National 5 Mathematics
Course Learning Outcomes
The course is based on :
Algebra , Geometry , Numeracy , Statistics and Trigonometry
An external SQA exam is sat at the end of the course, with calculator and non-calculator papers.
National 5 Maths Past Papers ScholarSQA National 5 Maths Check List
National 4 Maths National 5 Applications Higher Maths
Algebra
Algebraic Manipulation
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
Algebraic Fractions
Key subskills
Reducing an algebraic fraction to its simplest form.
Applying one of the four operations to algebraic fractions.
Quadratics
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
Recognise and determine the equation of a quadratic function from its graph.
Sketching a quadratic function.
Identifying features of a quadratic function.
Working with quadratic equations.
Quadratic formula.
Discriminant
Quadratic Equations
Simultaneous Equations
Key subskills
Working with simultaneous equations.
Straight Lines
Key subskills
Determining the equation of a straight line, given the gradient
Geometry
Arcs and Sectors
Key subskills
Calculating the length of arc or the area of a sector of a circle.
Pythagoras
Key subskills
Applying the Pythagoras’ theorem.
Applying the properties of shapes to determine an angle involving at least two steps.
Similarity
Key subskills
Using similarity .
Vectors
Key subskills
Working with 2D vectors.
Working with 3D coordinates.
Using vector components
.
Volume
Key subskills
Calculating the volume of a standard solid.
Numeracy
Fractions and Percentages
Key subskills
Working with percentages.
Working with fractions
Rounding
Key subskills
Round answers to the nearest significant figure or two decimal places .
Surds & Indices
Key subskills
Working with surds
Simplifying expressions using the laws of indices .
Statistics
Analysing Data
Key subskills
Comparing data sets using statistics.
Forming a linear model from a given set of data.
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
Course Overview and Learning Outcomes
Algebra
Learning Outcomes
- A1 Working with algebraic expressions involving expansion of brackets
- A2 Factorising an algebraic expression
- A3 Completing the square in a quadratic expression with unitary coefficient
- A4 Reducing an algebraic fraction to its simplest form
- A5 Applying the four operations to algebraic fractions
- A6 Determining the equation of a straight line
- A7 Working with linear equations and inequations
- A8 Working with simultaneous equations
- A9 Changing the subject of a formula
- A10 Recognise and determine the equation of a quadratic function from its graph
- A11 Sketching a quadratic function
- A12 Identify features of a quadratic function
- A13 Solving a quadratic equation
- A14 Solving a quadratic equation using the quadratic formula
- A15 Using the discriminant to determine the number of roots
Geometry
Learning Outcomes
- G1 Determining the gradient of a straight line, given two points
- G2 Circle Geometry
- G3 Calculating the volume of a standard solid
- G4 Applying Pythagoras' theorem
- G5 Applying the properties of shapes to determine an angle involving at least two steps
- G6 Using similarity
- G7 Working with two-dimensional vectors
- G8 Working with three-dimensional coordinates
- G9 Using vector components
- G10 Calculating the magnitude of a vector
Numeracy
Learning Outcomes
- N1 Working with surds
- N2 Simplifying expressions using the laws of indices
- N3 Rounding
- N4 Working with reverse percentages
- N5 Working with appreciation/depreciation
- N6 Working with fractions
Statistics
- S1 Comparing data sets using calculated/determined statistics
- S2 Forming a linear model from a given set of data
Trigonometry
Learning Outcomes
- T1 Working with the graphs of trigonometric functions
- T2 Working with trigonometric relationships in degrees
- T3 Calculate the area of a triangle using trigonometry
- T4 Using the sine and cosine rules to find a side or angle in a triangle
- T5 Using bearings with trigonometry
Books
A selection of resources available at Amazon
© Alexander Forrest