AS-Level Maths made completely easy!

Get better marks with our comprehensive AS level Maths help ? whether it’s for Edexcel (Pearson), AQA, OCR or WJEC. Our AS Maths tutors got you all covered!

Keeping with the specifications of all the exam boards, our thorough help for the exam includes topics such as Trigonometry, Factorisation, Quadratic functions, Exponential functions, Logarithms, Calculus, Statistics, and a lot more. Learn the concepts with our online video tutorials that show you step-by-step solutions to even the hardest maths problems. Then, strengthen your understanding with tons of as maths practice.

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Common Questions
I’m interested in AQA AS Maths. Which school board do you follow?

We follow as level maths syllabus of All exam boards. J We cover all topics in AS level Maths exam. Therefore, not only AQA, students taking the exam with all other exam boards, including, Edexcel, OCR, and WJEC, will find all the help you need here too.

I’m taking Statistics 1 (S1) too. Can StudyPug help?

Most certainly! You will find the Statistics 1 (S1 or MS1A) topics also covered in our AS-level maths course. If you want to learn more about statistics, check out our Statistics course.

I want to start my as maths revision by revising some of the more basic maths first. Which course should I sign up for?

It doesn’t matter ? Your StudyPug subscription gives you unlimited access to all maths help across all courses. You can review all maths help in all courses, including GCSE maths, year 11 and year 12 maths. To make the best use of your precious study time, you can skip, review and learn any materials anytime based on your needs.

AS-Level Maths Topics

We have plenty of free lessons for you to watch

1.Surds

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

2.Factorisation

2.1Factorise by taking out the greatest common factor (free lessons)
2.2Factorise by grouping
2.3Factorising difference of squares: x2−y2x^2 - y^2
2.4Factorising trinomials
2.5Factoring difference of cubes
2.6Factoring sum of cubes

3.Linear Functions

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

4.Quadratic Functions

4.1Introduction to quadratic functions (free lessons)
4.2Transformations of quadratic functions
4.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
4.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
4.5Completing the square
4.6Converting from general to vertex form by completing the square
4.7Shortcut: Vertex formula (free lessons)
4.8Finding the quadratic functions for given parabolas (free lessons)
4.9Applications of quadratic functions

5.Quadratic Equations

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

6.Inequalities

6.1Express linear inequalities graphically and algebraically (free lessons)
6.2Solving one-step linear inequalities
6.3Solving multi-step linear inequalities
6.4Solving quadratic inequalities

7.Simultaneous Equations

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

8.Operations with Algebraic Fractions

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

9.Algebraic Division

9.1Polynomial long division (free lessons)
9.2Polynomial synthetic division
9.3Remainder theorem
9.4Factor theorem

10.Functions

10.1Function notation (free lessons)
10.2Operations with functions
10.3Adding functions
10.4Subtracting functions
10.5Multiplying functions
10.6Dividing functions

11.Transformations of Functions

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

12.Rational Functions

12.1What is a rational function? (free lessons)
12.2Point of discontinuity
12.3Vertical asymptote
12.4Horizontal asymptote
12.5Slant asymptote
12.6Graphs of rational functions
12.7Solving equations with algebraic fractions
12.8Solving rational inequalities

13.Circle Theorems

13.1Angles in a circle (free lessons)
13.2Chord properties
13.3Tangent properties
13.4Circles and circumference
13.5Arcs of a circle
13.6Areas and sectors of circles
13.7Inscribed quadrilaterals in circles
13.8Central and inscribed angles in circles
13.9Circles in coordinate plane

14.Trigonometry

14.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
14.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
14.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
14.4Combination of SohCahToa questions (free lessons)
14.5Solving expressions using 45-45-90 special right triangles (free lessons)
14.6Solving expressions using 30-60-90 special right triangles
14.7Word problems relating ladder in trigonometry
14.8Word problems relating guy wire in trigonometry
14.9Other word problems relating angles in trigonometry

15.Trigonometric Ratios and Angle Measure

15.1Unit circle (free lessons)
15.2Converting between degrees and radians
15.3Trigonometric ratios of angles in radians
15.4Radian measure and arc length

16.Sine Rule and Cosine Rule

16.1Sine rule
16.2Cosine rule
16.3Sine rule and cosine rule word problems

17.Trigonometric Identities and Equations

17.1Pythagorean identities
17.2Solving first degree trigonometric equations (free lessons)
17.3Solving second degree trigonometric equations

18.Graphing Trigonometric Functions

18.1Sine graph: y = sin x
18.2Cosine graph: y = cos x
18.3Tangent graph: y = tan x

19.Laws of Indices

19.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
19.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
19.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
19.4Indices: Negative exponents
19.5Indices: Zero exponent: a0=1 a^0 = 1
19.6Indices: Rational exponents

20.Exponentials Functions

20.1Solving exponential equations using laws of indices
20.2Graphing exponential functions
20.3Graphing transformations of exponential functions
20.4Finding an exponential function given its graph

21.Logarithms

21.1What is a logarithm?
21.2Converting from logarithmic form to exponential form (free lessons)
21.3Evaluating logarithms without a calculator
21.4Common logarithms
21.5Natural log: ln
21.6Evaluating logarithms using change-of-base formula
21.7Converting from exponential form to logarithmic form (free lessons)
21.8Solving exponential equations with logarithms
21.9Product rule of logarithms (free lessons)
21.10Quotient rule of logarithms
21.11Combining product rule and quotient rule in logarithms
21.12Evaluating logarithms using logarithm rules
21.13Solving logarithmic equations (free lessons)
21.14Graphing logarithmic functions
21.15Finding a logarithmic function given its graph

22.Sequences and Series

22.1Arithmetic sequences (free lessons)
22.2Arithmetic series (free lessons)
22.3Geometric sequences
22.4Geometric series
22.5Infinite geometric series
22.6Sigma notation
22.7Arithmetic mean vs. Geometric mean

23.Binomial Expansion

23.1Factorial notation
23.2Pascal's triangle
23.3Binomial theorem

24.Differentiation

24.1Power rule
24.2Gradient and equation of tangent line
24.3Higher order derivatives
24.4Critical number & maximum and minimum values
24.5Curve sketching

25.Integration

25.1Antiderivatives
25.2Definite integral

26.Statistics

26.1Median and mode
26.2Mean
26.3Range and outliers
26.4Application of averages
26.5Standard deviation & variance

27.Data and Graphs

27.1Reading and drawing histograms
27.2Reading and drawing line graphs
27.3Box-and-whisker plots and scatter plots
27.4Reading and drawing Venn diagrams
27.5Stem-and-leaf plots

28.Probability

28.1Addition rule for "OR"
28.2Multiplication rule for "AND"
28.3Conditional probability

29.Discrete Probabilities

29.1Histogram, mean, variance & standard deviation
29.2Binomial distribution
29.3Mean and standard deviation of binomial distribution

30.Normal Distribution and Confidence Intervals

30.1Introduction to normal distribution
30.2Normal distribution and continuous random variable
30.3Z-scores and random continuous variables
30.4Sampling distributions
30.5Central limit theorem
30.6Confidence levels and critical values

31.Correlation and Regression

31.1Bivariate, scatter plots and correlation
31.2Regression analysis
31.3Equation of the best fit line
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