Course overview

National 4 Applications of Mathematics is built around real-life numeracy, finance, statistics, geometry, measurement and problem solving.

QS National 4 Applications of Mathematics

Official QS course information.

QS course page

Nat 4 Apps Checklist

Quick checklist of key skills and topics.

Download checklist (PDF)

Progression & related courses

Links to BGE, National 4 Maths and National 5 Applications.

BGE: S1, S2, S3 National 4 Maths National 5 Applications

Managing Finance & Statistics (F&S)

Interpreting financial and statistical situations, choosing appropriate strategies, carrying out calculations, and explaining or interpreting solutions in context.

Finance

Determining financial positions, investigating income, comparing deals, currency conversion, and the impact of interest rates for savings and borrowing.

Banking & Finance

General banking and finance links.

Banking and Finance Links

Rule of 3

Unitary method and proportional reasoning.

By the rule of 3

Profit & Loss

Basic profit and loss calculations.

Profit and Loss Percentage profit and loss

Back Percentage

Finding original values before a percentage change.

Back Percentage

VAT, Appreciation & Depreciation

Percentage changes in financial contexts.

VAT Appreciation Depreciation

Payslips & Income

Understanding payslips, net pay, overtime and deductions.

Payslips Net Pay Overtime Superannuation Income tax National Insurance

Bills, Loans & Credit

Utility bills, loans and hire purchase.

Utility Bills Loans Hire Purchase

Foreign Exchange & Conversions

Currency and unitary conversions.

Foreign Exchange Unitary Conversions

Insurance & Interest

Insurance, simple interest and compound interest.

Insurance Simple Interest Compound Interest

Statistics

Using statistics to investigate risk, working with diagrams, comparing data sets, and constructing tables and scattergraphs.

Averages & Range

Mean, median, mode and range.

Mean Median Mode Range

Statistical Diagrams

Bar charts, line graphs and pie charts.

Bar Charts Line Graphs Pie Charts

Frequency Tables

Ungrouped and grouped frequency tables.

Frequency tables Grouped frequency tables

Stem and Leaf

Organising data using stem and leaf diagrams.

Stem and leaf diagram

Scattergraphs & Line of Best Fit

Scatter diagrams and best fitting straight lines.

Scatter diagrams Line of best fit

Probability

Basic probability and risk.

Probability

Geometry & Measures (G&M)

Analysing situations involving measurement and geometry, choosing strategies, carrying out calculations and justifying solutions in context.

Geometry

Gradients, perimeter, area, volume, Pythagoras’ theorem and scale factor on shapes.

Straight Line & Gradients

Basic straight line work and gradients.

The straight line Gradients

Circles & Area

Radius, diameter, circumference and area.

Radius, Diameter and Circumference Area

Perimeter & Basic Areas

Perimeter and areas of rectangles and triangles.

Perimeter Area of rectangles and triangles

Quadrilaterals

Areas of parallelogram, rhombus, kite and trapezium.

Area of a parallelogram Area of a rhombus Area of a kite Area of a trapezium

Composite Area & Surface Area

Composite shapes and surface area.

Area of composite shapes Surface area

Volume

Volumes of cubes, cuboids and prisms.

Volume of cubes and cuboids Volume of prism

Pythagoras’ Theorem

Right-angled triangles and hidden Pythagoras.

The theorem of Pythagoras Finding the hypotenuse Finding a short side Hidden Pythagoras

Enlargements & Similarity

Scale factor, similar shapes and scaled area/volume.

Enlargements & reductions Scale factor Similar shapes Similar triangles Scaled area and volume

Measures

Time management, scale drawings, navigation, container packing, tolerance and measurement accuracy.

Time Calculations

Time intervals and time calculations.

Calculating time intervals

Compass & Bearings

Compass points and bearings.

Compass points Bearings

Map Scales & Scale Drawings

Working with map scales and example scale drawings.

Map scales Example scale drawing

Container Packing

Container packing and decreasing first fit algorithm.

Container Packing Decreasing First Fit Algorithm

Rounding & Tolerance

Significant figures, standard form and tolerance.

Significant figures Scientific Notation (Standard Form) Tolerance

Unit Conversions

Length, mass and volume conversions, plus unitary method.

Length conversions Mass conversions Volume conversions Unitary conversions

Numeracy

Selecting and using numerical notation and units, carrying out calculations, reading measurements, interpreting results and making justified decisions based on data and probability.

Calculations and Rounding

Whole number operations, decimals, negative numbers, order of operations and rounding.

Whole Number Calculations

Adding, subtracting, multiplying and dividing.

Adding Subtracting Multiplying Dividing

Decimal Calculations

Multiplying and dividing decimals.

Multiply decimals Dividing decimals

Negative Numbers

Working with negative integers.

Adding and subtracting negative numbers Multiplying integers Dividing integers

Order of Operations

BODMAS and calculation order.

BODMAS

Rounding & Significant Figures

Rounding to decimal places and significant figures.

Rounding Rounding decimals Significant figures Scientific Notation (Standard Form) Tolerance

Fractions, Percentages, Ratio

Fractions of amounts, percentages, conversions between forms, rates and proportional reasoning.

Fractions of Amounts

Finding fractions of quantities.

Fractions of amounts

Basic Percentages

Core percentage skills.

Basic percentages

Conversions

Converting between fractions, decimals and percentages.

Converting between fractions, decimals and percentages

Using 1% and 10%

Building percentages from simple parts.

Using 1% and 10%

Percentage Change

Percentage increase and decrease, percentage of a total.

Percentage increase and decrease Percentage of a total VAT

Ratio & Proportion

Ratios, proportion and direct proportion.

Use a ratio Proportion Direct proportion The rule of 3

Distance, Speed and Time

Calculating distance, speed and time, and working with 12- and 24-hour time.

Time Units & Clocks

Time units, 12- and 24-hour clock, and time differences.

Time units 12 and 24 hour clock Calculating time differences

Distance, Speed & Time

Using the DST relationship in problems.

Distance, Speed & Time

Measurements, Perimeter, Area and Volume

Using measuring instruments, reading scales, converting units, and calculating perimeter, area and volume.

Using Measuring Instruments

BBC Skillswise resources for common measuring tools.

Using a ruler Using a thermometer Using scales Using a measuring jug

Unit Conversions

Length, mass and volume conversions, plus unitary method.

Length conversions Mass conversions Volume conversions Unitary conversions

Perimeter & Area

Perimeter and basic areas.

Perimeter Area of a rectangle Area of a right angled triangle

Composite Area & Volume

Composite areas and volumes of cubes and cuboids.

Composite area Volume of cubes and cuboids

Course Overview ( QS Outcomes)

Finance (MFS)

MFS 1.1 Determining a financial position, given budget information
MFS 1.2 Investigating factors affecting income
MFS 1.3 Determining the best deal, given two pieces of information
MFS 1.4 Cconverting between currencies
MFS 1.5 Investigating the impact of interest rates for savings and borrowing in a basic situation

Statistics (MFS)

MFS 2.1 Using statistics to investigate risk
MFS 2.2 Using and presenting statistical information in diagrams
MFS 2.3 Using diagrams to illustrate data
MFS 2.4 Comparing data sets, using mean and range
MFS 2.5 Constructing a frequency table
MFS 2.6 Constructing a scattergraph
MFS 2.7 Drawing a best fitting straight line on a scattergraph

Geometry (GM 2)

GM 2.1 Determining the gradient of a slope
GM 2.2 Investigating a situation involving perimeter
GM 2.3 Investigating a situation involving area
GM 2.4 Investigating a situation involving volume
GM 2.5 Solving a problem involving the use of Pythagoras’ theorem
GM 2.6 Using a scale factor on the dimensions of a shape

Measurement (GM 1)

GM 1.1 Solving a basic problem involving time management
GM 1.2 Calculating a quantity based on a related measurement
GM 1.3 Constructing a scale drawing with a given scale
GM 1.4 Planning a basic navigation course
GM 1.5 Carrying out container packing using a first-fit algorithm
GM 1.6 Investigating the need for tolerance in a measurement

Numeracy (N 1)

N 1.1 Selecting and using appropriate numerical notation and units
N 1.2 Selecting and carrying out calculations
N 1.3 Recording measurements using a straightforward scale on an instrument
N 1.4 Interpreting the measurements and the results of calculations to make decisions
N 1.5 Explaining decisions based on the results of measurements or calculations

Graphical Data & Probability (N 2)

N 2.1 Extracting and interpreting data from straightforward graphical forms
N 2.2 Making and explaining decisions based on the interpretation of data
N 2.3 Making andexplaining decisions based on probability

Useful Links

Maths.scot

Free Maths resources for Scottish Secondary students

Free Nat 4 Apps

national5maths.co.uk - Free N4 Applications of Maths

Books

A selection of resources available at Amazon

Amazon: National 4 Applications of Maths MM Amazon Store UK school subjects Maths Mutt Publications

As an Amazon Associate I earn from qualifying purchases.