About this Course

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Learner Career Outcomes

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got a tangible career benefit from this course
Shareable Certificate
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100% online
Start instantly and learn at your own schedule.
Flexible deadlines
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Intermediate Level
Approx. 59 hours to complete
English

Learner Career Outcomes

50%

got a tangible career benefit from this course
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Intermediate Level
Approx. 59 hours to complete
English

Offered by

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The University of Sydney

Syllabus - What you will learn from this course

Content RatingThumbs Up98%(16,617 ratings)Info
Week
1

Week 1

9 hours to complete

Precalculus (Setting the scene)

9 hours to complete
10 videos (Total 109 min), 8 readings, 9 quizzes
10 videos
Real line, decimals and significant figures15m
The Theorem of Pythagoras and properties of the square root of 211m
Algebraic expressions, surds and approximations10m
Equations and inequalities17m
Sign diagrams, solution sets and intervals (Part 1)10m
Sign diagrams, solution sets and intervals (Part 2)10m
Coordinate systems8m
Distance and absolute value5m
Lines and circles in the plane14m
8 readings
Notes: Real line, decimals and significant figures20m
Notes: The Theorem of Pythagoras and properties of the square root of 220m
Notes: Algebraic expressions, surds and approximations20m
Notes: Equations and inequalities20m
Notes: Sign diagrams, solution sets and intervals20m
Notes: Coordinate systems20m
Notes: Distance and absolute value20m
Notes: Lines and circles in the plane20m
9 practice exercises
Real line, decimals and significant figures20m
The Theorem of Pythagoras and properties of the square root of 220m
Algebraic expressions, surds and approximations20m
Equations and inequalities30m
Sign diagrams, solution sets and intervals30m
Coordinate systems30m
Distance and absolute value30m
Lines and circles in the plane30m
Module 1 quiz1h
Week
2

Week 2

13 hours to complete

Functions (Useful and important repertoire)

13 hours to complete
13 videos (Total 142 min), 12 readings, 13 quizzes
13 videos
Parabolas and quadratics11m
The quadratic formula10m
Functions as rules, with domain, range and graph11m
Polynomial and power functions13m
Composite functions7m
Inverse functions12m
The exponential function13m
The logarithmic function8m
Exponential growth and decay13m
Sine, cosine and tangent9m
The unit circle and trigonometry16m
Inverse circular functions11m
12 readings
Notes: Parabolas and quadratics20m
Notes: The quadratic formula20m
Notes: Functions as rules, with domain, range and graph20m
Notes: Polynomial and power functions20m
Notes: Composite functions20m
Notes: Inverse functions20m
Notes: The exponential function20m
Notes: The logarithmic function15m
Notes: Exponential growth and decay20m
Notes: Sine, cosine and tangent20m
Notes: The unit circle and trigonometry20m
Notes: Inverse circular functions20m
13 practice exercises
Parabolas and quadratics30m
The quadratic formula30m
Functions as rules, with domain, range and graph30m
Polynomial and power functions30m
Composite functions30m
Inverse functions30m
The exponential function30m
The logarithmic function30m
Exponential growth and decay30m
Sine, cosine and tangent30m
The unit circle and trigonometry30m
Inverse circular functions30m
Module 2 quiz1h
Week
3

Week 3

12 hours to complete

Introducing the differential calculus

12 hours to complete
12 videos (Total 132 min), 10 readings, 11 quizzes
12 videos
Slopes and average rates of change10m
Displacement, velocity and acceleration11m
Tangent lines and secants10m
Different kinds of limits12m
Limit laws15m
Limits and continuity9m
The derivative as a limit10m
Finding derivatives from first principles14m
Leibniz notation14m
Differentials and applications (Part 1)13m
Differentials and applications (Part 2)7m
10 readings
Notes: Slopes and average rates of change20m
Notes: Displacement, velocity and acceleration20m
Notes: Tangent lines and secants20m
Notes: Different kinds of limits20m
Notes: Limit laws20m
Notes: Limits and continuity20m
Notes: The derivative as a limit20m
Notes: Finding derivatives from first principles20m
Notes: Leibniz notation20m
Notes: Differentials and applications20m
11 practice exercises
Slopes and average rates of change30m
Displacement, velocity and acceleration30m
Tangent lines and secants30m
Different kinds of limits30m
Limit laws30m
Limits and continuity30m
The derivative as a limit30m
Finding derivatives from first principles30m
Leibniz notation30m
Differentials and applications30m
Module 3 quiz1h
Week
4

Week 4

14 hours to complete

Properties and applications of the derivative

14 hours to complete
14 videos (Total 155 min), 13 readings, 14 quizzes
14 videos
Increasing and decreasing functions11m
Sign diagrams12m
Maxima and minima12m
Concavity and inflections10m
Curve sketching16m
The Chain Rule9m
Applications of the Chain Rule14m
The Product Rule8m
Applications of the Product Rule9m
The Quotient Rule8m
Application of the Quotient Rule10m
Optimisation12m
The Second Derivative Test16m
13 readings
Notes: Increasing and decreasing functions20m
Notes: Sign diagrams20m
Notes: Maxima and minima20m
Notes: Concavity and inflections20m
Notes: Curve sketching20m
Notes: The Chain Rule20m
Notes: Applications of the Chain Rule20m
Notes: The Product Rule20m
Notes: Applications of the Product Rule20m
Notes: The Quotient Rule20m
Notes: Application of the Quotient Rule20m
Notes: Optimisation20m
Notes: The Second Derivative Test20m
14 practice exercises
Increasing and decreasing functions30m
Sign diagrams20m
Maxima and minima30m
Concavity and inflections30m
Curve sketching30m
The Chain Rule30m
Applications of the Chain Rule30m
The Product Rule30m
Applications of the Product Rule30m
The Quotient Rule30m
Application of the Quotient Rule30m
Optimisation30m
The Second Derivative Test30m
Module 4 quiz1h

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