# Higher

UNIT 1

Straight Line

1-The Distance Formula

2-Midpoint of a Line

4-Collinearity

5-Special Forms of Line

6- Y=Mx+c

7- Ax + By +C = 0

8- Intersection Of Straight Lines

9- Concurrence

10- Perpendicular Lines

11- Y-b=m(x-a)

12- Triangles- Special Lines

Functions & Graphs

1-Set Notation

2-Functions & Mappings

3-Composition of functions

4-Inverse of a function

5-Graphs of the inverse

6- Exponential Functions

7- Logarithmic functions

8- Graph of F(x)+a

9- Graph of F(x+a)

10- Graph of- F(x)

11- Graph of F(-x)

12- Graph of K F(x)

13- Graph of F(Kx)

14- Summary of graph transformations

Differentiation

1-Intro to differentiation

2-The Derived Function

3- F(x) = ax^n

4- Complex Expressions

5- Leibniz Notation

6- Equation of the Tangent

7- Increasing and Decreasing Functions

8- Stationary Points

9- Curve Sketching

10- Closed Intervals

11- Graph of the Derived Function

12- Optimization

Recurrence Relations

1-The General Term of a Sequence

2-Recurrence Relations

3-Linear Recurrence Relations

4-Limit of a Recurrence Relation

5-Finding m and c

Triganometry

1-Amplitude and Period

3-Exact Values

4-Trig Equations

5-Trig Equations with compound angles

UNIT 2

Polynomials

1-Vocabulary of polynomials

2-Division by (x-a)

3-The Factor Theorem

4-Finding missing co-efficient

5-Solving Polynomial Equations

6-Polynomials and their graphs

7-Approximating Roots

3-Completing the square

3-Completing the square (Alternative)

6-Discriminant and nature of roots

7-Discriminant and finding missing coefficients

8-Discriminant and tangency

Higher – Unit 2- Factorisation

Integration

1 -Anti-differentiation1

2 -Rules of integration

3 -Definite Integrals

4 -Area under the curve

5 -Area above & below x-axis

6 -Area between two graphs

7 -Differential Equations

Integration – Area Under A Curve

Further Trigonometry

2 -Applications of the Addition Formulae

3 -Double Angle Formulae

4 -Equations

5 -Graphs & Equations

6 -Trig Identities

The Circle

1 -Circle (Centre Origin)

2 -Circle (Centre (a,b))

3 -General Equation of a circle

4 -Intersection of lines and circles

5 -Tangents to Circles

3-D TRig

3D-TRIG

UNIT 3

Vectors

2-Subtraction of vectors

3-Scalar Multiplication

4-Position vectors

5-Collinearity

6-Section Formula

7- Three Dimensions

8- Vector Problems

9- Scalar Product

10- Scalar Product (Component form)

11- Angle Between Vectors

12- Perpendicular Vectors

13- Properties of the scalar product

14- Applications of scalar product

Further Calculus

1-Differentiation of sin and cos

2-Integration of sin and cos

3-Derivative of (ax+b)^n

4-Integrating (ax+b)^n

5 -Integrating Sin(ax+b) etc

Logs and Expodentials

1-Exponential growth and decay

2-Logs

3-Laws of Logs

4-Solving log equations

5-Natural logs

6-Experimental Data

7-More Complex Log Graphs

Wave Function

1-Kcos(x-a)

2-Further expansions

3-Maximum & Minimum Values

4-Solving equations

5-Sketching the graph

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