## This course launched in July 2021 and is now fully available - take advantage of a huge discount on the full price of the course before the price increases to its regular price later in the summer!

• Remove any lingering doubts by revising and mastering the hardest GCSE and IGCSE topics you need for A-level

• Start the year ahead of your classmates having learnt some A-level material already (suitable for all exam boards)

• 25 original worksheets designed to lead you through interesting and challenging problems, all with full video solutions

• 5 themes/topic areas each with 5 sections. Study 2 hours per day over 5 weeks or 5 hours per day as an intensive 2 week course

• Sign up now and take the first module free of charge before committing to the full course (no payment details needed).

# Course curriculum

## The course is in partial pre-order mode and the exact content of the final lessons may differ slightly from that presented here. First section available as a free preview!

• 1

• 2

### Week 1: A: Index laws, including negative and fractional indices (FREE PREVIEW)

• 3

• Factorising examples

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6 Hint

• Question 6

• Question 7 Hint

• Question 7

• Question 8 Hint

• Question 8

• 4

### Week 1: C: Intro to co-ordinate geometry

• Distance between two points

• Midpoint of two points

• Gradient of a line segment

• Parallel and perpendicular lines

• Worksheet C1: Intro to co-ordinate geometry

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6

• Question 7

• Question 8 Hint

• Question 8

• Question 9 Hint

• Question 9

• 5

• 6

### Week 1: E: Introduction to sequences

• Linear sequences

• Geometric sequences

• Intro to the worksheet

• Worksheet E1: Introduction to sequences

• Question 1abc

• Question 1 def

• Question 1 ghi

• Question 1 jkl

• Question 1 mno

• 7

### Week 2: A: Surds - Introduction and simple rationalising

• Simplifying surds

• Multiplying out surd expressions

• Rationalising simple surd expressions

• Worksheet A2: Surds - Introduction and simple rationalising

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6 hint

• Question 6

• Question 7 Hint

• Question 7

• Question 8 hint

• Question 8

• Question 9 hint

• Question 9

• 8

### Week 2: B: Completing the square and the graph of a quadratic

• Completing the square

• Solving equations using completed square form

• The graph of a quadratic

• Using the calculator

• Worksheet B2: Completing the square and the graph of a quadratic

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6 hint

• Question 6

• 9

### Week 2: C: Straight lines and their equations

• The equation of a straight line in the form y-y1=m(x-x1)

• Other forms of the equation of a straight line

• Finding a perpendicular line

• Worksheet C2: Straight lines and their equations

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5 Hint

• Question 5

• Question 6 Hint

• Question 6

• Question 7 Hint

• Question 7

• Question 8 Hint

• Question 8

• 10

### Week 2: D Solving trig equations for any angles

• Solving equations involving sin(x) for any angle

• Solving equations involving cos(x) for any angle

• Solving equations involving tan(x) for any angle

• Worksheet D2: Solving trig equations for any angles

• Question 1

• Question 2

• Question 3

• Question 4 hint

• Question 4

• Question 5 hint

• Question 5

• 11

### Week 2: E: Iterative sequences and sigma notation for summing series

• Formal notation for sequences

• Sigma notation for summing series

• Worksheet E2 - Iterative sequences and sigma notation for summing series

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5 Hint

• Question 5

• Question 6 Hint

• Question 6

• 12

### Week 3: A: Surds - Harder rationalising

• Difference of two squares for surds

• Harder rationalising of surds

• Worksheet A3 - Harder rationalising

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6

• Question 7 Hint

• Question 7

• Question 8 Hint

• Question 8

• 13

### Week 3: B: The discriminant of a quadratic

• The discriminant of a quadratic

• Repeated roots

• Worksheet B3 - The discriminant of a quadratic

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6

• Question 7

• Question 8 Hint

• Question 8

• Question 9 Hint

• Question 9

• 14

### Week 3: C: Differentiating polynomials

• Differentiating single term polynomials

• Differentiating general polynomials

• The second derivative

• Harder examples

• Worksheet C3 - Differentiating polynomials

• Question 1

• Question 2

• Question 3

• Question 4 Hint

• Question 4

• Question 5 Hint

• Question 5

• Question 6 Hint

• Question 6

• Question 7 Hint

• Question 7

• 15

### Week 3: D: Exact trigonometric ratios

• Exact values of sin cos and tan

• Exact values beyond 90 degrees

• Worksheet D3 - Exact trigonometric ratios

• Question 1

• Question 2

• Question 3

• Question 4 hint

• Question 4

• Question 5

• 16

### Week 3: E: Arithmetic progressions and their sums

• Arithmetic Progressions

• Sums of Arithmetic Progressions

• Worksheet E3 - Arithmetic progressions and their sums

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6

• Question 7

• Question 8 hint

• Question 8

• Question 9 hint

• Question 9

• 17

### Week 4: A: Introduction to logarithms

• Introduction to logarithms

• Logarithms as an inverse function

• Harder Examples

• Worksheet A4 - Introduction to logarithms

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6

• Question 7 hint

• Question 7

• Question 8 hint

• Question 8

• 18

### Week 4: B: Sketching the graphs of polynomials from their roots

• Avaialble soon

• Intro 1

• Intro 2

• Intro 3

• Worksheet B4 - Sketching the graphs of polynomials from their roots

• Question 1

• Question 2

• Question 3abcd

• Question 3efgh

• Question 4 hint

• Question 4

• Question 5 hint

• Question 5

• Question 6 hint

• Question 6

• 19

### Week 4: C: Finding tangents and normals

• Finding tangents

• Finding normals

• Worksheet C4 - Finding tangents and normals

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5 hint

• Question 5

• Question 6 hint

• Question 6

• 20

### Week 4: D: Solving harder trig equations

• Harder trig equations part 1

• Harder trig equations part 2

• Worksheet D4 - Solving harder trig equations

• Question 1

• Question 2

• Question 3 hint

• Question 3

• Question 4 hint

• Question 4

• Question 5 hint

• Question 5

• 21

### Week 4: E: Geometric progressions

• Geometric progressions

• GPs and APs compared

• Finding the number of terms using logs

• Worksheet E4 - Geometric progressions

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6

• Question 7

• Question 8 hint

• Question 8

• Question 9 hint

• Question 9

• 22

### Week 5: A: The rules of logarithms

• Intro 1 - The addition rule of logarithms

• Intro 2 - The subtraction rule of logarithms

• Intro 3 - The power rule for logarithms

• Worksheet E1 - The rules of logarithms

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6 hint

• Question 6

• Question 7 hint

• Question 7

• 23

### Week 5: B: Quadratic (and other) inequalities

• Polynomial inequalities

• Worksheet B5 - Quadratic (and other) inequalities

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5 hint

• Question 5

• Question 6 hint

• Question 6

• Question 7 hint

• Question 7

• 24

### Week 5: C: Differentiation with fractional and negative indices

• Differentiation with fractional and negative indices

• Finding a tangent involving fractional and negative indices

• Worksheet C5 - Differentiation with fractional and negative indices

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6 hint

• Question 6

• Question 7 hint

• Question 7

• 25

### Week 5: D: Using trig identities to solve equations

• tanx=sinx/cosx

• sin^2(x)+cos^2(x)=1

• Example using tanx=sinx/cosx

• Example using sin^2(x)+cos^2(x)=1

• Worksheet D5 - Using trig identities to solve equations

• Question 1

• Question 2

• Question 3 hint

• Question 3

• Question 4 hint

• Question 4

• 26

### Week 5: E: The sum of a geometric progression

• Finite sums of geometric progressions

• Infinite sums of geometric progressions

• Worksheet E5 - The sum of a geometric progression

• Question 1

• Question 2

• Question 3

• Question 4

• Question 5

• Question 6

• Question 7

• Question 8 hint

• Question 8

# FAQ

• Is this course suitable for a student who has already taken IGCSE Further Maths or OCR FSMQ Add Maths?

No - much of the content of this course is also covered in these qualifications. The course has been designed to give most benefit to a student who has just taken GCSE or IGCSE maths and is preparing for A-level or any course that follows directly on from GCSE. It would be a great course for someone about to take one of these qualifications though, so long as they have mostly covered GCSE/GCSE maths already.

• How long will my enrolment last?

Access to the course lasts for one year or two years depending on the option chosen.

• I have another question you have not answered here

Please use the e-mail link in my instructor bio below to get in touch.

# Teacher Kevin Olding

Kevin Olding is an experienced teacher and tutor, having worked for 7 years at two leading independent schools in London, and for over a decade as a private tutor. He holds a First Class MMATH Mathematics degree from Magdalen College, Oxford, an MSc in Applied Statistics from Birkbeck, University of London (Distinction and prize for best overall performace), MRes in Statistical Applied Mathematics (Distinction and soon PhD) from the University of Bath, as well as a degree in Law. He is also the creator of the Mathsaurus YouTube channel, which has tens of thousands of subscribers and millions of video views.