Module Title:  Mathematics 1 
Language of Instruction:  English 
Teaching & Learning Strategies: 
This module will be delivered using a mixture of lectures and tutorials.
The Institute Managed Learning Environment will be used to interactively communicate with students e.g. tutorial sheets, online tests, discussion forums, reference information.

Module Aim: 
To give the students the knowledge, competencies and skills necessary to support the mathematical procedures encountered in the other modules of this programme. 
Learning Outcomes 
On successful completion of this module the learner should be able to: 
LO1 
Apply fundamental algebra theory to solve different types of problems, equations and formulae. 
LO2 
Produce and interpret graphs; analyse various mathematical functions. 
LO3 
Prove trigonometric identities and solve triangles. 
LO4 
Solve problems using complex numbers and apply De Moivre’s theorem. 
LO5 
Apply appropriate rules and methods to differentiate various functions and solve calculus problems. 
Prerequisite learning 
Module Recommendations
This is prior learning (or a practical skill) that is recommended before enrolment in this module.

No recommendations listed 
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. 
No incompatible modules listed 
Corequisite Modules

No Corequisite modules listed 
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. 
No requirements listed 
Module Content & Assessment
Indicative Content 
Basic Algebra
• Apply rules of precedence in calculation
• Use calculator
• Apply rules of indices
• Convert units and use prefixes
• Add, subtract, multiply fractions and algebraic expressions
• Factorise algebraic expressions
• Solve simple equations, simultaneous and quadratic equations
• Transpose formulae
• Use log laws and solve log and exponential equations
• Form Partial Fractions
• Convert between the following number bases: decimal, binary, octal, hexadecimal
• Represent negative numbers in the binary system
• Use and apply permutations and combinations.

Graphs and Functions
• Plot and note properties of straight line and quadratic graphs
• Plot and note properties of log and exponential graphs
• Prove laws using linear graphs
• Use and apply graphs in engineering applications.

Trigonometry and Waveforms
• Solve rightangled triangles using Pythagoras’ theorem, trigonometric ratios sine, tangent and cosine and the inverse trigonometric functions
• Use the sine and cosine rules in the solution of nonright angled triangles
• Use degree and radian measure
• Verify trigonometric identities involving all six trigonometric ratios, compound angle formulae and sums and products of sines and cosines
• Apply identities e.g. electrical principles and communications
• Sketch graphs of waves including amplitude, period, frequency, phase angle, wave addition
• Use wave theory and apply it to electrical/electronic principles and mechanics.

Complex Numbers
• Represent complex numbers in Cartesian and polar form
• Convert from one form to the other
• Understand phasors
• Add, subtract, multiply and divide complex numbers in Cartesian form
• Multiply and divide complex numbers in polar
• Use De Moivre’s Theorem for powers and roots of complex numbers.

Differential Calculus
• Evaluate simple limits
• Differentiate simple polynomial functions from first principles
• Differentiate by rule algebraic, trigonometric, exponential and logarithmic functions using chain, product and quotient rules
• Apply the derivative as a rate of change and as the slope of the tangent to a curve.

Assessment Breakdown  % 
Continuous Assessment  30.00% 
End of Module Formal Examination  70.00% 
Continuous Assessment 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Other 
Each student will be obliged to complete a continuous assessment programme for which 30% will be awarded. This will involve class tests and other assigned tasks. 
1,2,3,4,5 
30.00 
n/a 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
Each student will sit a formal written examination at the end of the module for which 70% will be awarded. 
1,2,3,4,5 
70.00 
EndofSemester 
ITCarlow reserves the right to alter the nature and timings of assessment
Module Workload
Workload: Full Time 
Workload Type 
Frequency 
Average Weekly Learner Workload 
Lecture 
Every Week 
3.00 
Independent Learning 
Every Week 
3.00 
Tutorial 
Every Week 
1.00 
Total Hours 
7.00 
Module Delivered In
