Mathematical equations
Project description
The Brief

a) Simplify as a single fraction: 4/(2x+1)- 2/(x+3)

(5 marks)

b) Express as the sum of partial fractions (5x-4)/((x-2)(x+1))
(10 marks)
c) Find the simultaneous solutions to:

y=4x^2+7x+4 and y=x+2

analytically and graphically (plot in the range -2=x=1)
(10 marks)

d) The velocity of an accelerating object was measured over equal time periods.

t (sec) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
v (m.s) 20.0 23.1 26.2 29.8 33.0 36.0 39.5 42.2 45.5 49.0 52.2

Draw a graph of the results and determine a relationship between v and t.
Check the relationship using regression
Compare the relationship obtained with standard equations of motion and determine the initial velocity and acceleration of the object

(10 marks)

e) An object starts from rest and accelerates uniformly. The distance travelled in equal time intervals is measured, and the results tabulated.

t (sec) 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
s (m) 0 14.8 59.7 136 240 375 535 740 965 1210 1500

Draw a graph of the results in a software package such as Excel
Use a trendline to obtain a relationship between s and t.
Verify the relationship by converting the plot to a straight line graph
Estimate the distance travelled in 12 seconds
(15 marks)

Module lecture and support notes.