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AS-Level Maths (Legacy) Topics

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1. Surds

1.1 Square and square roots
1.2 Cubic and cube roots
1.3 Evaluating and simplifying radicals
1.4 Converting radicals to mixed radicals
1.5 Converting radicals to entire radicals
1.6 Adding and subtracting surds
1.7 Multiplying and dividing surds
1.8 Rationalize the denominator

2. Factorisation

2.1 Factorise by taking out the greatest common factor
2.2 Factorise by grouping
2.3 Factorising difference of squares: x^2 - y^2
2.4 Factorising trinomials
2.5 Factoring difference of cubes
2.6 Factoring sum of cubes

3. Linear Functions

3.1 Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
3.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
3.3 Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
3.4 Gradient intercept form: y = mx + b
3.5 General form: Ax + By + C = 0
3.6 Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
3.7 Rate of change
3.8 Graphing linear functions using table of values
3.9 Graphing linear functions using x- and y-intercepts
3.10 Graphing linear functions using various forms
3.11 Graphing linear functions using a single point and gradient
3.12 Word problems of graphing linear functions
3.13 Parallel and perpendicular lines in linear functions
3.14 Applications of linear relations

4. Quadratic Functions

4.1 Introduction to quadratic functions
4.2 Transformations of quadratic functions
4.3 Quadratic function in general form: y = ax^2 + bx + c
4.4 Quadratic function in vertex form: y = a(x-p)^2 + q
4.5 Completing the square
4.6 Converting from general to vertex form by completing the square
4.7 Shortcut: Vertex formula
4.8 Graphing quadratic functions: General form VS. Vertex form
4.9 Finding the quadratic functions for given parabolas
4.10 Applications of quadratic functions

5. Quadratic Equations

5.1 Solving quadratic equations by factorising
5.2 Solving quadratic equations by completing the square
5.3 Using quadratic formula to solve quadratic equations
5.4 The discriminant: Nature of roots of quadratic equations
5.5 Applications of quadratic equations

6. Inequalities

6.1 Express linear inequalities graphically and algebraically
6.2 Solving one-step linear inequalities
6.3 Solving multi-step linear inequalities
6.4 Compound inequalities
6.5 Solving quadratic inequalities

7. Simultaneous Equations

7.1 Simultaneous linear equations
7.2 Simultaneous linear-quadratic equations
7.3 Simultaneous quadratic-quadratic equations
7.4 Solving 3 variable simultaneous equations by substitution
7.5 Solving 3 variable simultaneous equations by elimination
7.6 Solving 3 variable simultaneous equations (no solution, infinite solutions)
7.7 Word problems relating 3 variable simultaneous equations

8. Operations with Algebraic Fractions

8.1 Simplifying algebraic fractions and restrictions
8.2 Adding and subtracting algebraic fractions
8.3 Multiplying algebraic fractions
8.4 Dividing algebraic fractions
8.5 Solving equations with algebraic fractions
8.6 Applications of equations with algebraic fractions
8.7 Simplifying complex fractions
8.8 Partial fraction decomposition

9. Algebraic Division

9.1 Polynomial long division
9.2 Polynomial synthetic division
9.3 Remainder theorem
9.4 Factor theorem

10. Functions

10.1 Function notation
10.2 Operations with functions
10.3 Adding functions
10.4 Subtracting functions
10.5 Multiplying functions
10.6 Dividing functions

11. Transformations of Functions

11.1 Transformations of functions: Horizontal translations
11.2 Transformations of functions: Vertical translations
11.3 Reflection across the y-axis: y = f(-x)
11.4 Reflection across the x-axis: y = -f(x)
11.5 Transformations of functions: Horizontal stretches
11.6 Transformations of functions: Vertical stretches

12. Reciprocal Functions

12.1 Graphing reciprocals of linear functions
12.2 Graphing reciprocals of quadratic functions

13. Rational Functions

13.1 What is a rational function?
13.2 Point of discontinuity
13.3 Vertical asymptote
13.4 Horizontal asymptote
13.5 Slant asymptote
13.6 Graphs of rational functions
13.7 Solving rational inequalities

14. Circle Theorems

14.1 Angles in a circle
14.2 Chord properties
14.3 Tangent properties
14.4 Circles and circumference
14.5 Arcs of a circle
14.6 Areas and sectors of circles
14.7 Inscribed quadrilaterals in circles
14.8 Central and inscribed angles in circles
14.9 Circles in coordinate plane

15. Trigonometry

15.1 Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
15.2 Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
15.3 Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
15.4 Combination of SohCahToa questions
15.5 Solving expressions using 45-45-90 special right triangles
15.6 Solving expressions using 30-60-90 special right triangles
15.7 Word problems relating ladder in trigonometry
15.8 Word problems relating guy wire in trigonometry
15.9 Other word problems relating angles in trigonometry

16. Trigonometric Ratios and Angle Measure

16.1 Unit circle
16.2 Converting between degrees and radians
16.3 Trigonometric ratios of angles in radians
16.4 Radian measure and arc length

17. Sine Rule and Cosine Rule

17.1 Sine rule
17.2 Cosine rule
17.3 Sine rule and cosine rule word problems

18. Bearings

18.1 Introduction to bearings
18.2 Bearings and direction word problems
18.3 Angle of elevation and depression

19. Trigonometric Identities and Equations

19.1 Pythagorean identities
19.2 Solving first degree trigonometric equations
19.3 Solving second degree trigonometric equations

20. Graphing Trigonometric Functions

20.1 Sine graph: y = sin x
20.2 Cosine graph: y = cos x
20.3 Tangent graph: y = tan x

21. Laws of Indices

21.1 Indices: Product rule (a^x)(a^y) = a^(x+y)
21.2 Indices: Division rule (a^x / a^y) = a^(x-y)
21.3 Indices: Power rule (a^x)^y = a^(x * y)
21.4 Negative indices
21.5 Zero index: a^0 = 1
21.6 Rational indices

22. Exponentials Functions

22.1 Solving exponential equations using laws of indices
22.2 Graphing exponential functions
22.3 Graphing transformations of exponential functions
22.4 Finding an exponential function given its graph

23. Logarithms

23.1 What is a logarithm?
23.2 Converting from logarithmic form to exponential form
23.3 Evaluating logarithms without a calculator
23.4 Common logarithms
23.5 Natural log: ln
23.6 Evaluating logarithms using change-of-base formula
23.7 Converting from exponential form to logarithmic form
23.8 Solving exponential equations with logarithms
23.9 Product rule of logarithms
23.10 Quotient rule of logarithms
23.11 Combining product rule and quotient rule in logarithms
23.12 Evaluating logarithms using logarithm rules
23.13 Solving logarithmic equations
23.14 Graphing logarithmic functions
23.15 Finding a logarithmic function given its graph

24. Sequences and Series

24.1 Arithmetic sequences
24.2 Arithmetic series
24.3 Geometric sequences
24.4 Geometric series
24.5 Infinite geometric series
24.6 Sigma notation
24.7 Arithmetic mean vs. Geometric mean

25. Binomial Expansion

25.1 Factorial notation
25.2 Pascal's triangle
25.3 Binomial theorem

26. Differentiation

26.1 Power rule
26.2 Gradient and equation of tangent line
26.3 Higher order derivatives
26.4 Critical number & maximum and minimum values
26.5 Curve sketching

27. Integration

27.1 Antiderivatives
27.2 Definite integral

28. Statistics

28.1 Median and mode
28.2 Mean
28.3 Range and outliers
28.4 Application of averages
28.5 Standard deviation & variance

29. Data and Graphs

29.1 Reading and drawing bar graphs
29.2 Reading and drawing histograms
29.3 Reading and drawing line graphs
29.4 Box-and-whisker plots and scatter plots
29.5 Reading and drawing Venn diagrams
29.6 Stem-and-leaf plots

30. Probability

30.1 Addition rule for "OR"
30.2 Multiplication rule for "AND"
30.3 Conditional probability

31. Discrete Probabilities

31.1 Histogram, mean, variance & standard deviation
31.2 Binomial distribution
31.3 Mean and standard deviation of binomial distribution

32. Normal Distribution and Confidence Intervals

32.1 Introduction to normal distribution
32.2 Normal distribution and continuous random variable
32.3 Z-scores and random continuous variables
32.4 Sampling distributions
32.5 Central limit theorem
32.6 Confidence levels and critical values

33. Correlation and Regression

33.1 Bivariate, scatter plots and correlation
33.2 Regression analysis
33.3 Equation of the best fit line

33 Chapters · 190 Topics · 1311 Videos

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).

AS-Level Maths (Legacy) FAQ

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Full access to step-by-step video lessons, diagnostic assessments, adaptive practice, Photo Search, and progress tracking for AS-Level Maths and all other courses.

How quickly will I improve in AS-Level Maths?

Most students see better understanding within the first week. With consistent practice, expect measurable improvement in exam scores within 2-4 weeks.

Does this cover my AS-Level Maths curriculum?

Yes — our AS-Level Maths content covers Core 1, Core 2, Statistics 1, Mechanics 1, and all major topics aligned to UK examination boards.

What AS-Level Maths modules are covered?

We cover all standard AS-Level modules including Core Pure Maths (C1, C2), Statistics (S1), and Mechanics (M1) with comprehensive video lessons and practice.

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