# Higher Mathematics

This course is spread across three units :

Expressions and Functions (E&F),Relationships and Calculus (R&C) and Applications (Apps)

An external SQA exam is sat at the end of the course.

### Applications

Apps 1.1 Applying algebraic skills to rectilinear shapes.
Apps 1.2 Applying algebraic skills to circles.
Apps 1.3 Applying algebraic skills to sequences.
Apps 1.4 Applying calculus skills to optimisation and area.

### Expressions and Functions

E&F 1.1 : Applying algebraic skills to logarithms and exponentials.
E&F 1.2 : Applying trigonometric skills to manipulating expressions.
E&F 1.3 :Applying algebraic and trigonometric skills to functions.
E&F 1.4 :Applying geometric skills to vectors.

### Relationships and Calculus

R&C 1.1 : Applying algebraic skills to solve equations.
R&C 1.2 : Applying trigonometric skills to solve equations.
R&C 1.3 : Applying calculus skills of differentiation.
R&C 1.4 : Applying calculus skills of integration.

Prerequisite Knowledge

You must have a good grasp of the following :

• Completing the Square.
• Changing the subject of the formula.
• Manipulating Algebraic fractions.
• Factorising.
• Manipulating Surds and Indices.
• Basic Trigonometry.

## Algebra

Key subskills:
Factorising a polynomial expression .
Solving polynomial equations.
Using the discriminant.
Find the co-ordinates of intersections of curves and straight lines.

Polynomials

Sequences

R&C 1.1 Applying algebraic skills to solve equations.
Apps 1.3Applying algebraic skills to sequences.
Unit 2 LO1Use the factor/remainder theorem and apply quadratic theory.

## Differentiation

Key subskills:
Differentiating functions.
Determining the equation of a tangent to a curve at a given point by differentiation.
Determining where a function is strictly increasing/decreasing.
Using nature tables.
Using differentiation to determine the optimal solution for a given problem.
Solve problems using rate of change.

R&C 1.3 Applying calculus skills of differentiation.
Apps 1.4 Applying calculus skills to optimisation and area.
Unit 1 LO3 Use basic differentiation .
Unit 3 LO2 Use further differentiation and integration .

## Exponentials and Logarithms

Key subskills:
Simplifying a numerical expression, using the laws of logarithms and exponents.
Solving logarithmic and exponential equations.
Using the laws of logarithms and exponents.

E&F 1.1 Applying algebraic skills to logarithms and exponentials.
E&F 1.3 Applying algebraic and trigonometric skills to functions.
Unit 3 LO3 Logarithmic and exponential functions.

## Functions and Graphs

Key subskills:
Identifying and sketching related functions.
Determining composite and inverse functions.

E&F 1.3 Applying algebraic and trigonometric skills to functions.
Unit 1 LO2 Associate functions and graphs and solve related equations.

## Integration

Key subskills:
Integrating functions.
Calculating definite integrals of polynomial functions.
Finding the are between a curve and the x axis.
Finding area under and between curves.

R&C 1.4 Applying calculus skills of integration.
Apps 1.4 Applying calculus skills to optimisation and area.
Unit 2 LO2 Use basic integration .
Unit 3 LO2 Use further differentiation and integration .

## The Circle

Key subskills:
Determining and using the equation of a circle.
Using properties of tangency.
Determining intersections.

Apps 1.2    Applying algebraic skills to circles.
Unit 2 LO4 Use the equation of the circle.

## The Straight Line

Key subskills:
Find the equation of parallel and perpendicular lines.
Using m = tan θ to calculate a gradient or angle.
Using properties of medians, altitudes and perpendicular bisectors.

Apps 1.1 Applying algebraic skills to rectilinear shapes.
Unit 1 - LO1 -Use the properties of the Straight Line

## Trigonometry

Key subskills:
Application of the addition or double angle formulae.
Application of trigonometric identities.
Converting acos x± bsin x to k cos(x ±α) or k sin(x ±α, k > 0

E&F 1.2 Applying trigonometric skills to manipulating expressions.
E&F 1.3 Applying algebraic and trigonometric skills to functions.
R&C 1.2 Applying trigonometric skills to solve equations.
Unit 1 LO2 Associate functions and graphs and solve related equations.
Unit 2 LO3 Apply trigonometric formulae.
Unit 3 LO4 Apply further trigonometric relationships .

## Vectors

Key subskills:
Working with 2D vectors.
Working with 3D coordinates.
Using vector components .

E&F 1.4 Applying geometric skills to vectors
Unit 3 LO1 Use vectors in three dimensions.

# Books

### Printed resources available at Amazon

Maths Mutt is provided by Beagle Bytes, which is a participant in the Amazon EU Associates Programme: an affiliate advertising programme designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.co.uk.               © Alexander Forrest