Further Mathematics for Construction
Scenario:
You are working as an Engineering Research Technician in a research and development
laboratory where good analytical skills and understanding of mathematics is essential for
everyday work. Your line manager has informed you that you need to improve and update your
present Mathematical skills to work effectively & contribute to the research team. The essential
skills include Number theory, Matrices, graphical and numerical methods, Models of engineering systems using ordinary differential equations . To test your suitability for this position in research, the following tasks have been compiled for
you to complete.
Unit Learning Outcomes
LO1 Apply instances of number theory in practical construction situations.
Assignment Brief and Guidance
Task 1
a) Convert each number into denary,
• 11001.01
• 4D
b) calculate the following in both binary and denary
• 1101+1001
Task 2
Apply de’Moivre’s theorem or otherwise to solve for Zo and C from these expressions given
below :
Z0=Z/Y and C=Z*Y
Where:
• Z is a complex number.
• Y is also a complex number.
• Re (Z0) >0 and Re (C) >0
Find Z0 and C when:
Z = 1 + 5 j,Y = 1 − 3 j
Task 3
Create an identity and find the formula for cos (3θ) in terms of cos (θ) and sin (θ) using de Moivre’s
Theorem and test the identity with real values to confirm its validity.