Advanced Mathematics 2

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Advanced Mathematics 2

Free Course
XSIQ
2-3 Hours
Assessment
Certification
50 Pts

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 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

Maths

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
  
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- Look for key words
  
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- Check level of accuracy
  
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- What form should the answer take?
  
  Start Topic
- Don't waste time on work that is not assessed
  
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- Use all the information provided in the question
  
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- Work out the solution before you look at the answers
  
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- Rationalise or realise denominators
  
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- 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
  
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- Learning pattern questions
  
  Start Topic
- Learning pattern questions: graphs
  
  Start Topic
- Learning pattern questions: complex numbers
  
  Start Topic
- Learning pattern questions: differentiation
  
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- Learning pattern questions: integration
  
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- Learning pattern questions: vectors
  
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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
  
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- 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
  
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- 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
  
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- 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
  
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- Velocity time graphs - introduction
  
  Start Topic
- Finding the acceleration from the velocity time graph
  
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- 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
- Forces-weight
  
  Start Topic
- Diagram of forces
  
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- Basic equation of motion
  
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- 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
  
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- Motion under a constant force
  
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- Motion under a constant force - example 1
  
  Start Topic
- Motion under a constant force - example 2
  
  Start Topic
- Motion under a variable force
  
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- Motion under a variable force - example 1
  
  Start Topic
- Motion under a variable force - example 2
  
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- Motion under a variable force - example 3
  
  Start Topic
- Momentum and impulse
  
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- Momentum and impulse example
  
  Start Topic
- Moving up the slope
  
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- Motion under a constant force - example 1 continued
  
  Start Topic
- Forces-normal reaction
  
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- Forces-friction
  
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- Forces-tension
  
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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
- Assessment
- Advanced Mathematics 2 Assessment
  
  Start Topic

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