# National 5 Mathematics

This course is spread across three units :

Expressions and Formulae (E&F), Relationships (Rel) and Applications (Apps)

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

### Applications

Apps 1.1 Applying trigonometric skills to triangles which do not have a right angle.
Apps 1.2 Applying geometric skills to vectors.
Apps 1.3 Applying numerical skills to fractions and percentages.
Apps 1.4 Applying statistical skills to analysing data.

Apps 2.1: Interpreting a situation where mathematics can be used and identifying a strategy.
Apps 2.2: Explaining a solution and/or relating it to context.

### Expressions and Formulae

E&F 1.1 : Applying numerical skills to simplify surds/ expressions using the laws of indices.
E&F 1.2 : Applying algebraic skills to manipulate expressions.
E&F 1.3 : Applying algebraic skills to algebraic fractions.
E&F 1.4 :Applying geometric skills linked to the use of formulae.
E&F 2.1: Interpreting a situation where mathematics can be used and identifying a strategy.
E&F 2.2: Explaining a solution and/or relating it to context.

### Relationships

Rel 1.1 : Applying algebraic skills to linear equations.
Rel 1.2 : Applying algebraic skills to graphs of quadratic relationships.
Rel 1.3 : Applying algebraic skills to quadratic equations.
Rel 1.4 : Applying geometric skills to lengths, angles and similarity.
Rel 1.5 : Applying trigonometric skills to graphs and identities.
Rel 2.1: Interpreting a situation where mathematics can be used and identifying a strategy.
Rel 2.2: Explaining a solution and/or relating it to context.

## Algebra

Key subskills:
Working with algebraic expressions involving expansion of brackets.
Factorising an algebraic expression.
Completing the square in a quadratic expression with unitary x2 coefficient .

Completing the Square

Functions

E&F 1.2 Applying algebraic skills to manipulate expressions.

## Algebraic Fractions

Key subskills:
Reducing an algebraic fraction to its simplest form.
Applying one of the four operations to algebraic fractions .

E&F 1.3 Applying algebraic skills to algebraic fractions.

## Analysing Data

Key subskills:
Comparing data sets using statistics.
Forming a linear model from a given set of data.

Apps 1.4 Applying statistical skills to analysing data.

## Arcs and Sectors

Key subskills:
Calculating the length of arc or the area of a sector of a circle.

E&F 1.4 Applying geometric skills linked to the use of formulae

## Fractions and Percentages

Key subskills:
Working with percentages.
Working with fractions .

Apps 1.3    Applying numerical skills to fractions and percentages.    E&F 1.3 Applying algebraic skills to algebraic fractions.

## Pythagoras

Key subskills:
Applying the Pythagoras’ theorem.
Applying the properties of shapes to determine an angle involving at least two steps.

Rel 1.4 Applying geometric skills to lengths, angles and similarity.

Key subskills:
Recognise and determine the equation of a quadratic function from its graph.
Identifying features of a quadratic function.

Discriminant .
Roots .

Rel 1.2 Applying algebraic skills to graphs of quadratic relationships.
Rel 1.3 Applying algebraic skills to quadratic equations..
E&F 1.2 Applying algebraic skills to manipulate expressions.

## Similarity

Key subskills:
Using similarity .

Rel 1.4 Applying geometric skills to lengths, angles and similarity.

## Simultaneous Equations

Key subskills:
Working with simultaneous equations.

Rel 1.1 Applying algebraic skills to linear equations. E&F 1.4 Applying geometric skills linked to the use of formulae.

## Straight Lines

Key subskills:
Determining the equation of a straight line, given the gradient.

Rel 1.1 Applying algebraic skills to linear equations. E&F 1.4 Applying geometric skills linked to the use of formulae.

## Surds & Indices

Key subskills:
Working with surds
Simplifying expressions using the laws of indices

E&F 1.1 Applying numerical skills to simplify surds/ expressions using the laws of indices.

## Trigonometry

Key subskills:
Calculating the area of a triangle using trigonometry.
Using the sine and cosine rules to find a side or angle.
Using bearings with trigonometry.

Working with the graphs of trigonometric functions
Working with trigonometric relationships in degrees

Trigonometric Graphs and Equations

Apps 1.1 Applying trigonometric skills to triangles which do not have a right angle.
Rel 1.5: Applying trigonometric skills to graphs and identities.

## Vectors

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

Apps 1.2 Applying geometric skills to vectors

## Volume

Key subskills:
Calculating the volume of a standard solid.
Rounding to a given number of significant figures.

E&F 1.4 Applying geometric skills linked to the use of formulae

# 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.              