Applied Maths Lessons

St. Andrew’s College – 6th Years

Course Curriculum

Welcome to A.M. Online!

Introduction
Site Navigation
Additional Information

1 – Introduction to Vectors

Overview
1.1 – Scalars and Vectors
1.2 – Visual Representation of Vectors
Exercise Set 1A
Exercise Set 1A Solutions
1.3 – Arbitrary Vectors
1.4 – Vectors in Polar Form
Exercise Set 1B
Exercise Set 1B Solutions
1.5 – Vector Addition
Exercise Set 1C
Exercise Set 1C Solutions
1.6 – Vector Multiplication
Exercise Set 1D
Exercise Set 1D Solutions
1.7 – Vector Decomposition 1
Exercise Set 1E
Exercise Set 1E Solutions
1.8 – Vector Decomposition 2
Exercise Set 1F
Exercise Set 1F Solutions
1.9 – Vectors in Component Form
Exercise Set 1G
Exercise Set 1G Solutions
Revision Sheet

2 – 1D Horizontal Motion

Overview
2.1 – Displacement, Velocity and Acceleration
2.2 – SUVAT Vector Equations
2.3 – 1D SUVAT Scalar Equations
Exercise Set 2A
Exercise Set 2A Solutions
2.4 – Graphical Representation of 1D Motion
Exercise Set 2B
Exercise Set 2B Solutions
2.5 – Using Time-Velocity Graphs
Exercise Sets 2C & 2D
Exercise Sets 2C & 2D Solutions
2.6 – Instantaneous Acceleration Change
Exercise Set 2E
Exercise Set 2E Solutions
2.7 – Motion with Partial Variables
Exercise Set 2F
Exercise Set 2F Solutions
2.8 – Motion with Connected Variables
Exercise Set 2G
Exercise Set 2G Solutions
2.9 – Dimensional Analysis
Revision Sheet

3 – Motion due to Gravity

Overview
3.1 – 1D Motion due to Gravity
Exercise Sets 3A & 3B
Exercise Sets 3A & 3B Solutions
3.2 – 2D Motion due to Gravity
Exercise Sets 3C & 3D
Exercise Sets 3C & 3D Solutions
3.3 – Features of Projectile Motion
Exercise Sets 3E & 3F
Exercise Sets 3E & 3F Solutions
Revision Sheet

4 – Continuous Change (Calculus)

Overview
4.1 – Introduction to Derivatives
4.2 – Known Derivatives
4.3 – Unknown Derivatives
Exercise Set 4A
Exercise Set 4A Solutions
4.4 – Indefinite Integrals
4.5 – Definite Integrals
4.6 – Unknown Integrals
Exercise Set 4B
Exercise Set 4B Solutions
4.7 – Differential Equations
Exercise Set 4C
Exercise Set 4C Solutions
4.8 – Applications of Differential Equations
Exercise Set 4D
Exercise Set 4D Solutions
Revision Sheet

5 – Forces and Systems

Overview
5.1 – Newton’s Laws of Motion
Exercise Set 5A
Exercise Set 5A Solutions
5.2 – Types of Force
Exercise Sets 5B & 5C
Exercise Sets 5B & 5C Solutions
5.3 – Friction
Exercise Set 5D
Exercise Set 5D Solutions
5.4 – Work and Power
Exercise Set 5E
Exercise Set 5E Solutions
5.5 – Introduction to Systems
Exercise Sets 5F & 5G
Exercise Sets 5F & 5G Solutions
5.6 – Systems with Moveable Pulleys
Exercise Set 5H
Exercise Set 5H Solutions
5.7 – Systems on Inclined Planes
Exercise Sets 5I & 5J
Exercise Sets 5I & 5J Solutions
Revision Sheet

6 – Introduction to Energy and Momentum

Overview
6.1 – Energy and Work
Exercise Set 6A
Exercise Set 6A Solutions
6.2 – Conservation of Energy
Exercise Set 6B
Exercise Set 6B Solutions
6.3 – Conservation of Momentum
Exercise Sets 6C & 6D
Exercise Sets 6C & 6D Solutions
Revision Sheet

7 – Impacts and Collisions

Overview
7.1 – Impacts and Bouncing
Exercise Sets 7A & 7B
Exercise Sets 7A & 7B Solutions
7.2 – Direct Collisions and Restitution
Exercise Set 7C
Exercise Set 7C Solutions
7.3 – Oblique Collisions and Restitution
Exercise Set 7D
Exercise Set 7D Solutions
Revision Sheet

8 – Uniform Circular Motion

Overview
8.1 – Radians
8.2 – Linear and Angular Velocity
Exercise Set 8A
Exercise Set 8A Solutions
8.3 – Centripetal Acceleration
Exercise Set 8B
Exercise Set 8B Solutions
8.4 – Horizontal Circular Motion
Exercise Sets 8C & 8D
Exercise Sets 8C & 8D Solutions
8.5 – Vertical Circular Motion
Exercise Set 8E
Exercise Set 8E Solutions
Revision Sheet

9 – Difference Equations

Overview
9.1 – Introduction to Sequences
Exercise Set 9A
Exercise Set 9A Solutions
9.2 – Introduction to Series
Exercise Set 9B
Exercise Set 9B Solutions
9.3 – First Order Difference Equations
Exercise Set 9C
Exercise Set 9C Solutions
9.4 – Second Order Homogeneous Difference Equations
Exercise Set 9D
Exercise Set 9D Solutions
9.5 – Second Order Inhomogeneous Difference Equations
Exercise Set 9E
Exercise Set 9E Solutions
Revision Sheet

10 – Introduction to Graph Theory

Overview
10.1 – Graphs
10.2 – Features of Graphs
Exercise Set 10A
Exercise Set 10A Solutions
10.3 – Introduction to Matrices
Exercise Set 10B
Exercise Set 10B Solutions
10.4 – Adjacency Matrices
Exercise Set 10C
Exercise Set 10C Solutions
Revision Sheet

11 – Path Optimisation

Overview
11.1 – Dijkstra’s Algorithm
Exercise Set 11A
Exercise Set 11A Solutions
11.2 – Dynamic Programming
Exercise Set 11B
Exercise Set 11B Solutions
11.3 – Applications of Dynamic Programming
Exercise Set 11C
Exercise Set 11C Solutions
Revision Sheet

12 – MST Optimisation

13 – Project Optimisation

Overview
13.1 – Activity Networks
Exercise Set 13A
Exercise Set 13A Solutions
13.2 – Dummy Activities
Exercise Set 13B
Exercise Set 13B Solutions
13.3 – Critical Path Method
Exercise Set 13C
Exercise Set 13C Solutions
13.4 – Gantt Charts
Exercise Sets 13D & 13E
Exercise Sets 13D & 13E Solutions
13.5 – Project Scheduling
Exercise Sets 13F & 13G
Exercise Sets 13F & 13G Solutions
Revision Sheet

Mathematical Modelling Project

Revision Sheets

Introduction to Vectors
1D Horizontal Motion
Motion due to Gravity
Continuous Change
Forces and Systems
Introduction to Energy and Momentum
Impacts and Collisions
Uniform Circular Motion
Difference Equations
Introduction to Group Theory
Path Optimisation
MST Optimisation
Project Optimisation

HL Past Papers (by year)

HL Past Papers (by topic)

Introduction to Vectors
1D Horizontal Motion
Motion due to Gravity
Continuous Change (Calculus)
Forces and Systems
Introduction to Energy and Momentum
Impacts and Collisions
Uniform Circular Motion
Difference Equations
Introduction to Graph Theory
Path Optimisation
MST Optimisation
Project Optimisation

HL Mock Exams (by year)

HL Mock Exams (by topic)

Introduction to Vectors
1D Horizontal Motion
Motion due to Gravity
Continuous Change (Calculus)
Forces and Systems
Introduction to Energy and Momentum
Impacts and Collisions
Uniform Circular Motion
Difference Equations
Introduction to Graph Theory
Path Optimisation
MST Optimisation
Project Optimisation

OL Past Papers (by year)

OL Past Papers (by topic)

Introduction to Vectors
1D Horizontal Motion
Motion due to Gravity
Continuous Change (Calculus)
Forces and Systems
Introduction to Energy and Momentum
Impacts and Collisions
Uniform Circular Motion
Difference Equations
Introduction to Graph Theory
Path Optimisation
MST Optimisation
Project Optimisation

Weekly Grinds

Upcoming Grinds
Grinds #19: Sample Papers Q4 & Q4(a) (OL & HL)
Grinds #18: Sample Papers Q3(b) (OL & HL)
Grinds #17: Sample Papers Q3(a) (OL & HL)
Grinds #16: Sample Papers Q2 (OL & HL)
Grinds #15: Sample Papers Q1 (OL & HL)
Grinds #10: Types of Force and Minimum Spanning Trees
Grinds #9: Differential Equations and Applications of Dynamic Programming
Grinds #8: Derivatives & Integrals & Dynamic Programming
Grinds #7: Features of Projectile Motion & Dijkstra’s Algorithm
Grinds #6: Motion due to Gravity & Difference Equations
Grinds #5: Time-Velocity Graphs and Sequences & Series
Grinds #4: SUVAT Equations and Adjacency Matrices
Grinds #3: Vectors in Component Form and Introduction to Matrices
Grinds #2: Vector Decomposition and Motion with Partial Variables
Grinds #1: Introduction

St. Andrew’s College – 6th Years

Course Curriculum

Welcome to A.M. Online!

Introduction

Site Navigation

Additional Information

1 – Introduction to Vectors

Overview

1.1 – Scalars and Vectors

1.2 – Visual Representation of Vectors

Exercise Set 1A

Exercise Set 1A Solutions

1.3 – Arbitrary Vectors

1.4 – Vectors in Polar Form

Exercise Set 1B

Exercise Set 1B Solutions

1.5 – Vector Addition

Exercise Set 1C

Exercise Set 1C Solutions

1.6 – Vector Multiplication

Exercise Set 1D

Exercise Set 1D Solutions

1.7 – Vector Decomposition 1

Exercise Set 1E

Exercise Set 1E Solutions

1.8 – Vector Decomposition 2

Exercise Set 1F

Exercise Set 1F Solutions

1.9 – Vectors in Component Form

Exercise Set 1G

Exercise Set 1G Solutions

Revision Sheet

2 – 1D Horizontal Motion

Overview

2.1 – Displacement, Velocity and Acceleration

2.2 – SUVAT Vector Equations

2.3 – 1D SUVAT Scalar Equations

Exercise Set 2A

Exercise Set 2A Solutions

2.4 – Graphical Representation of 1D Motion

Exercise Set 2B

Exercise Set 2B Solutions

2.5 – Using Time-Velocity Graphs

Exercise Sets 2C & 2D

Exercise Sets 2C & 2D Solutions

2.6 – Instantaneous Acceleration Change

Exercise Set 2E

Exercise Set 2E Solutions

2.7 – Motion with Partial Variables

Exercise Set 2F

Exercise Set 2F Solutions

2.8 – Motion with Connected Variables

Exercise Set 2G

Exercise Set 2G Solutions

2.9 – Dimensional Analysis

Revision Sheet

3 – Motion due to Gravity

Overview

3.1 – 1D Motion due to Gravity

Exercise Sets 3A & 3B

Exercise Sets 3A & 3B Solutions

3.2 – 2D Motion due to Gravity

Exercise Sets 3C & 3D

Exercise Sets 3C & 3D Solutions

3.3 – Features of Projectile Motion

Exercise Sets 3E & 3F

Exercise Sets 3E & 3F Solutions

Revision Sheet

4 – Continuous Change (Calculus)

Overview

4.1 – Introduction to Derivatives

4.2 – Known Derivatives

4.3 – Unknown Derivatives

Exercise Set 4A

Exercise Set 4A Solutions

4.4 – Indefinite Integrals

4.5 – Definite Integrals

4.6 – Unknown Integrals

Exercise Set 4B

Exercise Set 4B Solutions