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National 5 Mathematics

Algebra, Geometry, Numeracy, Statistics and Trigonometry

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Course Overview

The National 5 Mathematics course covers Algebra, Geometry, Numeracy, Statistics and Trigonometry. Learners sit an external SQA exam with calculator and non‑calculator papers.

National 5 Past Papers Scholar QS National 5 Maths Checklist

Prerequisites

Before starting National 5, learners should be confident with:

Algebra

Removing Brackets

Removing brackets FOIL

Factorising

Factorising basics Difference of two squares

Equations & Inequalities

Solving equations Inequalities Changing the subject

Completing the Square

Overview General method Solving quadratics Why it's useful

Functions

Function notation Using functions

Algebraic Fractions

Algebraic fractions Fraction operations

Simultaneous Equations

Graphical method Elimination method Vedic method

Straight Line

Gradient formula Equations & graphs Plotting graphs Finding equations y − b = m(x − a) Function notation Using functions
Quadratics

Quadratic Graphs

Graph shapes y = ax² y = a(x − b)² y = a(x + b)² + c Axis of symmetry Turning point Roots Interactive – Quick Quadratic Graph

Sketching Quadratics

Factorising quadratics Sketching parabolas From completed squareQuadratic Factoriser Practice PDF

Quadratic Equations

Solving quadratics Quadratic formula Discriminant Formula derivation Tangency
Geometry

Arcs & Sectors

Arcs & sectors overview Arc lengths Sector areas Interactive – Arc Lengths Interactive – Sector Areas

Pythagoras

The theorem Hypotenuse Shorter side Converse Hidden Pythagoras Coordinates & Pythagoras

Similarity

Similar shapes Similar triangles Scaled area Scaled volume

Vectors

Scalar & vector quantities Components Magnitude Position vectors Unit vector Zero vector Equal vectors Adding vectors Subtracting vectors Interactive – Vector Magnitudes

Volume

Volume of a sphere Volume of a cone Volume of a cylinder Volume of a pyramid Surface area Composite area Composite volume
Numeracy

Fractions & Percentages

Reverse percentage Appreciation Depreciation Compound interest Fractions revision Adding/subtracting fractions Multiplying fractions Dividing fractions Alternative division method Fractions of amounts

Rounding

Rounding Rounding decimals Significant figures Scientific notation Tolerance

Surds & Indices

Indices Surds Surds test
Statistics

Analysing Data

5‑figure summary Box plot Interquartile range Standard deviation Line of best fit

Interactives

Interactive – Box Plots Interactive – Line of Best Fit Interactive – Standard Deviation
Trigonometry

Triangles & Bearings

Area of a triangle Sine Rule Cosine Rule Triangle Solver Which rule to use? Bearings with trigonometry

Trig Graphs & Equations

Trig graphs Amplitude & period Trig refresher Exact values Solving trig equations Trig identities Interactive – trig graphs Interactive – CAST diagram Interactive – y = A sin(x + φ) Interactive – y = a·sin/cos/tan(bx + c) + d Interactive – Trig Function Grapher
Course Overview & Learning Outcomes

Algebra

Learning Outcomes

Geometry

Learning Outcomes

Numeracy

Learning Outcomes

Statistics

Learning Outcomes

Trigonometry

Learning Outcomes

Useful Links
Maths.scot

Free Maths resources for Scottish Secondary students

Free Nat 5 Maths

national5maths.co.uk – free Nat 5 resources

Clelland Maths

An excellent app. National 5, Higher, Advanced Higher.

Books

A selection of resources available at Amazon

Leckie: National 4 to 5 Maths Bridging Skills Book Leckie: National 5 Maths Student Book TeeJay National 5 Mathematics

Useful Revision

Scottish Secondary Mathematics Red 3 Student Book Scottish Secondary Mathematics Red 4 Student Book Zeta Maths: National 5+ Mathematics

Maths Mutt at Amazon

Nat5/GCSE Mathematics Revision Questions With Worked Solutions Basic Algebra Quadratics Revision Factorising Quadratics
Pocket Revision: Basic Trigonometry Trig Graphs Sine and Cosine Rules, Area of a Triangle

Amazon: National 5 Maths MM Amazon Store UK School Subjects Maths Mutt Publications

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