
Free Course

XSIQ

23 Hours

Assessment

Certification

50 Pts
Advanced Mathematics 2

Description

Outcome

Certification

The Advanced Mathematics UpperSecondary 2 course completes our suit of uppersecondary maths. This free online course covers differential equations, kinematics, vector calculus and dynamics. This course is suitable for maths students, and for anyone interested in exploring the world of mathematics.

Upon completion of this course you will effectively learn the most important factors to be considered when answering questions in a maths exam. You will be aware of the most common mistakes in maths exams. You will gain a good knowledge of first and second order differential equations and second derivatives. You will learn about kinematics including acceleration, distance and velocity. You will understand Newton's laws of motion, Newton's laws of cooling, and Euler's method for solution of differential equations. This course will teach you the resolution of forces and how to calculate vectors.

All Alison courses are free to study. To successfully complete a course you must score 80% or higher in each course assessments. Upon successful completion of a course, you can choose to make your achievement formal by purchasing an official Alison Diploma, Certificate or PDF.
Having an official Alison document is a great way to celebrate and share your success. It is: Ideal to include with CVs, job applications and portfolios
 A way to show your ability to learn and achieve high results
Modules List( 12 )

Module
1 Successfully completing mathematics exams
Successfully completing mathematics exams This free online course covers how to answer questions in examinations. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Look for key words

Check level of accuracy

What form should the answer take?

Don't waste time on work that is not assessed

Use all the information provided in the question

Work out the solution before you look at the answers

Rationalise or realise denominators

Essential skills you need to brush up on before the exams

Decide on the order you answer questions

Timing of questions

Setting out

Don't panic

If you are stuck

Guessing

Learning pattern questions

Learning pattern questions: graphs

Learning pattern questions: complex numbers

Learning pattern questions: differentiation

Learning pattern questions: integration

Learning pattern questions: vectors


Module
2 Common exam mistakes
Common exam mistakes This free online course covers basic exam techniques such dividing by fractions and using negative signs. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Basic algebra exam mistakes

Using correct notation in exams

Dividing by fractions

Negative signs

Applying half remembered rules incorrectly


Module
3 Differential equations
Differential equations This free online course covers topics related to differential equations such as first order and second order differential equations and rates of change . The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Order and degree of differential equations

Verifying solutions

Rates of change

Rates of change  chain rule

The rates of change example

First order differential equations  type 1

First order differential equations  type 2

Second order differential equations


Module
4 Second derivatives
Second derivatives This free online course covers the use of the second derivative. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Use of the second derivative

Examples

Second derivatives


Module
5 Kinematics
Kinematics This free online course covers topics related to kinematics such as velocity and acceleration. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Finding displacement from velocity

Solving differential equations (rectilinear motion)
example

Finding acceleration or velocity from displacement

Constant acceleration  introduction

Constant acceleration  example 1

Velocity time graphs  introduction

Finding the acceleration from the velocity time
graph

Finding the distance travelled from a velocity
time graph

Velocity time graphs  example

Constant acceleration  example 2


Module
6 Motion
Motion This free online course covers topics related to motion such as motion under a constant force and motion under a variable force. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Newton's laws of motions

Forcesweight

Diagram of forces

Basic equation of motion

Resolution of forces

Horizontal and vertical

Equations of motion

Parallel and perpendicular to a plane

Equations of motion

Moving down the slope

Connected masses

Motion under a constant force

Motion under a constant force  example 1

Motion under a constant force  example 2

Motion under a variable force

Motion under a variable force  example 1

Motion under a variable force  example 2

Motion under a variable force  example 3

Momentum and impulse

Momentum and impulse example

Moving up the slope

Motion under a constant force  example 1 continued

Forcesnormal reaction

Forcesfriction

Forcestension


Module
7 Advanced Mathematics: Problems
Advanced Mathematics: Problems This free online course covers topics such as chemical concentrations and chemical reactions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Activity

Using differential equations

Newton's laws of cooling

Growth and decline

Chemical concentrations

Water flow from a hole in a tank

Chemical reactions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Euler's method for solution of differential equations

Euler's example 1

Euler's example 2


Module
8 Resolution of forces
Resolution of forces This free online course covers topics related to resolution of forces such as static friction, and angle of friction. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Resolution of forces

Three forces

Static friction

Angle of friction


Module
9 Vectors
Vectors This free online course covers topics related to vectors such as parametric equations The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Position vectors as functions of time (Parametric
Equations)

Finding cartesian equations from parametric equations

Example 1

Example 2

Collision

Example 3

Using a graphic calculator with parametric equations

Using a graphic calculator with two parametric
equations to show a collision

The closest distance to a path

Example 4


Module
10 Vectors 2
Vectors 2 This free online course covers the differentiation and antidifferentiation of vectors. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

The garden activity

Notation used in vector calculus

Differentiation and anti differentiation of vectors

Example 1

Example 2


Module
11 Glossary
Glossary This free online course is a glossary of mathematical terms. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Glossary


Assessment

Assessment

Advanced Mathematics 2 Assessment
