraic fractions and restrictions
Adding and subtracting algebraic fractions
Multiplying algebraic fractions
Dividing algebraic fractions
Solving equations with algebraic fractions
Applications of equations with algebraic fractions
Simplifying complex fractions
Partial fraction decomposition
video
Functions
Function notation
Operations with functions
Adding functions
Subtracting functions
Multiplying functions
Dividing functions
Composite functions
Inequalities of combined functions
Inverse functions
One to one functions
Difference quotient: applications of functions
video
Transformations of Functions
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
Combining transformations of functions
Even and odd functions
video
Reciprocal functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
video
Exponential Functions
Exponents: Product rule (a^x)(a^y) = a^(x+y)
Exponents: Division rule (a^x / a^y) = a^(x-y)
Exponents: Power rule (a^x)^y = a^(x * y)
Exponents: Negative exponents
Exponents: Zero exponent: a^0 = 1
Exponents: Rational exponents
Solving exponential equations using exponent rules
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
video
Logarithmic Functions
What is a logarithm?
Converting from logarithmic form to exponential form
Evaluating logarithms without a calculator
Common logarithms
Natural log: ln
Evaluating logarithms using change-of-base formula
Converting from exponential form to logarithmic form
Solving exponential equations with logarithms
Product rule of logarithms
Quotient rule of logarithms
Combining product rule and quotient rule in logarithms
Evaluating logarithms using logarithm rules
Solving logarithmic equations
Graphing logarithmic functions
Finding a logarithmic function given its graph
video
Applications of Exponential and Logarithmic Functions
Exponential growth and decay by a factor
Exponential decay: Half-life
Exponential growth and decay by percentage
Finance: Compound interest
Continuous growth and decay
Logarithmic scale: Richter scale (earthquake)
Logarithmic scale: pH scale
Logarithmic scale: dB scale
Finance: Future value and present value
video
Circles and Parabolas
Angles in a circle
Chord properties
Tangent properties
Circles and circumference
Arcs of a circle
Areas and sectors of circles
Inscribed quadrilaterlas in circles
Central and inscribed angles in circles
Circles in coordinate plane
Parabola
video
Introduction to Trigonometry
Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h}ho​ )
Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h}ha​ )
Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a}ao​ )
Combination of SohCahToa questions
Solving expressions using 45-45-90 special right triangles
Solving expressions using 30-60-90 special right triangles
Word problems relating ladder in trigonometry
Word problems relating guy wire in trigonometry
Other word problems relating angles in trigonometry
video
Trigonometry
Angle in standard position
Coterminal angles
Reference angle
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
Unit circle
Converting between degrees and radians
Trigonometric ratios of angles in radians
Radian measure and arc length
video
Sine Rule and Cosine Rule
Sine rule
Cosine rule
Applications of the sine rule and cosine rule
video
Bearings
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
video
Graphing Trigonometric Functions
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
video
Trigonometric Identities
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Cofunction identities
Double-angle identities
video
Sequences and Series
Arithmetic sequences
Arithmetic series
Geometric sequences
Geometric series
Infinite geometric series
Sigma notation
Arithmetic mean vs. Geometric mean
video
Set Theory
Set notation
Set builder notation
Intersection and union of 2 sets
Intersection and union of 3 sets
video
Probability
Determining probabilities using tree diagrams and tables
Probability of independent events
Finding probabilities using two-way frequency tables
Probability with Venn diagrams
video
Permutations and Combinations
Fundamental counting principle
Factorial notation
Path counting problems
Permutation vs. Combination
Permutations
Combinations
Problems involving both permutations and combinations
Pascal's triangle
Binomial theorem
video
Statistics
Median and mode
Mean
Range and outliers
Application of averages
Influencing factors in data collection
Data collection
video
Data and Graphs
Reading and drawing bar graphs
Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Stem-and-leaf plots
Reading and drawing Venn diagrams
video
Parametric Equations and Polar Coordinates
Defining curves with parametric equations
Polar coordinates
video
Limits
Finding limits from graphs
Continuity
Finding limits algebraically - direct substitution
Finding limits algebraically - when direct substitution is not possible
Infinite limits - vertical asymptotes
Limits at infinity - horizontal asymptotes
Intermediate value theorem
Squeeze theorem
video
Differentiation
Definition of derivative
Power rule
Slope and equation of tangent line
Chain rule
Derivative of trigonometric functions
Derivative of exponential functions
Product rule
Quotient rule
Implicit differentiation
Derivative of inverse trigonometric functions
Derivative of logarithmic functions
Higher order derivatives
Critical number & maximum and minimum values
video
Integration
Antiderivatives
Riemann sum
Definite integral
Fundamental theorem of calculus
video
Integration Applications
Areas between curves
Volumes of solids with known cross-sections
Volumes of solids of revolution - Disc method
Volumes of solids of revolution - Shell method
Average value of a function
Arc length

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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).

Statistics

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

Mechanics

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

Decision

  • Algorithms
  • Algorithms on graphs
  • Route inspection
  • Critical path analysis
  • Linear programming
  • Matchings
  • Flows in a network

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