ENM1500
Assignment 1
When answering, link your mathematical working with short explanations, use good English and write in grammatically correct sentences.
Question 1.
For the following expressions, arrange and simplify A+B-C, [12 marks]
A = a3 – b, B = -2c + b – 2a3 , C = -4c + 2b + 2.
Question 2.
Simplify the expression [12 marks]
px – 3{p2 – 1 – [1 + (p – x)2 + px]}.
Question 3.
Open brackets in the expression [12 marks]
(x – 3)2(x + 1 – x2).
Question 4.
Simplify [12 marks]
.
Question 5.
By hand, without using a calculator, roughly sketch the linear functions [12 marks] represented by the following equations. High accuracy is not required. On your graphs, indicate only values of x-intercepts and y-intercepts (if they exist).
1. y = -4,
2.
y = 3x + 2.
Question 6.
By hand, without using a calculator, roughly sketch the functions [30 marks]
1.
,
2.
,
3. y = -x2 – 3,
4. y = 2×2 + 1,
5.
y = x2 + x – 2.
High accuracy is not required. On your graphs, indicate the values of xintercepts and y-intercepts (if they exist) and any other special values which, in your opinion, deserve being shown.
Question 7.
Express y in terms of x:
1. lne + lnx – lny = 0,
2.
5x – 3y+1 = 0,
3. log2 1 – log4 x + log4 y = 2,
4.
x = 2(1 + ey) ,
In your answers do not replace logarithms or exponentials by their decimal approximations.
Question 8. [20 marks]
Solve the equations
(a) AxB1+x = Cx+5
(express x through A, B and C). [20 marks]
(b) ln(
(if your answer includes number e, do not replace it by a decimal approximation but keep as a symbol).
Question 9.
The time t required to chemically change certain amount of substance into another is given by [20 marks]
,
where x is the mass that have been changed by the time t. Sketch the graph x versus t (with axis x going vertically and axis t going horizontally).
[Total:
150 marks]