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AS-Level Maths Topics

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video
Set Theory
Set notation
Set builder notation
Intersection and union of 2 sets
Intersection and union of 3 sets
video
Number System
Understanding the number systems
Prime factorization
Greatest Common Factors (GCF)
Least Common Multiple (LCM)
Rational vs. Irrational numbers
Converting repeating decimals to fractions
video
Surds
Square and square roots
Cubic and cube roots
Evaluating and simplifying radicals
Converting radicals to mixed radicals
Converting radicals to entire radicals
Adding and subtracting radicals
Multiplying and dividing radicals
Rationalize the denominator
video
Laws of Indices
Indices: Product rule (a^x)(a^y) = a^(x+y)
Indices: Division rule (a^x / a^y) = a^(x-y)
Indices: Power rule (a^x)^y = a^(x * y)
Indices: Negative indices
Zero index: a^0 = 1
Rational indices
Combining laws of indices
Solving for indices
Standard form
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 slope-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
Quadratic Functions
Introduction to 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 quadratic functions: General form VS. Vertex form
Finding the quadratic functions for given parabolas
Applications of quadratic functions
video
Quadratic Equations
Solving quadratic equations by factorising
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
The discriminant: Nature of roots of quadratic equations
Applications of quadratic equations
video
Simultaneous Equations
Simultaneous linear equations
Simultaneous linear-quadratic equations
Simultaneous quadratic-quadratic equations
video
Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Solving quadratic inequalities
video
Factorisation
Factorise by taking out the greatest common factor
Factorise by grouping
Factorise difference of squares: x^2 - y^2
Factorise trinomials
Factorise difference of cubes
Factorise sum of cubes
video
Operations with Algebraic Fractions
Simplifying algebraic fractions and restrictions
Adding and subtracting algebraic fractions
Multiplying algebraic fractions
Dividing algebraic fractions
Solving algebraic fraction equations
Applications of algebraic fraction equations
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
video
Algebraic Division
Polynomial long division
Polynomial synthetic division
Remainder theorem
Factor theorem
video
Reciprocal Functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
video
Rational Functions
What is a rational function?
Point of discontinuity
Vertical asymptote
Horizontal asymptote
Slant asymptote
Graphs of rational functions
Solving rational inequalities
video
Circle Theorems
Angles in a circle
Chord properties
Tangent properties
Circle and circumference
Arcs of a circle
Areas and sectors of circles
Inscribed quadrilaterlas in circles
Central and inscribed angles in circles
video
Binomial Expansion
Factorial notation
Pascal's triangle
Binomial theorem
video
Trigonometry
Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h}ho​ )
Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h}ha​ )
Use tangent ratio to calculate angles and sides (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
Trigonometric Ratios and Angle Measure
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
Sine rule and cosine rule word problems
video
Trigonometric Identities and Equations
Pythagorean identities
Solving first degree trigonometric equations
Solving second degree trigonometric equations
video
Graphing Trigonometric Functions
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Graphing transformations of trigonometric functions
video
Exponentials Functions
Solving exponential equations using laws of indices
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
video
Logarithms
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
video
Growth and Decay
Exponential growth and decay by a factor
Exponential growth and decay by percentage
Finance: Compound interest
Finance: Future value and present value
video
Differentiation
Definition of derivative
Power rule
Gradient and equation of tangent line
Higher order derivatives
Critical number & maximum and minimum values
video
Integration
Antiderivatives
Definite integral
Fundamental theorem of calculus
Indefinite integral
video
Vectors
Introduction to vectors
Magnitude of a vector
Direction angle of a vector
Scalar multiplication
Equivalent vectors
Adding and subtracting vectors in component form
Operations on vectors in magnitude and direction form
Unit vector
Word problems on vectors
video
Statistics
Sampling methods
Median and mode
Mean
Range and outliers
Application of averages
Standard deviation and variance
Quartiles, Percentile, and Outliers
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
Frequency distribution and histograms
video
Correlation and Regression
Bivariate, scatter plots, and correlation
Regression analysis
Equation of the best fit line
video
Probability
Determining probabilities using tree diagrams and tables
Probability of independent and combined events
Probability with Venn diagrams
Addition rule for "OR"
Binomial distribution
video
Hypothesis Testing
Null hypothesis and alternative hypothesis
Proving claims
Confidence levels, significance levels, and critical values
Test statistics
Traditional hypothesis testing
P-value hypothesis testing
Type 1 and type 2 errors
video
Scalars, Vectors, and Motion
Scalars, vectors, and one dimensional motion
Vector operations in one dimension
Vector operations in two dimensions
video
Kinematics
Kinematics in a straight line
Position velocity acceleration: Derivative
video
Forces
Newton's first law of motion
Newton's second law of motion
Multiple forces acting on an object
Newton's third law of motion
Friction: Static and kinetic
video
Momentum
Momentum and motion
Momentum and impulse
Conservation of momentum in one dimension

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Is AS level Maths Hard?

As the name suggests, advanced subsidiary (AS) level maths, expands beyond the basic concepts of maths and into more complex or "advanced" areas of mathematics. If the thought of this seems a little daunting to you, you're not alone. There are many students across the UK that are put off by the complex sounding maths problems and terms like simultaneous equations, algebraic expressions, and more.

From the outside looking in, AS level maths can seem like a hard course of study, but if you have a firm grasp of the basics and you paid attention in secondary school maths, you should be well equipped to tackle even the trickiest of problems within this course.

Even if you struggled in year 10 or year 11 maths, you could still earn a good grade within AS level maths. All it would take is some organization, studying and an effective revision tool like StudyPug.

Our platform has a vast collection of video tutorials and revision guides for each topic of AS level maths. Our content will walk you through all the relevant topics that are bound to come up during your course of study, providing AS level maths step-by-step with videos on the following:

  • Simultaneous Equations
  • Differentiation
  • Circle Theorems
  • Operations with Surds
  • Law of Indices
  • Binomial Expansion
  • And more.

If you want to familiarize yourself with the topics you studied in secondary school before you take on an A level course, we have an extensive collection of materials for revision in trigonometry, statistics, integration vectors, and all other topic studied across the GCSE curriculum.

Our AS level Maths tutoring service will show you easy to understand solutions to even the hardest AS level maths questions. Furthermore, the information that we deliver, reflects everything you'd expect to find in modern maths textbooks and covers the content most likely to appear on your AQA, Edexcel, MEI, WJEC or OCR maths exams.

We understand that each student will have their own unique learning style and not every student will come to us at the same skill level. That's why we offer an "AS level maths for dummies" approach that starts with the basics and assumes no prior knowledge. The beauty of our on-demand video service is in is flexibility. You don't need to sit through lessons you already know. You can skip them entirely or simply fast-forward to the section you need.

If you join StudyPug today as a subscriber, you'll have direct access to all of our GCSE and AS level maths help, giving you unprecedented access to a wealth of quality videos and resources that can supplement your studies and help you find your way to the right maths solutions.

What is AS level Maths Like?

A level maths is separated into two variants. An AS Level maths course is one year long, whereas the A level Maths course, is a 2 year program with the AS acting as its first year.

Within the structure of the course, students are given a choice as to what modules they study. The modules are as follows:

  • C1-4 - Core Maths
  • S1 & S2 - Statistics
  • M1 & M2 - Mechanics
  • D1 & D2 - Decisions

Regardless of whether you're studying AS or A level maths, you will be required to study the C1-4 modules. AS students then pick one further module to study (statistics, mechanics, or decisions) and A level students, will pick two.

As an example, nrich.maths.org has drafted what a typical AS student studying statistics might encounter on their course (see below).

  1. Laws of indices
  2. Integration and differentiation of xn
  3. Integration gives areas under curves
  4. Laws of logarithms (log(ab)=log(a)+log(b) etc)
  5. Solution of quadratic equations
  6. Linear and quadratic graphs
  7. Simple use of sin, cos and tan functions and graphs, including
    1. cos2(x)+sin2(x)=1
    2. Radians
    3. Sin rule
  8. Expanding brackets and geometric series.
  9. Basic ideas of statistics: Mean, standard deviation, variance, outliers
  10. Various methods of plotting data and linear regression.
  11. The shape of the normal distribution and use of tables

How to Get an A in AS Level Maths?

To stand a chance of getting an A grade in your AS level exams, you'll need to be prepared to get yourself into a good study routine, which should include homework, worksheets, and AS level maths past papers. Using these past papers to sit mock exams, you will be better prepared for you actual tests, and it could help with your confidence and time management. Work within the time limits for each paper and review your performance to single out any areas of weakness.

If you get a few questions wrong within a specific topic, revisit the whole topic on StudyPug and review your class notes. Our content is broken down into individual topics, so you'll be able to find the videos that are relevant to you with ease. Watch the videos, resit mock papers, and chart your progress. Eventually, you'll see an improvement in your scores, and by addressing your weaker areas, you'll be better prepared for whatever arises in your end of year exam.

When the examiners are marking papers, they're not just looking for the right answers. Examiners are looking to see if you arrived at the solution through an understanding of the problem or via simple memorization. This is why its key to always show you working out! Even if its a simple question don't just answer it and move on, show how you arrived at the solution. There's always the potential to receive extra marks for showing your thought process, and that could mean the difference between a B and an A grade.

How to Revise for AS level Maths

When it comes to maths revision, as mentioned above, you should highlight your areas of weakness so that you know what to focus on. Once you know the topics of AS level maths you need to work on, you can visit StudyPug to find video tutorials that cover each topic with handy step-by-step examples.

You, much like many of students, may find that revising via our video format is a lot more engaging and easier to follow than the traditional textbook revision methods. To help get you started, we're offering a collection of free AS Level Maths lessons across the following subject areas:

  • Understanding the Number Systems
  • Least Common Multiple (LCM)
  • Converting Radicals to Entire Radicals
  • Slope Intercept Form: y = mx + b
  • Graphing Linear Functions Using x- and y- Intercepts
  • And Many More

Think of StudyPug as your own personal AS level maths tutor that's available 24/7.

What Calculators are Allowed in AS level Maths?

All examining boards will follow the regulations of the JCQ (Joint Council for Qualifications) with regards to calculators in exams.

The regulations are as follows:

Calculators must be:

  • Of a size suitable for use on the desk
  • Either battery or solar powered
  • Free of lids, cases and covers which have printed instructions or formulas

Calculators must not:

  • Be designed or adapted to offer any of these facilities:
    • translators
    • Symbolic algebra manipulation
    • Symbolic differentiation or integration
    • Communication with other machines or the internet
  • Be borrowed from another candidate during an examination for any reason
  • Have retrievable information stored in them - this includes:
    • Databanks
    • Dictionaries
    • Mathematical formulas
    • Text

Is it Worth Getting my AS Level Maths Paper Remarked?

If you don't receive the marks you were expecting, having your paper remarked could help. Firstly, you'll need to consult with your teacher and see if they also expected a higher score from your test paper (based on previous tests and in-class performance). Accessing the papers may be free for the school, but it can cost anywhere from £11 - £15, depending on the exam board.

There will also be an additional cost for the actual remarking and this will vary between exam boards and the nature of the remark (please see below).

AQAEdexcelOCRWJECDeadline
Access to Marked Paper£13.95Free£11.40£11.40Aug 24
Priority Remark£50.30£49.70£56.30£46Aug 24
Full Re-mark£42.25£41.70£45.60£36Sept 21
Clerical Re-check£16.10£11.20£16.40£10Sept 21
Pricing as of 2017

It's not a cheap process and in most cases, remarking will only add a few extra marks, it won't change a D grade to an A. With that in mind, check how far away you are from the next possible grade, if you're 2-3 marks away, it may be worth the cost of a remark, specially it its the difference between a failing and passing grade.

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