Advanced Higher

Unit 1

Partial Fractions and Binomial Theorem  

Notes

1. Type 1 - distinct, linear factors

2. Type 2 - repeated factor

3. Type 3 - irreducible factor

4. Using algebraic long division

5. Binomial Theorem

6. Factorials and Binomial Coefficients

7. Pascals Triangle

8. Approximation

 

Skill Worksheets

Partial Fractions

Binomial Theorem

 

Video

2014 Question 2

2015 Question 1

 

Past Papers and Solutions

Partial Fractions | Solutions

Binomial Theorem | Solutions

 

Differentiation

Notes

1. Chain, Product and Quotient Rules

2. Differentiating Trig, Exponential and Log Functions

 

Skill Worksheets

Differentiation

 

Video

2014 Question 1(a)

2015 Question 2

2015 Question 6

 

Past Papers and Solutions

Differentiation | Solutions

 

Integration

Notes

1. Revision of Integrals from Higher

2. Exponential Functions

3. Logarithmic Functions

4. Partial Fractions

5. Trigonometric Functions

6. Substitution

7. Choosing a suitable integral

8. Definite integrals

9. Volume of Solid of Revolution

 

Skill Worksheets

Integration

 

Video

2014 Question 10

2014 Question 12

 

Past Papers and Solutions

Integration | Solutions

 

Functions and Graphs

Notes

1. Functions

2. The Modulus Function

3. Inverse Functions

4. Inverse Trig. Functions

5. Odd and Even Functions

6. Stationary Points and Points of Inflexion

7. Asymptotes

8. Curve Sketching

 

Skill Worksheets

Functions

Finding Asymptotes

 

Video

2014 Question 11

2015 Question 14

 

Past Papers and Solutions

Curve Sketching | Solutions

 

 

Matrices

Notes

1. Introduction to Matrices

2. Gaussian Elimination

3. Redundant, Inconsistent and Ill-Conditioned

4. The Determinant

5. The Inverse

6. The Identity Matrix

7. Matrix Transformations

 

Skill Worksheets

Matrices

 

Video

2014 Question 3

2015 Question 5

2015 Question 11

 

Past Papers and Solutions

Matrices | Solutions

 

 

Unit 2

Further Differentiation

Notes

1. All notes

 

Skill Worksheets

Further Differentiation

 

Video

2014 Question 4

2014 Question 6

2015 Question 4

2015 Question 8

 

Past Papers and Solutions

Further Differentiation | Solutions

 

Further Integration

Notes

1. Integration involving inverse trig functions

2. Integration techniques

3. Integration by Parts

 

Skill Worksheets

Further Integration

 

Video

2014 Question 15

2015 Question 10

2015 Question 17

 

Past Papers and Solutions

Further Integration | Solutions

 

First Order Differential Equations

Notes

1. Variable Separable method

2. Integrating Factor method

 

Skill Worksheets

First Order Differential Equations

 

Video

2015 Question 18

 

Past Papers and Solutions

First Order Differential Equations | Solutions

 

Complex Numbers

Notes

1. Introduction to Complex Numbers

2. Division and finding square roots

3. Argand Diagram and Polar Form

4. Multiplication and Division in Polar Form

5. De Moivre

6. Polynomial Equations

7. Finding nth Roots

8. Geometrical Interpretation

 

Skill Worksheets

Complex Numbers

 

Video

2014 Question 16

2015 Question 13

 

Past Papers and Solutions

Complex Numbers | Solutions

 

Sequences and Series

Notes

1. Arithmetic Sequences

2. Sigma Notation

3. Arithmetic Series

4. Geometric Sequences

5. Geometric Series

6. Infinite Geometric Series

 

Skill Worksheets

Sequences and Series

Summation

 

Video

2014 Question 14

2015 Question 3

 

Past Papers and Solutions

Sequences and Series | Solutions

 

 

Proofs

Notes

1. Direct Proof

2. Contradiction

3. Induction

4. Induction (summation)

 

Skill Worksheets

Proofs

 

Video

2014 Question 7

2015 Question 9

2015 Question 12

 

Past Papers and Solutions

Proofs | Solutions

 

 

Unit 3

Second Order Differential Equations

Notes

1. Homogeneous

2. Non-Homogeneous

 

Skill Worksheets

Second Order Differential Equations

 

Video

2014 Question 8

2015 Question 16

 

Past Papers and Solutions

Second Order Differential Equations | Solutions

 

Maclaurin's Theorem

Notes

1. All notes

 

Skill Worksheets

Maclaurin's Theorem

 

Video

2014 Question 9

 

Past Papers and Solutions

Maclaurin's Theorem | Solutions

 

 

Vectors

Notes

1. The Vector Product

2. The Scalar Triple Product

3. The Equation of a Line

4. The Intersection of Two Lines

5. The Angle between Two Lines

6. The Equation of a Plane

7. The Angle between a Line and a Plane

8. The Intersection of a Line and a Plane

9. The Angle between Two Planes

10. The Intersection of Two Planes

11. The Intersection of Three Planes

 

Skill Worksheets

Vectors

 

Video

2014 Question 5

2015 Question 15

 

Past Papers and Solutions

Vectors | Solutions

 

Euclidean Algorithm

Notes

1. Division Algorithm

2. Number Bases

 

Skill Worksheets

Euclidean Algorithm

 

Video

2015 Question 7

 

Past Papers and Solutions

Euclidean Algorithm | Solutions | Other