# KL3008 - Foundation Trigonometry and Calculus

## What will I learn on this module?

You will learn about basic calculus such as graphs and equations of common functions, including trigonometric functions. The module further shows you how these mathematical concepts can be used in a variety of ways to help you in understanding and solving physical problems.

You will learn the below highlighted topics which is indicative rather than prescriptive:

1. You will learn to use of Pythagoras’ Theorem. Calculation of areas and volumes of common solids (10%)
2. You will learn to use Cartesian coordinates and simple coordinate geometry. Linear graphs. (10%)
3. You will learn to use the derivative related to the rate of change. Differentiation of standard functions. The second derivative. Maximum and minimum values of a function. (20%)
4. You will learn integration as the inverse of differentiation. Integration of standard functions. Area and definite integrals. (10%)
5. You will learn measurement of angles: degrees and radians. Right angled triangles: Pythagoras’ Theorem. Definition of sine, cosine, and tangent in a right angled triangle. Application problems. Graphs of sine and cosine functions over one cycle. Sine and cosine rules. (20%)
6. You will learn the definition of secant, cosecant, cotangent. Arc length and sector area. Definition of sine and cosine as co-ordinates on a unit circle (of angles in all quadrants). Graphs of sine, cosine, and tangent to emphasise their periodic nature. General solution to elementary trigonometric equations. Phase angle. Use of standard trigonometrical identities (Pythagorean, compound angle, double angle), in manipulation of expressions and their use in solving trigonometrical equations. (30%)

# How will I learn on this module?

You will learn on this module via a group approach where you and the staff will work together on developing methods and solving problems.

The module is assessed by means of an in-course assessment and a formal written examination, weighting 30% and 70% of the final mark, respectively. The in-course assessment is a test on trigonometrical and algebraic problems. The written examination will assess your competence on (1) the use of methods of coordinate geometry to obtain the equation of a line, (2) the solution of a variety of trigonometric equations making use of trigonometric identities and of the periodic nature of trigonometric functions where appropriate, and (3) the basic principles of differentiation and integration of standard functions, applying to simple mathematical and physical problems.

Coursework feedback will be provided individually and also generically to indicate where the cohort has a strong or a weaker answer to questions. You will receive both written and oral feedback from the coursework assessment, as well as formative feedback throughout the course, in particular during exercise classes/seminars.

# How will I be supported academically on this module?

You will be supported through lectures and exercise classes/seminars which will provide you with a formal teaching environment for core learning. In particular, exercise classes/seminars will provide you with opportunities for one-to-one interactions. Outside formal scheduled teaching, you will be able to contact the module team (module tutor, module demonstrator when assigned) either via email or the open door policy operated throughout the programme. Further academic support will be provided through technology-enhanced resources via the e-learning portal. You will also have the opportunity to give your feedback formally through periodic staff-student committees and directly to the module tutor at the end of the module.

# What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk

• Johnson A. & Sherwin, Foundations of Mechanical Engineering. Chapman and Hall 1996, Reprinted in 2001, Nelson Thomas.
• Watson K.L., Foundation Science for Engineerings Macmillan Press 1993.
• Gentle R, Edwards P & Bolton B, Mechanical Engineering Systems Butterworth - Heinemann 2001
• Ogrodnik P.J., Fundamental Engineering Mechanics, Longman 1997

# What will I be expected to achieve?

You will be able to:

Knowledge & Understanding:
MLO1. Use the methods of coordinate geometry to obtain the equation of a line.
MLO2. Solve a variety of trigonometric equations making use of trigonometric identities and the periodic nature of trigonometric functions where appropriate.
MLO3. Understand the basic principles of differentiation and integration of standard functions, applying to simple engineering problem.

Intellectual / Professional skills & abilities:
MLO4. Develop a firm foundation in the mathematics needed to cope with the demands of your degree course.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
MLO5. Communicate mathematical concepts at a fundamental level and understand the need to work to and meet prescribed deadlines.

# How will I be assessed?

Summative Assessments

Summative assessment is by two pieces of coursework to test concepts and method at an appropriate level, for students with varied backgrounds in Algebra and Trigonometry.

1. closed book assessment (30%)
Module Learning Outcomes addressed: MLO1, 2
Feedback will be made available within 20 working days.

2. Exam – 2 hours (70%)
Module Learning Outcomes addressed: MLO1, 2, 3, 4, 5
Feedback will be made available within 20 working days.

Formative Assessments

1. Problem-solving workshops
Module Learning Outcomes addressed: MLO1, 2, 3, 4, 5

Feedback will take several forms, including verbal feedback during the workshops; individual verbal and written comments on the coursework assessment delivered in class and via blackboard; written feedback on the exam.

NA

NA

# Module abstract

Foundation Trigonometry and Calculus introduces you to elementary calculus necessary to embark on undergraduate degrees and further study in scientific subjects. The module focuses on elementary analysis (equations and graphs of common functions) as well as elementary trigonometry. The module further shows how these mathematical concepts can be used in a variety of ways to help you in understanding and solving physical problems. Smaller group exercise classes/seminars will allow you to obtain help with specific problems. The module is assessed by means of an in-course assessment and a formal written examination, weighting 30% and 70% of the final mark, respectively. The module provides a good grounding for quantitative study as part of undergraduate study.

# What will I learn on this module?

You will learn about basic calculus such as graphs and equations of common functions, including trigonometric functions. The module further shows you how these mathematical concepts can be used in a variety of ways to help you in understanding and solving physical problems.

You will learn the below highlighted topics which is indicative rather than prescriptive:

1. You will learn to use of Pythagoras’ Theorem. Calculation of areas and volumes of common solids (10%)
2. You will learn to use Cartesian coordinates and simple coordinate geometry. Linear graphs. (10%)
3. You will learn to use the derivative related to the rate of change. Differentiation of standard functions. The second derivative. Maximum and minimum values of a function. (20%)
4. You will learn integration as the inverse of differentiation. Integration of standard functions. Area and definite integrals. (10%)
5. You will learn measurement of angles: degrees and radians. Right angled triangles: Pythagoras’ Theorem. Definition of sine, cosine, and tangent in a right angled triangle. Application problems. Graphs of sine and cosine functions over one cycle. Sine and cosine rules. (20%)
6. You will learn the definition of secant, cosecant, cotangent. Arc length and sector area. Definition of sine and cosine as co-ordinates on a unit circle (of angles in all quadrants). Graphs of sine, cosine, and tangent to emphasise their periodic nature. General solution to elementary trigonometric equations. Phase angle. Use of standard trigonometrical identities (Pythagorean, compound angle, double angle), in manipulation of expressions and their use in solving trigonometrical equations. (30%)

### Course info

UCAS Code F232

Credits 20

Mode of Study 1 year full-time followed by a further 3 years full-time study or 4 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2020

## Mathematics and Physics Foundation Year

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