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





Geometry



Arcs and Sectors


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



Similarity


Key subskills
Using similarity .


Vectors


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


Numeracy


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


© Alexander Forrest