
Free Course

XSIQ

23 Hours

Assessment

Certification

Academic  Secondary  Level 3

50 Pts
Advanced Mathematics 2

Description

Outcome

Certification

The Advanced Mathematics UpperSecondary 2 course completes our suit of uppersecondary maths. This 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
Start Topic

Look for key words
Start Topic

Check level of accuracy
Start Topic

What form should the answer take?
Start Topic

Don't waste time on work that is not assessed
Start Topic

Use all the information provided in the question
Start Topic

Work out the solution before you look at the answers
Start Topic

Rationalise or realise denominators
Start Topic

Essential skills you need to brush up on before the exams
Start Topic

Decide on the order you answer questions
Start Topic

Timing of questions
Start Topic

Setting out
Start Topic

Don't panic
Start Topic

If you are stuck
Start Topic

Guessing
Start Topic

Learning pattern questions
Start Topic

Learning pattern questions: graphs
Start Topic

Learning pattern questions: complex numbers
Start Topic

Learning pattern questions: differentiation
Start Topic

Learning pattern questions: integration
Start Topic

Learning pattern questions: vectors
Start Topic


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
Start Topic

Using correct notation in exams
Start Topic

Dividing by fractions
Start Topic

Negative signs
Start Topic

Applying half remembered rules incorrectly
Start Topic


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
Start Topic

Order and degree of differential equations
Start Topic

Verifying solutions
Start Topic

Rates of change
Start Topic

Rates of change  chain rule
Start Topic

The rates of change example
Start Topic

First order differential equations  type 1
Start Topic

First order differential equations  type 2
Start Topic

Second order differential equations
Start Topic


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
Start Topic

Use of the second derivative
Start Topic

Examples
Start Topic

Second derivatives
Start Topic


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
Start Topic

Finding displacement from velocity
Start Topic

Solving differential equations (rectilinear motion)
example
Start Topic

Finding acceleration or velocity from displacement
Start Topic

Constant acceleration  introduction
Start Topic

Constant acceleration  example 1
Start Topic

Velocity time graphs  introduction
Start Topic

Finding the acceleration from the velocity time
graph
Start Topic

Finding the distance travelled from a velocity
time graph
Start Topic

Velocity time graphs  example
Start Topic

Constant acceleration  example 2
Start Topic


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
Start Topic

Newton's laws of motions
Start Topic

Forcesweight
Start Topic

Diagram of forces
Start Topic

Basic equation of motion
Start Topic

Resolution of forces
Start Topic

Horizontal and vertical
Start Topic

Equations of motion
Start Topic

Parallel and perpendicular to a plane
Start Topic

Equations of motion
Start Topic

Moving down the slope
Start Topic

Connected masses
Start Topic

Motion under a constant force
Start Topic

Motion under a constant force  example 1
Start Topic

Motion under a constant force  example 2
Start Topic

Motion under a variable force
Start Topic

Motion under a variable force  example 1
Start Topic

Motion under a variable force  example 2
Start Topic

Motion under a variable force  example 3
Start Topic

Momentum and impulse
Start Topic

Momentum and impulse example
Start Topic

Moving up the slope
Start Topic

Motion under a constant force  example 1 continued
Start Topic

Forcesnormal reaction
Start Topic

Forcesfriction
Start Topic

Forcestension
Start Topic


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
Start Topic

Using differential equations
Start Topic

Newton's laws of cooling
Start Topic

Growth and decline
Start Topic

Chemical concentrations
Start Topic

Water flow from a hole in a tank
Start Topic

Chemical reactions
Start Topic

Example 1
Start Topic

Example 2
Start Topic

Example 3
Start Topic

Example 4
Start Topic

Example 5
Start Topic

Example 6
Start Topic

Euler's method for solution of differential equations
Start Topic

Euler's example 1
Start Topic

Euler's example 2
Start Topic


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
Start Topic

Resolution of forces
Start Topic

Three forces
Start Topic

Static friction
Start Topic

Angle of friction
Start Topic


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)
Start Topic

Finding cartesian equations from parametric equations
Start Topic

Example 1
Start Topic

Example 2
Start Topic

Collision
Start Topic

Example 3
Start Topic

Using a graphic calculator with parametric equations
Start Topic

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

The closest distance to a path
Start Topic

Example 4
Start Topic


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
Start Topic

Notation used in vector calculus
Start Topic

Differentiation and anti differentiation of vectors
Start Topic

Example 1
Start Topic

Example 2
Start Topic


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
Start Topic


Assessment