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
Equations and Functions
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
Reducing an algebraic fraction to its simplest form.
Applying one of the four operations to algebraic fractions.
Working with simultaneous equations.
Determining the equation of a straight line, given the gradient
Removing Brackets
Factorising
Equations & Inequalities
Completing the Square
Functions
Algebraic Fractions
Simultaneous Equations
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 Graphs
Sketching Quadratics
Quadratic Equations
Geometry
Key subskills
Calculating the length of arc or the area of a sector of a circle.
Applying the Pythagoras’ theorem.
Applying the properties of shapes to determine an angle involving at least two steps.
Using similarity .
Working with 2D vectors.
Working with 3D coordinates.
Using vector components
Calculating the volume of a standard solid.
Arcs & Sectors
Pythagoras
Similarity
Vectors
Numeracy
Key subskills
Working with percentages.
Working with fractions
Round answers to the nearest significant figure or two decimal places
Working with surds
Simplifying expressions using the laws of indices .
Fractions & Percentages
Surds & Indices
Statistics
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
Triangles and Bearings
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 (unitary coefficient)
- A4 Simplifying algebraic fractions
- A5 Four operations with algebraic fractions
- A6 Determining the equation of a straight line
- A7 Linear equations and inequations
- A8 Simultaneous equations
- A9 Changing the subject of a formula
- A10 Recognise quadratic from graph
- A11 Sketching a quadratic
- A12 Identify features of a quadratic
- A13 Solving quadratic equations
- A14 Quadratic formula
- A15 Using the discriminant
Geometry
Learning Outcomes
- G1 Gradient from two points
- G2 Circle geometry
- G3 Volume of standard solids
- G4 Pythagoras’ theorem
- G5 Multi‑step angle problems
- G6 Similarity
- G7 2D vectors
- G8 3D coordinates
- G9 Vector components
- G10 Magnitude of a vector
Numeracy
Learning Outcomes
- N1 Working with surds
- N2 Laws of indices
- N3 Rounding
- N4 Reverse percentages
- N5 Appreciation/depreciation
- N6 Working with fractions
Statistics
Learning Outcomes
- S1 Comparing data sets using statistics
- S2 Forming a linear model from data
Trigonometry
Learning Outcomes
- T1 Working with trig graphs
- T2 Trigonometric relationships in degrees
- T3 Area of a triangle using trig
- T4 Sine and cosine rules
- T5 Bearings with trigonometry
Books
A selection of resources available at Amazon
© Alexander Forrest