# ONLINE COURSES

**AS AND A-LEVEL MATHS REVISION ONLINE CLASSES**

SUMMER COURSES

Maths Revision summer courses are designed for the Cambridge exam specification. By giving students tips and tricks to save time and identifying common mistakes, I will provide students with the tools to perform at their very best during the exam season. Students are supported beyond the course as we provide handouts that include both course notes and relevant past-paper questions.

I will teach topics by going through past paper questions to consolidate learning and practice exam technique. This past paper practice will be used to give tips about how to get the most marks and the best approach to answering questions. Any weaknesses can be identified and worked on before moving on to the next topic. My courses cover the whole range of AS and A Level Maths which means they are a great way to kick start revision or can be used to identify and fill in any gaps in knowledge. You should leave the courses feeling confident and prepared for your exams.

#### AS- Level Online Summer Course Content

Day 1

Session 1: **Algebra & Functions**

– Linear equations

– Algebraic Manipulation

– Quadratic Functions

*Break*

Session 2: **Algebra & Functions**

– Graphs and Transformations

– Functions

– Simultaneous Equations

– Inequalities

*LUNCH*

Session 3: **Coordinates**

Day 2

Session 3: **Coordinates**

– The gradient of a line

– Straight Lines

*Break*

Session 3: **Coordinates**

– Finding the equation of a line

– The intersection of two lines

– The intersection of a line and a curve

– Circles

*LUNCH*

Session 4: **Sequences & Series**

– Arithmetic and Geometric Sequences

– Binomial Expansion

Day 3

Session 5: **Trigonometry**

– Definitions and Graphs

– Sine and Cosine Rules

– Identities and Proofs

– Solving Equations

*LUNCH*

Session 3: **Coordinates**

– Circular measure

– The length of an arc of a circle

– The area of a sector of a circle

Day 4

Session 6: **Differentiation**

– First Principles and Interpretation

– Methods of Differentiation

– Tangents and normal

– Maximum and minimum points

*LUNCH*

Session 6: **Differentiation**

– Increasing and decreasing functions

– Second Derivate

– Applications of Differentiation

– Chain Rule

Day 5

Session 7: **Integration**

– Finding the area under the curve

– Area between two curves

– Methods of Integration

– Definite Integrals

*LUNCH*

Session 8:

Past paper resolution and extra question practice on topics students request

#### Statistics Online Summer Course Contents

Day 1

Session 1

– Mean, Median and Quartiles

– Standard Deviation

– Statistical Diagrams

*Break*

Session 2

– Probability Trees

– Independent, Dependent, Mutually Exclusive Events

*LUNCH*

Session 3

– Discrete Probability Distributions

– Binomial Distribution; Normal Distribution

– Normal Approximation to the Binomial Distribution

Day 2

Session 4

– Extra question practice on topics students request

#### A-Level Online Summer Course Content

Day 1

Session 1: **Algebra & Functions**

– Modulus functions

– Solving modulus inequalities

– Division of polynomials

*Break*

Session 2: **Exponentials & Logarithms**

– Logarithms to base 10

– Logarithms to base a

– The laws of logarithms

*LUNCH*

Session 3: **Exponentials & Logarithms**

– Solving logarithmic equations

– Solving exponential equations

– Solving exponential inequalities

Day 2

Session 1: **Trigonometry**

– The cosecant, secant and cotangent ratios

– Compound angle formulae

– Further trigonometric identities

*Break*

Session 2: **Trigonometry**

– Expressing a sin(β)+bcos(β) in the form Rsin(β±α)

– Identities and Proofs

*Break*

Session 3: **Differentiation**

– Product and Quotient Rules

– Derivates of exponential functions

Session 4: **Differentiation**

– Derivates of natural logarithmic functions

– Derivates of trigonometric functions

Day 3

Session 1: **Differentiation**

– Implicit differentiation

– Parametric differentiation

*Break*

Session 2: **Further algebra**

– Improper algebraic fractions

– Partial fractions

– Binomial expansion of (1+x)n for values of n that are not positive integers

– Binomial expansion of (a+x)n for values of n that are not positive integers

– Partial fractions and binomial expansions

Day 4

Session 1: **Integration**

– Integration of exponential functions

– Integration of 1/ax+b

– Integration of sin(ax+b), cos(ax+b) and sec2(ax+b)

– Further integration of trigonometric functions

*Break*

Session 2: **Integration**

– Derivate of tan-1x

– Integration of 1/x2+a2

– Integration of k f’(x)/f(x)

*LUNCH*

Session 3: **Integration**

– Integration by Substitution and Parts

– The use of partial fractions in integrations

Day 5

Session 1: **Numerical Methods**

– Change of Sign Method

– Iterative Methods

*Break*

Session 2: **Differential equations**

– The technique of separating the variables

– Forming a differential equation from a problem

– Integration of k f’(x)/f(x)

*LUNCH*

Session 3: **Vectors**

– Displacement or translation vectors

– The scalar product

– The vector equation of a line

– Intersection of two lines

Day 6

Session 1: **Complex Numbers**

– Imaginary numbers

– Complex numbers

– The complex plane

– Solving equations

– LOCI

*LUNCH*

Session 2:

– Extra question practice on topics students request

– **Past papers**

### Summer Course Rates

Choose a single course or a combination of courses.