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Martinborough Manor, Flowers, Homesteading and Mathematics/Introductory Mathematics for Engineers FS3128/also known as CP3060 Introductory Maths for Engineers
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Introductory Mathematics for Engineers FS3128/also known as CP3060 Introductory Maths for Engineers

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Contents

How it all works

FS3128 also known as CP3060-01 is THE introductory maths course for the New Zealand Diploma of Engineering.  The course is for students who do not have the prerequisites to directly enter the DE4102 course, or for whom maths study was a long time ago
Getting started on Podia
Before you start

Really important information for the course

FS3128 course outline generic.docx
FS3128 lesson timetable generic.xlsx
FS3128 lesson timetable generic.xlsx
FS3128 Student_Registration_Handout_deboer85000.pdf
fx-82AU_PLUS_II_E.pdf
Forms of dishonest practice.pdf
Introductory Excel

Module 1 Arithmetic of whole numbers

After completing this topic you will be able to:
  • use the rules for adding, subtracting, multiplying, and dividing positive and negative integers
  • explain what an integer is
  • define and recognise what is meant by a prime number
  • prime factorise a number
  • find the highest common factor and the lowest common multiple of two or three numbers
  • explain what a fraction is
  • define the terms improper fraction, proper fraction and mixed fraction
  • write fractions in different but equivalent forms
  • simplify fractions by cancelling common factors
  • add, subtract, multiply and divide fractions
  • write a number to a given number of decimal places
  • write a number to a given number of significant figures
FS3128 On-line Module 1 Arithmetic of whole numbers and fractions.pptx
Class 1
Pre quiz
Topic 1 Class 1 Arithmetic of whole numbers
Post quiz
Extra video on Multiplying and dividing real numbers, if you need it
Extra video on GCF if you need it
Extra video on prime factoring if you need it
Topic 1 class 1 HCF and LCM
textbook questions
mymathlab
Class 2
Pre quiz
Topic 1 Class 2 Arithmetic of fractions
Post quiz
textbook questions
mymathlab
Extra video on adding and subtracting fractions if you need it
Extra video on multiplying and dividing fractions if you need it
Class 3
Pre quiz
Topic 1 Class 3 Decimals
Post quiz
textbook questions
mymathlab
Quick decimal practice if you need it
Rounding to a given number of decimal places if you need it
Rounding to a given number of sig figs if you need it
Not compulsory FS3128 Assignment 1.pdf

Topic 2 Introduction to algebra

By the end of this topic you will be able to:
  • explain the terms percentage and ratio
  • perform calculations using percentages and ratios
  • calculate the percentage change in a quantity
  • explain what is meant by algebra
  • recognize common algebraic notations
  • evaluate an expression
  • explain what is meant by a formula
  • state the three "laws" used for manipulating indices
  • show how expressions involving indices can be simplified using these three laws
  • explain square roots, cube roots and fractional powers
  • multiply and divide by powers of 10
  • explain scientific notation for representing very large and very small numbers
FS3128 On-line Topic 2 Algebra.pptx
Class 1
Pre quiz
Topic 2 Class 1 Percentages and ratios
Post quiz
textbook questions
mymathlab
Class 2
Pre quiz
Topic 2 Class 2 Introductory algebra
Post quiz
textbook questions
mymathlab
Class 3
Pre quiz
Topic 2 Class 3 Laws of indices and negative indices
Post quiz
textbook questions
mymathlab
Class 4
Pre quiz
Topic 2 Class 4 Square and cube roots, fractional powers, multiplication by powers of 10, scientific notation
Post quiz
textbook questions
mymathlab
Not compulsory FS3128 Assignment 2.pdf

Topic 3 Simplification, factorisation and algebraic fractions

After studying this topic, you will be able to:
  • add and subtract like terms in an algebraic expression
  • simplify algebraic expressions by removing brackets
  • explain what a factor of an expression is
  • find common factors of a simple expression (put brackets in)
  • find factors of quadratic expressions (put brackets in to an expression wtih x to the power of two)
  • cancel common factors in algebraic fractions
  • multiply and divide algebraic fractions
FS3128 On-line Topic 3 Algebra (2).pptx
Class 1
Pre quiz
Topic 3 Class 1 Simplification - adding and subtracting like terms
textbook questions
mymathlab
Class 2
Topic 3 Class 2 Simplification - removing brackets
textbook questions
mymathlab
Class 3
Pre quiz
Topic 3 Class 3 Factorisation
textbook questions
mymathlab
Class 4
Topic 3 Class 4 - Factorising quadratics
textbook questions
mymathlab
Class 5
Pre quiz
Topic 3 Class 5 Algebraic fractions
Post quiz
textbook questions
mymathlab
Not compulsory FS3128 Assignment 3.pdf

Topic 4 Transposing formulae and solving equations

By the end of this topic you will be able to:
  • rearrange or transpose formulae
  • explain what is meant by an equation and its solution
  • solve linear, simultaneous and quadratic equations
FS3128 On-line Topic 4 Algebra 3.pptx
Class 1
Pre quiz
Topic 4 Class 1 Transposing formulae
textbook questions
mymathlab
Class 2
Topic 4 Class 2 Solving linear equations
Solving LINEAR equations
Class 3
Topic 4 class 3 Solving simultaneous equations
Solving SIMULTANEOUS equations
Class 4
Topic 4 Class 4 Solving quadratic equations
Post quiz
Solving QUADRATIC equations

Topic 5 Functions, graphs and properties of straight lines

By the end of the this topic you will be able to:
  • explain what is meant by a function
  • describe the notation used to write functions
  • write functions mathematically from their descriptions and vice versa
  • explain what is meant by a composite function
  • find a given composite function and express it mathematically
  • explain what is meant by the inverse of a function
  • find the inverse of a given function
  • show how coordinates are plotted on the x-y plane
  • use notation to denote intervals on the x axis
  • use the 'greater than' and 'less than' symbols
  • explain what is meant by and how to find the domain and range of a function
  • solve equations using a graph
  • solve equations simultaneously using graphs
  • describe the properties of a straight line
  • explain the equation y = mx + c
  • explain the terms 'vertical intercept'  and 'gradient'
  • explain what the tangent to a curve is
  • show how to find the equation of a line
  • explain what is meant by the gradient of a curve
  • explain how the gradient of a curve can be estimated by drawing a tangent
FS3128 On-line Topic 5 – Functions and graphs.pptx
Class 1 Functions
Pre quiz
Topic 5 Class 1 Functions
Post quiz
textbook questions
mymathlab
Class 2 Plotting the graph of a function
Post quiz
Pre quiz
Topic 5 Class 2 Graphs of functions
textbook questions
mymathlab
Class 3 Straight line graphs
Pre quiz
Topic 5 Class 3 The straight line
Post quiz
textbook questions
mymathlab
Class 4 Finding the equation of a straight line from its graph
Topic 5 Class 4 Finding the equation of a straight line
textbook questions
mymathlab

Topic 6 Exponents, logarithms and measurement

By the end of this topic you will be able to:
  • show how to simplify exponential expressions
  • describe the form of the exponential function
  • list the properties of the exponential function
  • show how to solve equations with exponential terms using graphs
  • explain what is meant by the base of a logarithm
  • calculate the logarithm of a number to any base
  • understand and use the laws of logarithms to simplify expressions
  • solve equations that involve exponents and logarithms
  • define the logarithm function
  • illustrate graphically the logarithm function
  • explain the use of SI units and prefixes, and the conversions between them
  • explain the use of degrees and radians and the conversions between them
  • use common formulae for areas and volumes of common shapes
FS3128 On-line Topic 6 – More functions.pptx
Class 1 Exponential expressions
Topic 6 Class 1 Exponential expressions
textbook questions
mymathlab
Class 2 The exponential function, its graph and using the graph to solve exponential equations
Topic 6 Class 2 Exponential functions and their graphs, and Solving exponential equations graphically
textbook questions
mymathlab
Class 3
Topic 6 Class 3 Introducing Logarithmic functions
textbook questions
mymathlab
Class 4
Topic 6 Class 4 Laws of logarithms, Solving equations with logs, the Properties and graphs of logarithmic functions
textbook questions
mymathlab
Solving an equation using logs extra video #1
Solving an equation using logs - extra video #2
Class 5
Topic 6 Class 5 Measurement
textbook questions
mymathlab

Topic 7 Trigonometry

After studying this module, you will be able to:
  • use the terminology associated with right angle triangles
  • define the trigonometrical ratios, sine, cosine and tangent with reference to the lengths if the sides of a right angled triangle
  • explain how to calculate an angle given one of the trigonometrical ratios
  • extend the trigonometrical ratios to angles greater than 90 degrees
  • sketch the graphs of the common trigonometrical functions, and simple variations of these 
  • explain what is meant by a trigonometrical identity, and use a table of simple identities
  • show how identities can be used to relate the trigonometrical ratios of angles in the second, third and fourth quadrants to those in the first
  • show how complicated trigonometrical expressions can be simplified using the identities
  • explain how to solve equations involving trigonometrical functions

FS3128 On-line Topic 7 Trigonometry 1.pptx
Class 1
Topic 7 class 1 Introduction to trigonometry
Class 2 - trig ratios for angles greater than a right angle
Topic 7 Class 2 Trig ratios for angles greater than a right angle
Trigonometry: quadrant method
Class 3 - trig functions and their graphs
Topic 7 Class 3 Trig functions and their graphs
Interactive unit circle for trig
Trigonometric graphs (not my video)
Class 4 - trigonometrical identities
Topic 7 Class 4 Trig identities
Class 5 - solving trigonometric equations
Topic 7 Class 5 Solving trig equations

Topic 8 Last class on Trig, and introductory Statistics

After studying this module, you will be able to:
  • explain the terms scalene, isosceles, equilateral and right angled as applied to triangles
  • state Pythagoras' theorem and show how it can be used in the solution of right angled triangles
  • state the sine rule and the cosine rule and show how they are used to solve triangles
  • explain the difference between discrete and continuous data
  • show how raw data can be organised by using a tally chart
  • explain what is meant by a frequency distribution and a relative frequency distribution
  • show how data can be represented in the form of bar charts, pie charts, pictograms and histograms
  • show how to calculate three common averages, mean, median and mode
  • explain what is meant by the variance and standard deviation and how to calculate them
  • explore the association between two variables using a scatter diagram
  • explain what is meant by positive, negative and zero correlation
  • show at an introductory level what a correlation coefficient means 
  • show how to find a regression line of Y on X on a calculator, and use this to predict values of the dependent variable, Y, given values of the independent variable, X
FS3128 On-line Topic 8 Trigonometry 2.pptx
Class 1
Topic 8 Class 1 - last of the trig, non-right angle triangles
Using the cosine rule to find an angle (not my video)
Using the cosine rule to find a length (not my video)
Using the sine rule to find an angle (not my video)
Using the sine rule to find a length (not my video)
Class 2 Tables and charts
Topic 8 Class 2 Tables and Charts
Class 3 Common averages and deviations
Topic 8 class 3 Statistics
how do I add a frequency column on casio Fx-82AU plus II

Topic 9 Probability

After studying this module you will be able to:
  • calculate theoretical and experimental probability
  • explain the meaning of the term complementary events
  • explain the meaning of the term independent events
FS3128 On-line Topic 9 Statistics and Probability.pptx
Class 1 - Probability
Topic 9 Class 1
Class 2 - Scatter diagrams and correlation coefficients
Topic 9 Class 2
Class 3 - The regression equation
Topic 9 Class 3

Topic 10 Differentiation

After you have studied this module you will be able to:
  • explain what differentiation as a process does
  • find the gradient function of several common functions using a table
  • use simple rules for finding a gradient function
  • explain what is meant by the terms first derivative, second derivative
  • explain the terms maximum and minimum when applied to functions
  • apply the technique of differentiation to locating maximum and minimum values of functions
  • explain and illustrate the product, quotient rule and chain rule for differentiation 
FS3128 On-line Topic 10 - Differentiation.pptx
Class 1 - why engineers need to understand differentiation
Topic 10 Class 1
Class 2 - Some rules for finding gradient functions
Class 3 - higher derivatives and finding maximums and minimums
Topic 10 Class 3 - higher derivatives and finding the maximums and minimums of a curve
Topic 10 class 4, 5 and 6
Class 4 - the product rule
Topic 10 class 4 The product rule
Class 5 the quotient rule
Topic 10 Class 5 - The quotient rule
Class 6 - the chain rule
Topic 6 class 6 - The chain rule

Topic 11 Integration

After studying this module you will be able to:
  • explain integration as the reverse process to differentiation 
  • explain what is meant by definite integral and indefinite integral
  • show how integration can be used to find area under a curve
FS3128 On-line Topic 11 - Integration.pptx
Class 1 - integration is the reverse of differentiation, and some rules of integration
Topic 11 Class 1
Class 2 - definite areas and areas under curves
Topic 11 class 2
Class 3 - integration by substitution
Topic 11 class 3

"Live" class notes

FS3128 T1 C1 2 2022.pptx
FS3128 T1 C2 2 2022.pptx
FS3128 T1 C3 2 2022.pptx
FS3128 T2 C1 2022.pptx
FS3128 T2 C2 2022.pptx
FS3128 T2 C3 2 2022.pptx
FS3128 T3 C1 2022.pptx
FS3128 T3 C2 2 2022.pptx
FS3128 T3 C3 and C4 2 2022.pptx
FS3128 T4 C1 and C2 2 2022.pptx
FS3128 T4 C3 2 2022.pptx
FS3128 T4 C4 2 2022.pptx
FS3128 T5 C1 2 2022.pptx
FS3128 T5 C2 2 2022.pptx
FS3128 T5 C3 2 2022.pptx
FS3128 T6 C1 Otago 2 2022.pptx
FS3128 T6 C2 2 2022.pptx
FS3128 T6 C3 2 2022.pptx
FS3128 T6 C4 2 2022.pptx
FS3128 T6 C5 2 2022.pptx
FS3128 T7 c1 2 2022.pptx
FS3128 T7 C2 2 2022.pptx
FS3128 T7 c3 2 2022.pptx
FS3128 T7 C4 2 2022.pptx
FS3128 T7 C5 2 2022.pptx
FS3128 T8 c1 2 2022.pptx
FS3128 T8 C2 2 2022.pptx
FS3128 T8 C3 2 2022.pptx
FS3128 T9 c1 2 2022.pptx