# Advanced Mathematics 2 Free Course

• Description
• Outcome
• Certification
• The Advanced Mathematics Upper-Secondary 2 course completes our suit of upper-secondary 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 share your success. Plus it’s:

• Ideal for including in CVs, job applications and portfolios
• An indication of your ability to learn and achieve high results
• An incentive to continue to empower yourself through learning
• A tangible way of supporting the Alison mission to empower people everywhere through education.

###### Modules List( 12 )
• Successfully completing mathematics exams
• 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
• Common exam mistakes
• Basic algebra exam mistakes
• Using correct notation in exams
• Dividing by fractions
• Negative signs
• Applying half remembered rules incorrectly
• Differential equations
• 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
• Second derivatives
• Introduction
• Use of the second derivative
• Examples
• Second derivatives
• Kinematics
• 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
• Motion
• Introduction
• Newton's laws of motions
• Forces-weight
• 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
• Forces-normal reaction
• Forces-friction
• Forces-tension
• 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
• Resolution of forces
• Introduction
• Resolution of forces
• Three forces
• Static friction
• Angle of friction
• Vectors
• 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
• Vectors 2
• The garden activity
• Notation used in vector calculus
• Differentiation and anti differentiation of vectors
• Example 1
• Example 2
• Glossary
• Glossary
• Assessment
###### Topics List ( 21 )
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.
###### Topics List ( 5 )
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.
###### Topics List ( 9 )
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.
###### Topics List ( 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.
###### Topics List ( 11 )
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.
###### Topics List ( 26 )
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.
###### Topics List ( 16 )
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.
###### Topics List ( 5 )
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.
###### Topics List ( 10 )
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.
###### Topics List ( 5 )
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.
###### Topics List ( 1 )
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.
Assessment
Assessment
##### Course Features
• Duration

2-3 Hours

• Publisher

XSIQ

• Video

Yes

• Audio

Yes

• Assessment

Yes

• Certification

Yes

• Price

Free

• Reward

50 Pts

• Responsive

No