Maths

National 5 Applications of Mathematics

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

Numeracy Skills

The key areas covered are:

• Selecting and using appropriate numerical notation and units
• Selecting and carrying out calculations
• Recording measurements and the results of calculations to make decisions
• Justifying decisions by using the results of measurements and calculations

Financial Skills

The key areas covered are:

• Analysing a financial position using budget information
• Analysing and interpreting factors affecting income
• Determining the best deal
• Converting between several currencies
• Investigating the impact of interest rates on savings and borrowing

Statistical Skills

The key areas covered are:

• Using a combination of statistics to investigate risk and its impact on life
• Using a combination of statistical information presented in different diagrams
• Using statistics to analyse andcompare data sets
• Drawing a line of best fit from given data

Measurement Skills

The key areas covered are:

• Calculating a quantity
• Constructing a scale drawing, including choosing a scale
• Planning a navigation course
• Carrying out efficient container packing
• Using precedence tables to plan tasks
• Solving a problem involving time management
• Considering the effects of tolerance

Geometric Skills

The key areas covered are:

• Investigating a situation involving gradient
• Solving a problem involving a composite shape
• Solving a problem involving the volume of a composite solid
• Using Pythagoras’ theorem

Graphical Data and Probability Skills

The key areas covered are:

• Extracting and interpreting data from different graphical forms
• Making and justifying decisions using evidence from the interpretation of data
• Making and justifying decisionsbased on probability

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 x² 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 Pythagoras’ 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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