## Mathematics

Introduction

• Name: Raymund O’Connor
• Email: raymund.oconnor@csn.ie

Required for Class and Assessments

• Scientific Calculator (eg. as used for Leaving Certificate)
• Geometry Set (pencil, ruler, eraser, compass, protractor, etc)

IT Rules & Regulations

• From Student Handbook on www.csn.ie

Login / Log out of Office365/Moodle

(Default username: student, !CSN.letmein)

File Management

• IT Induction (log into OneDrive – demo create, print, save files, etc)
• Create a folder for each component (files and folders)
• Backup to OneDrive (similar to Google Drive, iCloud, Dropbox, etc)
• Use OneDrive app on your smartphone to photograph your written work and save as a PDF.
• Submitting assessment work using Moodle
• Microsoft Excel – useful for calculating Mean, Standard Deviation, drawing graphs, etc)

• Assignment 1 – 30%
• Assignment 2 – 30%
• Exam – 40%

Sample Assessment Resources

Sample Word files (Download the relevant file below and save with your own name. Once you type your solutions save the Word file in PDF format and upload to Moodle)

Examination – 40%    Date available from Exams Department (End of April/Start of May) – Due to Covid19 the usual exam will be replaced by an open book assignment which must be typed, saved as a PDF file format and uploaded to Moodle.

Maths Study Support (Note: Room and time may change from year to year)

• Day: Details available from your course coordinator

Component

Resources

Self Directed Learning(Revision) – Maths Basics

Course Topics

1 MODELLING USING MATHEMATICS
1.1 Explain the concept of a mathematical model to include the difference between mathematical models and physical models
1.2 Explain the modeling process in diagrammatic form
1.3 Solve simple mathematical models to include identifying situations requiring mathematical modeling, and using appropriate mathematical skills and processes
1.4 Apply simple mathematical models to explain and predict behavior

2 STATISTICS AND PROBABILITY
2.1 Discuss statistical concepts to include discrete and continuous variables, sampling, variance, skewness
2.2 Present information in a range of graphical and tabular forms, using pie charts, trend graphs, correlation diagrams (+/-), cumulative frequency curves, histograms and frequency tables with both discrete and continuous variables
2.3 Calculate the statistics for measuring and contrasting averages and dispersion of grouped data by calculating the mean, mode, median, weighted average, range, inter-quartile range and standard deviation
2.4 Calculate the number of possible outcomes on tests with no repetitions by using the Fundamental Principle of Counting, and Permutations and Combinations
2.5 Demonstrate an understanding of relative frequency and probability by using Information Technology simulations
2.6 Solve simple probability problems of one or two events including where two events are mutually exclusive and where two events are independent
2.7 Discuss findings, to include interpretation of results and distortions which may arise, and reasons for findings

Permutations/Combinations/Principle of Counting

Probability

3 FUNCTIONS AND GRAPHS
3.1 Describe the properties of basic mathematical functions to include linear, quadratic, exponential, log and trigonometric functions
3.2 Define the inverse of a function
3.3 Graph linear and quadratic functions showing the relationship between the domain and range
3.4 Derive the inverse of a function from its algebraic expression
3.5 Calculate the equation of a straight line using a range of formulae to include distance between two points, slope, parallel lines and perpendicular lines
3.6 Solve maximum and minimum problems with limitations given by linear inequalities from graphs of linear inequalities and half planes
3.7 Analyse graphs of linear and quadratic functions for important properties to include domain and range, maximum and minimum values, increasing and decreasing intervals, periodicity

Linear Programming

4 CALCULUS
4.1 Outline the key concepts of calculus to include limits, differentiation and integration
4.2 Explain the fundamental theorem of calculus
4.3 Calculate average rates of change for related variables x and y for a variety of standard functions y=f(x)
4.4 Differentiate simple standard functions using a table of derivatives
4.5 Use the Product Rule, Quotient Rule and Chain Rule to calculate the derivative of composite functions
4.6 Integrate standard integrals, polynomials, trigonometric and exponential functions
4.7 Calculate the area enclosed between a curve and the x-axis using integration
4.8 Apply differentiation to solve simple rates of change models to include maximum and minimum
4.9 Apply integration to solve simple practical real life problems

Videos

1. The following videos cover examples and exercises found in the notes below (4-5 Differentiation)
2. Differentiating polynomial equations – https://youtu.be/ZAfKwWzSaOE
3. Evaluating derivatives https://youtu.be/SvNH-BilB4U
4. Evaluating derivatives 2 https://youtu.be/WOVhKY9hTYI
5. Differentiation using Product Rule https://youtu.be/3fBqGnTaIig
6. Differentiation using Quotient Rule https://youtu.be/rQw7Bg8E8WE
7. Differentiation using Chain Rule https://youtu.be/BmjWL5LqLgM
8. Second Derivative 1 https://youtu.be/olFoFnw3XRM
9. Second Derivative 2 https://youtu.be/w0UT-HxVrmE
10. Slope and Turning Points https://youtu.be/wXjrA3W8PF4
11. Quadratic graph https://youtu.be/Fn73UiV6CIs
12. Quadratic graph continued https://youtu.be/3pnGXz60DAE
13. Graphs using differentiation https://youtu.be/UmqgoqZtf4c
14. Graphs using differentiation continued https://youtu.be/KCuMQyC4twQ
15. Cubic Graph & Turning Points https://youtu.be/I4svq9tc88M
16. Find where Cubic curve cuts X-axis https://youtu.be/mth8lmlIY9M
17. Speed and Acceleration https://youtu.be/1wFD7i6gKzQ
18. Speed/Acceleration P539Q9 https://youtu.be/P_cJK5H_h5s
19. Velocity (Rocket Example) https://youtu.be/Ft-P7mMcIaE
1. Integration – Power Rule https://youtu.be/SlakHC5VjBs
2. Integrals – Trigonometric https://youtu.be/WlOhmdx8GQA
3. Definite Integrals 1 – https://youtu.be/OlaS_h5RLJA
4. Definite Integrals 2 – https://youtu.be/YRCvp6STb_k
5. Area between graph and X-axis https://youtu.be/2zQiqzNTFgs
6. Area under graph y = x^2 +2 https://youtu.be/IsAjRDUszmo
7. Volume generated by rotating area between curve and x-axis about the X-axis https://youtu.be/1sbFpuQx3cQ

Notes and Exercises

5 Complex Numbers

5.1 Explain what is meant by a complex number
5.2 Represent complex numbers on the Argand diagram to include distinguishing between the modulus and the argument
5.3 Solve quadratic equations with complex roots
5.4 Perform mathematical functions on complex numbers including addition, subtraction, multiplication, division, conjugate, modulus, and plot on an Argand diagram

Videos

1. Writing a complex number in Polar form https://youtu.be/ZH8dcgxr-Zc
2. Complex number to a power and applying De Moivres Theorem https://youtu.be/gECgxudKcsM
3. Solving equations with Complex roots https://youtu.be/k0uvv-iBqdI
4. Solving equations with Complex roots continued https://youtu.be/7y4iAdCTnXU

Notes

5.5 Apply de Moivre’s Theorem to finding powers of Z and the cube root of 1

6 TRIGONOMETRY

6.1 Explore the uses of trigonometry in everyday life
6.2 Define sine, cosine and tangent functions as related to the unit circle
6.3 Solve practical, simple problems using appropriate trigonometric formulae and terminology, including the sine, cosine and tangent ratios for right angled triangles, area of triangle=1/2absin C, Sine Rule, Cosine Rule
6.4 Analyse the functions y = sinx, y = cosx, y = tanx and y = asinbx from plotted graphs by determining period, and amplitude.

Sample Exam Papers

End of Year Review

Moodle Quizes

Additional Notes, Exercises and Resources

Frequency Distribution – Standard Deviations

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Online Tests

Sample Exam Paper

Teaching Maths Resources

• Video how to teach Maths using OneNote – click here