Vectors in 3-Dimensions | My Maths Guy

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National 5 Mathematics

Working with Numbers

Decimal Places (3:38)
Significant Figures (5:52)
Scientific Notation (6:19)
Rational & Irrational Numbers (5:43)
Adding and Subtracting Surds (7:59)
Multiplying and Dividing Surds (9:45)
Rationalising Fractions (8:23)
Rules of Indices (7:56)
How Surds and Indices Relate (11:00)
Quick Practice Questions
Full Practice Questions
Reference Notes

Algebraic Operations

Simplifying Algebraic Expressions (5:50)
Expanding Brackets (8:58)
Factorising Using a Common Factor (7:53)
Factorising as a Difference of Two Squares (8:53)
Factorising a Trinomial (11:30)
Completing the Square (7:27)
Simplifying Algebraic Fractions (10:52)
Multiplying and Dividing Algebraic Fractions (8:59)
Adding and Subtracting Algebraic Fractions (11:29)
Quick Practice Questions
Full Practice Questions
Reference Notes

Geometry & The Properties of Shapes

The Properties of Shapes (7:52)
Similar Figures (11:35)
Using Similar Figures to find Area and Volume (10:32)
Arc Length (11:30)
Sector Area (11:54)
Volume of Cuboids & Prisms (8:35)
Volume of Cones, Pyramids and Spheres (7:15)
Quick Practice Questions - Properties of Shapes
Quick Practice Questions - Arcs & Sectors
Quick Practice Questions - Volume
Quick Practice Questions - Similar Figures
Full Practice Questions
Reference Notes

Straight Line Graphs

Introduction to Straight-Line Graphs (5:14)
The Gradient of a Straight-Line Graph (14:55)
The Equation of a Straight Line (15:28)
Straight Lines not in Standard Form (9:45)
Horizontal and Vertical Lines (8:16)
X and Y Intercept of Straight Line Graphs (14:05)
Quick Practice Questions
Full Practice Questions
Reference Notes

Equations

Solving Linear Equations (13:29)
Solving Linear Equations with Brackets (10:09)
Solving Linear Equations with Fractions (11:44)
Solving Inequations (10:35)
Inequations – Multiplying or Dividing by a Negative (11:35)
Solving Simultaneous Equations by Eliminating a Variable (10:32)
Solving Simultaneous Equations by Eliminating a Variable – More Difficult (12:48)
Rearranging Formulas (13:35)
Quick Practice Questions - Equations & Inequations
Quick Practice Questions - Simultaneous Equations
Quick Practice Questions - Rearranging Formulas
Full Practice Questions
Reference Notes

Quadratic Functions & Quadratic Equations

Quadratic Expressions & Functions (6:10)
Quadratic Equations – Solving by Factorising (13:27)
Quadratic Equations – Solving by the Quadratic Formula (12:04)
Using the Discriminant to Determine the Number of Roots (10:28)
Graphs of Quadratic Functions (9:25)
The Roots of Quadratic Functions (11:22)
The Turning Point of the Graph of a Quadratic Function (11:34)
Finding the Y-Intercept of the Graph of a Quadratic Function (11:11)
The Axis of Symmetry of the Graph of a Quadratic Function (10:12)
Transforming the Graph of a Quadratic Function (15:08)
Quick Practice Questions - Quadratic Equations
Quick Practice Questions - Quadratics Graphs
Full Practice Questions
Reference Notes

Pythagoras' Theorem & Trigonometry

Pythagoras’ Theorem (9:32)
The Converse of Pythagoras’ Theorem (7:30)
Pythagoras’ Theorem in Circles (9:06)
Trigonometric Functions (10:30)
The Graph of the Sine Function (9:52)
The Graph of the Cosine Function (9:30)
The Graph of the Tangent Function (8:21)
Transforming Graphs of Trigonometric Functions (13:45)
The CAST Method (10:07)
Introduction to Trigonometric Equations (10:13)
Solving Trigonometric Equations Using a Calculator in Degrees (15:56)
Quick Practice Questions - Pythagoras Theorem
Quick Practice Questions - Trigonometry
Full Practice Questions
Reference Notes

Using Trigonometry

Introduction to The Sine and Cosine Rules (7:15)
Using the Sine Rule to Find Missing Angles (11:20)
Using the Sine Rule to Find Missing Sides (8:13)
Using the Cosine Rule for Missing Angles (9:41)
Using the Cosine Rule for Missing Sides (8:04)
Problems Involving Bearings (8:45)
Area of a Non-Right Triangle (6:59)
Quick Practice Questions
Full Practice Questions
Reference Notes

Vectors

Vector Introduction and Notation (6:28)
Component Form of a Vector (7:49)
Vectors in 3-Dimensions (4:43)
Magnitude of a Vector (7:23)
Resultant Vectors (8:11)
Quick Practice Questions
Full Practice Questions
Reference Notes

Comparing Distributions

Comparing Distributions (6:24)
Mean and Median (6:17)
Quartiles (7:09)
Interquartile and Semi-Interquartile Range (9:31)
Box Plots (8:45)
Standard Deviation (12:05)
Scatter Graphs and Lines of Best Fit (9:28)
Quick Practice Questions
Full Practice Questions
Reference Notes

Fractions & Percentages

Simple and Compound Measures (6:40)
Appreciation and Depreciation (9:26)
Multiplying and Dividing Fractions (8:36)
Adding and Subtracting Fractions (7:43)
Fractions of a Number (5:59)
Quick Practice Questions
Full Practice Questions
Reference Notes

Exam Video Solutions

2023 Paper 1 Video Solutions (37:55)
2023 Paper 2 Video Solutions (35:17)
2022 Paper 1 Video Solutions (58:42)
2019 Paper 1 Video Solutions (65:41)
2019 Paper 2 Video Solutions (80:29)
2018 Paper 1 Video Solutions (69:32)
2018 Paper 2 Video Solutions (83:47)

Exam Written Solutions (download link at the end of each document)

2023 National 5 Maths Solutions
2022 National 5 Maths Solutions
2019 National 5 Maths Solutions
2018 National 5 Maths Solutions
2017 National 5 Maths Solutions
2016 National 5 Maths Solutions
2015 National 5 Maths Solutions
2014 National 5 Maths Solutions

Past Exam Papers (download link at the end of each paper)

2022 National 5 Maths Papers
2019 National 5 Maths Papers
2018 National 5 Maths Papers
2017 National 5 Maths Papers
2016 National 5 Maths Papers
2015 National 5 Maths Papers
2014 National 5 Maths Papers

Past Exam Questions by Topic (download link at the end of each document)

Algebraic Fractions
Algebraic Operations
Arcs & Sectors
Equations & Inequations
Fractions
Functions
Graphs of Quadratic Functions
Indices
Percentages
Properties of Shapes
Pythagoras Theorem
Quadratic Equations
Quartiles
Rearranging Formulas
Similar Figures
Simultaneous Equations
Standard Deviation
Straight Lines
Surds
Trigonometry
Using Trigonometry
Vectors
Volume

Additional Resources

Extended Formula List
Trigonometric Function Graphs
Practice Paper A - Non-Calculator
Practice Paper B - Calculator
Key Skills Practice

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Vectors in 3-Dimensions

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