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 = 2x2 + 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]

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 = 2x2 + 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]

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