Using and Managing Data and Information

November 2020 cohort

BA3020QA - Assignment 2

Note to students:

You are required to complete all Ten tasks by word processor on a single MS Word file. The submission of this assignment is by uploading it on Turnitin.

The deadline for this assignment is (Monday 12th April 2021 before 3pm).

Task 1: (5 marks)

Identify the numbers and buttons you would press on your calculator. Showing the steps in reaching your answer (2 decimal places), explain in words how you would calculate the following:

a) 1.64

b)

c) 1 / (1 + 0.7)3

d) 2500 × 5-2 e)

Task 2: (5 marks)

a) John phones his manager in New York.

Phone calls to New York are charged at the rate of £2.90 for a 5-minute call. John’s call costs £7.86. How long (in minutes) was his call?

b) A first time house buyer can make 240 monthly payments of £675 to repay the mortgage. How many monthly payments are required if she can pay £600 per month?

Task 3: (4 marks)

Simplify the following, leaving your answers in index form:

i) 53 × 55 ÷ 52 ii) 10-4 × 10-6 × 103 iii) (1/2)2 × (1/2)5 iv) 2-3 ÷ 2-5

Task 4: (2 marks)

How many combinations of 5 students can we make from a class of 12 students?

Show all your workings.

Task 5: (5 marks)

a) The equation of a line is given as y = 2x + 1

Explain the meaning of the values 2 and 1

b) In the diagram below:

i) Find the gradient of the line ii) Write the equation of the line in the form y = mx + b iii) Find the exact value of y when x is 5 Explain your methods clearly.

Task 6: (4 marks)

The length of a rectangle is double its width as shown:

(2x+3) width

length

Write down an expression for the perimeter of the rectangle.

Task 7: (12 marks)

Solve the following equations. Show each step of your workings.

a) 5x + 22 = 32

b) ?? = -4

5

c) 5(x +1) = 40

d) 5(x + 2) + 6(x + 3) = 39

e) ?? +7 = -5

2

f) x + 5 = 13 – x

g) 2(x + 3) = 4x – 4

h) 3(2x+3) + (2x-1) = 7(x-4) i) x – 3 = x

j) 5 - 2 ?? = 1 + ?? 5

k) 2??+7 = 5-5??

l) 5x + (?? + 3) = (?? - 1)

Task 8: (4 marks)

A furniture shop sells only one type of chair and one type of table. The following sales were recorded for two weeks:

5 Tables and 4 Chairs total £220

5 Tables and 1 Chair total £130

By solving these simultaneous equations, calculate the price of one chair and the price of one table, explain your reasoning.

Task 9: (4 marks)

Three friends are discussing their savings in the bank. Ali says he has £1,500 more than Banko and Cheng says he has triple the amount that Banko has. If Banko has

£x, write down an expression for the total amount of money that the three friends have in their bank.

Task 10: (5 marks)

In this task, you are asked to formulate the linear programming problem below. You are not required to solve it.

A sub-contractor produces two types of units for a kitchen manufacturer, a base unit (B) and cabinet unit (C).

The base unit requires 40 minutes in the production department and 30 minutes in the assembly department.

The cabinet unit requires 15 minutes in the production department and 25 minutes in the assembly department.

The production and assembly of these two units are done by specialist carpenters who are in short supply. Each day only 14 hours in the production department are available and only 8 hours are available in the assembly department.

Once sold, the base units contribute £16 to profit and the cabinet units £33 to profit.

Required:

Formulate the Linear Programming problem above by defining the control variables, stating the object function and the two constraints.

November 2020 cohort

BA3020QA - Assignment 2

Note to students:

You are required to complete all Ten tasks by word processor on a single MS Word file. The submission of this assignment is by uploading it on Turnitin.

The deadline for this assignment is (Monday 12th April 2021 before 3pm).

Task 1: (5 marks)

Identify the numbers and buttons you would press on your calculator. Showing the steps in reaching your answer (2 decimal places), explain in words how you would calculate the following:

a) 1.64

b)

c) 1 / (1 + 0.7)3

d) 2500 × 5-2 e)

Task 2: (5 marks)

a) John phones his manager in New York.

Phone calls to New York are charged at the rate of £2.90 for a 5-minute call. John’s call costs £7.86. How long (in minutes) was his call?

b) A first time house buyer can make 240 monthly payments of £675 to repay the mortgage. How many monthly payments are required if she can pay £600 per month?

Task 3: (4 marks)

Simplify the following, leaving your answers in index form:

i) 53 × 55 ÷ 52 ii) 10-4 × 10-6 × 103 iii) (1/2)2 × (1/2)5 iv) 2-3 ÷ 2-5

Task 4: (2 marks)

How many combinations of 5 students can we make from a class of 12 students?

Show all your workings.

Task 5: (5 marks)

a) The equation of a line is given as y = 2x + 1

Explain the meaning of the values 2 and 1

b) In the diagram below:

i) Find the gradient of the line ii) Write the equation of the line in the form y = mx + b iii) Find the exact value of y when x is 5 Explain your methods clearly.

Task 6: (4 marks)

The length of a rectangle is double its width as shown:

(2x+3) width

length

Write down an expression for the perimeter of the rectangle.

Task 7: (12 marks)

Solve the following equations. Show each step of your workings.

a) 5x + 22 = 32

b) ?? = -4

5

c) 5(x +1) = 40

d) 5(x + 2) + 6(x + 3) = 39

e) ?? +7 = -5

2

f) x + 5 = 13 – x

g) 2(x + 3) = 4x – 4

h) 3(2x+3) + (2x-1) = 7(x-4) i) x – 3 = x

j) 5 - 2 ?? = 1 + ?? 5

k) 2??+7 = 5-5??

l) 5x + (?? + 3) = (?? - 1)

Task 8: (4 marks)

A furniture shop sells only one type of chair and one type of table. The following sales were recorded for two weeks:

5 Tables and 4 Chairs total £220

5 Tables and 1 Chair total £130

By solving these simultaneous equations, calculate the price of one chair and the price of one table, explain your reasoning.

Task 9: (4 marks)

Three friends are discussing their savings in the bank. Ali says he has £1,500 more than Banko and Cheng says he has triple the amount that Banko has. If Banko has

£x, write down an expression for the total amount of money that the three friends have in their bank.

Task 10: (5 marks)

In this task, you are asked to formulate the linear programming problem below. You are not required to solve it.

A sub-contractor produces two types of units for a kitchen manufacturer, a base unit (B) and cabinet unit (C).

The base unit requires 40 minutes in the production department and 30 minutes in the assembly department.

The cabinet unit requires 15 minutes in the production department and 25 minutes in the assembly department.

The production and assembly of these two units are done by specialist carpenters who are in short supply. Each day only 14 hours in the production department are available and only 8 hours are available in the assembly department.

Once sold, the base units contribute £16 to profit and the cabinet units £33 to profit.

Required:

Formulate the Linear Programming problem above by defining the control variables, stating the object function and the two constraints.

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