RECENT ASSIGNMENT

ENM1500 Assignment 1 (Problem Solving 1)
You do not have to type your answers. Write by hand neatly and scan into a single PDF file for submission. If you are keen to type, go ahead but make sure to convert into a single PDF file for submission. Present working details.
Rubric:
1. 60-90 % marks will be awarded for a generally correct method of solving but occasional errors
2. 20-60 % marks for a sensible method of solving but serious or multiple errors
3. 10-20 % marks for an honest attempt showing some knowledge but largely incorrect solution
Question 1.
For the following expressions, arrange and simplify A - B - C, [30 marks]
A = x2 + xy - z , B = xy + y2 - 3z2 , C = 3x2 - y + z .
Your answer will be a formula A - B - C = ... with x, y and z in the right-hand side.
Question 2.
Simplify the expression [30 marks]
2y2 - z2 + y + xyz - 2{xzy + 3 - [1 + (z - y)2 + yz]}.
Question 3.
Open brackets in the given expression and simplify, [25 marks]
(a - b)2(a2 + 1 - b2).
Question 4.
Simplify [25 marks]
.
Question 5.
By hand, without using a calculator, sketch the following linear functions. High accuracy is not required. On your graphs, indicate only values of xintercepts and y-intercepts if they exist. Each item is worth 10 marks.
1. y = 1,
2.
y = -3x + 2.
Question 6. [20 marks]
By hand, without using a calculator, sketch the following functions. Each item is worth 10 marks. [50 marks]
1.
,
2.
,
3. y = x2 + 3,
4. y = -2x2 - 1,
5.
y = x2 - 2x - 3.
High accuracy is not required. On your graphs show: (a) the values of xintercepts and y-intercepts, (b) coordinates of maximum or minimum, (c) asymptotes (if exist).
Question 7.
Express y in terms of x. Your answer will be a formula y = ... with x in the
right-hand side. Each item is worth 10 marks.
1. lne - 2lnx - lny = 0,
2. log2 1 + log3 x + log3 y = 2,
3.
x = 3(1 + 3ey) ,
Do not replace symbol e by its decimal approximation, do not replace ordinary fractions by decimal fractions (for example, do not replace 1/3 by
0.33).
Question 8. [30 marks]
Solve the following equations. Each item is worth 15 marks.
1.
AxB1+x = Cx+5 .
Your answer will be a formula x = ... with A, B and C in the right-hand side.
2. [30 marks]
.
Same comment as for Q7.
Question 9.
The time t required to chemically change certain amount of substance into [30 marks]
another is given by
,
where M is the mass at the time t.
1. Sketch the graph t versus M with axis t going vertically and axis M going horizontally.
2. Re-arrange and express M as a function of t.
3. Sketch the graph M versus t with axis M going vertically and axis t going horizontally.
Each item is worth 10 marks.
Question 10.
[30 marks]
The amount of pollutant M in the atmosphere is decreasing with time t according to the formula
M = e-t/2 + 3.
1. Sketch the graph M versus t with axis M going vertically and axis t going horizontally.
2. Re-arrange and express t as a function of M.
3. Sketch the graph t versus M with axis t going vertically and axis M going horizontally.
Each item is worth 10 marks.
[Total:
300 marks]