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## Maths

### National 5 Maths Tuition

The Physics Coach maths tuition classes include the following area of Mathematics:

#### Numerical Skills

The key areas covered are:

- Working with reverse percentages
- Working with appreciation / depreciation
- Working with fractions

#### Algebraic Skills

The key areas covered are:

- Working with algebraic expressions involving expansion brackets
- Factorising an algebraic expression
- Completing the square in a quadratic expression with unitary x
^{2 }coefficient - Reducing an algebraic fraction to its simplest form
- Applying the four operations to algebraic fractions
- Determining the equation of a straight line
- Working with linear equations and inequations
- Working with simultaneous equations
- Changing the subject of a formula
- Recognise and determine the equation of a quadratic function from its graph
- Sketching a quadratic function
- Identifying features of a quadratic function
- Solving a quadratic equation
- Solving a quadratic equation using the quadratic formula
- Using the discriminant to determine the number of roots

#### Geometric Skills

The key areas covered are:

- Determining the gradient of a straight line, given two points
- Circle geometry
- Calculating the volume of a standard solid
- Applying Pythagorasâ€™ theorem
- Applying the properties of shapes to determine an angle involving at least two steps
- Using similarity
- Working with two-dimensional vectors
- Working with three dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector

#### Trigonometric Skills

The key areas covered are:

- Working with the graphs of trigonometric functions
- Working with trigonometric relationships in degrees
- Calculating the area of a triangle using trigonometry
- Using the sine and cosine rules to find a side or angle in a triangle
- Using bearings with trigonometry

#### Statistical Skills

The key areas covered are:

- Comparing data sets using statistics
- Forming a linear model from a given set of data

#### Reasoning Skills

The key areas covered are:

- Interpreting a situation where mathematics can be used and identifying a strategy
- Explaining a solution and relating it to context

### Higher Maths

The course content includes the following areas of Mathematics:

#### Algebraic and Trigonometric Skills

The key areas covered are:

- Manipulating algebraic expressions
- Manipulating trigonometric expressions
- Identifying and sketching related functions
- Determining composite and inverse functions
- Solving algebraic equations
- Solving trigonometric equations

#### Geometric Skills

The key areas covered are:

- Determining vector connections
- Working with vectors

#### Calculus Skills

The key areas covered are:

- Differentiating functions
- Using differentiation to investigate the nature and properties of functions
- Integrating functions
- Using integration to calculate definite integrals
- Applying differential calculus
- Applying integral calculus

#### Algebraic and Geometric Skills

The key areas covered are:

- Applying algebraic skills to rectilinear shapes
- Applying algebraic skills to circles and graphs
- Modelling situations using sequences

#### Reasoning Skills

The key areas covered are:

- Interpreting a situation where mathematics can be used and identifying a strategy
- Explaining a solution and relating it to context

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