Numeracy 2 (MAII3007) Coursework Portfolio

This is the Numeracy 2 e-portfolio for the semester commencing August 2019 (Summer 2019). It consists of 9 questions, an in-class task and three tasks. The questions cover topics like scientific notation, NPV, linear equations and inequalities, histogram, scatter plot and more. The document also includes examples of positive, negative and no correlation.

Numeracy 2 (MAII3007) Coursework
Portfolio
Summer 2019
Student Name
Student ID
Tutor
This is your Numeracy 2 e-portfolio which you must submit by Tuesday 20th
August 2019 via the Student Portal.
1

Please read this carefully
This is your Numeracy 2 e-portfolio for the semester commencing August 2019 (Summer 2019).
Please save a copy on your computer and back it up regularly (e.g. by saving it on your
computer/ in the cloud (e.g. Google Drive) / emailing it to yourself). You should print a working
copy and bring it to all lectures and tutorials. However, at the end of the course, you will need
to submit a completed electronic copy.
Please read carefully the module handbook, the marking criteria and the grade descriptors.
Academic Misconduct
You are responsible for ensuring that you understand the policy and regulations about
academic misconduct. You must:
• Complete this work alone except where required or allowed by the assignment briefing
paper and ensure it has not been written or composed by or with the assistance of any
other person.
• Make sure all sentences or passages quoted from other people’ work in this assignment
(with or without trivial changes) are in quotation marks, and are specifically acknowledged
by reference to the author, work and page.
The portfolio’s structure
Section 1 - is worth 65% of the final mark and consists of 9 questions.
Section 2 - is an in-class task and is worth 15% of the final mark.
Section 3 - is worth 20% of the final mark and consists of three tasks
2

Section 1
9 questions 65 marks
You are required to complete this section immediately after completing the class sessions
related to each question. Answer all questions and show your calculation and/or explain your
results. Marks will be awarded for good presentation.
You must show your workings.
QUESTION 1
[4 marks]
Which of these two numbers is bigger?
a) 5 - 3
b) 8.1 x 10-2
To answer this question, you must compare both numbers. For this purpose, convert both
numbers into decimals.
[TYPE YOUR ANSWER TO QUESTION 1 HERE]
a)5-3 b)8.1 x 10-2
= 1
53 = 1
125 = 0.008 = 8.1 x 1
102 = 8.1
100 = 0.081
Therefore, it is evident that 8.1 x 10-2 is bigger.
3
Scientific notation

QUESTION 2
[6 marks]
The car factory is considering an investment project to build a new production line. The initial
cost is £500,000. The annual cash inflows (income) are projected to be as follows:
Year 1 Year 2 Year 3
£420,000 £180,000 £160,000
After 4 years the equipment will add no cost. The discount rate for this investment is 7% p.a.,
compounded annually.
a) Work out the Net Present Value (NPV) of this investment
(5 marks)
b) Should the factory proceed with this project? Explain your reasoning.
(1 mark)
TYPE YOUR ANSWER TO QUESTION 2 HERE]
a) Discount Rate 7%
Year 0 1 2 3
Initial Investment
£5,00,000.0
0
Annual Cash Inflows £4,20,000.00 £1,80,000.00 £1,60,000.00
Discount Factor @ 7% 0.934579439 0.873438728 0.816297877
Present Value of Cash Inflows
£3,92,523.3
6
£1,57,218.9
7
£1,30,607.6
6
Net Present Value (PV of Cash Inflows - Initial Investment) £1,80,350.00
b) Yes the factory should proceed with this project as its Profitability Index is greater than 1,
i.e. £ 650,380
£ 500,000 = 1.3607.
4
NPV

QUESTION 3
[10 marks]
a) Solve the following equation: 3 x +2
7 = 2 x
2
(3 marks)
b) Solve the following inequality: 7 ( 3 x−2 ) >−8+3 x (3
marks)
c) What are the integer values of x that satisfy the inequality –2 < x ≤ 5
(1 mark)
d) Calculate the intersect point for lines: y=−8 x−5∧ y =4 x + 4 (3
marks)
TYPE YOUR ANSWER TO QUESTION 3 HERE]
a) 3 x +2
7 = 2 x
2 b) 7(3x – 2) > -8 + 3x
→ 6x + 4 = 14x → 21x - 14 > -8 + 3x
→ 4 = 14x – 6x → 21x - 3x > -8 + 14
→ 4 = 8x → 18x > 6
→ x = ½ or 0.5 → x > 6
18
→ x > 1
3
5
Linear equations and inequalities

c) The integer values of x that will satisfy the inequality are -1, 1, 2, 3, 4, 5. Zero (0 ) will
not satisfy as
integers can either be positive or negative but not zero.
d) y=−8 x−5 y=4 x +4
or, 8 x + y=−5→ equation (1) or, −4 x+ y=4 → equation(2)
Multiplying equation (2) by 2, and then adding equation (1) and (2) by simultaneous
equation
method, we have:-
8 x + y=−5 →equation (1)
−8 x +2 y=8 →equation (2)
-----------------------------------------------
3 y=3 or y=1
Now, substituting the value of ‘y’ in equation (1), we have:-
1=−8 x −5
or, 8 x=−1−5
or, 8 x=−6
or, x=−3
4 . Therefore, the two lines intersect at point (1, −3
4 ¿.
QUESTION 4
[5 marks]
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
Which of the linear equations is presented by the graph above?
(Justify your answer)
6

a. y=−3 x −2
b. y=3 x +2
c. y=3 x−2
d. y=−3 x +2
TYPE YOUR ANSWER TO QUESTION 4 HERE]
As can be seen from the graph, the co-ordinates of X-axis and Y-axis are as follows:-
X Y
0 -2
1 1
2 4
-1 -5
-2 -8
Now let us put the values of X in each equation to find the value of Y.
a) y=−3 x −2 or, y=−3(0)−2 or, y=0−2 or, y=−2
or, y=−3(1)−2 or, y=−3−2 or, y=−5
or, y=−3 (2 )−2 or, y=−6−2 or, y=−8
or, y=−3 (−1 )−2 or, y=3−2 or, y=1
or, y=−3(−2)−2 or, y=6−2 or, y=4
b) y=3 x +2 or, y=3 ( 0 )+ 2 or, y=0+2 or, y=2
or, y=3 ( 1 ) +2 or, y=3+ 2 or, y=5
or, y=3 ( 2 ) +2 or, y=6+2 or, y=8
or, y=3 (−1 )+2 or, y=−3+2 or, y=−1
or, y=3 ( −2 ) +2 or, y=−6+2 or, y=−4
c) y=3 x−2 or, y=3 (0)−2 or, y=0−2 or, y=−2
or, y=3 (1)−2 or, y=3−2 or, y=1
or, y=3 ( 2 ) −2 or, y=6−2 or, y=4
or, y=3 (−1 )−2 or, y=−3−2 or, y=−5
or, y=3 (−2)−2 or, y=−6−2 or, y=−8
d) y=−3 x +2 or, y=−3 ( 0 ) +2 or, y=0+2 or, y=2
or, y=−3 (1 )+2 or, y=−3+2 or, y=−1
or, y=−3 ( 2 ) +2 or, y=−6+2 or, y=−4
or, y=−3 (−1 )+ 2 or, y=3+ 2 or, y=5
or, y=−3 (−2 ) + 2 or, y=6+2 or, y=8
7

From the above calculations we find that equation (c) satisfies the above graph and hence we
can say that the graph is represented by the linear equation y=3 x−2.
QUESTION 5
[6 marks]
You have overrun your monthly phone limit of free minutes. Now, you have to pay 2 pence for
each minute you call. How long can you call if you have already gone beyond the bill by £4.50
and you do not want to exceed £10 of total additional cost?
a) Create the linear equation for this task. Explain what the slope and y-intercept represent.
(4 marks)
b) Calculate how many more minutes you can talk until you will exceed £10 of total additional
cost? (2 marks)
TYPE YOUR ANSWER TO QUESTION 5 HERE]
8

Here the ceiling for additional cost to pay for calls over and above the month free limit is £10.
Additionally, £4.5 has already been spent. Call rate per minute is 2 pence or £0.02. From the
information provided, the linear equation for the task is as follows:
£10 = £0.02x + £4.5
Here, the slope, i.e. £0.02 represents the rate at which the call is being charged per minute
and y-intercept, i.e. £4.5 represents the fixed amount (cost) that has already been spent. A
further increase in call duration (minutes) will lead to an increase in cost over and above the
fixed amount.
Number of more minutes that can be spent until the cost reaches £10:-
£10 = £0.02x + £4.5
or, £10 - £4.5 = £0.02x
or, £5.5 = £0.02x
or, x= £ 5.5
£ 0.02 =275 minutes .
QUESTION 6
[8 marks]
The data below represents the monthly average a person spends on clothes:
9
Histogram

72 50 68 68
80 69 78 70
95 64 85 71
106 79 80 69
a) Produce a tally of the data set. The tally must include 4 classes.
(3 marks)
b) Draw a histogram of the data set.
(4 marks)
c) Comment on the distribution of the data.
(1 mark)
TYPE YOUR ANSWER TO QUESTION 6 HERE]
Here the lowest monthly average is 50 and highest monthly average is 106. We now find the
width as the tally must include 4 classes as mentioned.
Calculation for tally width
106−50
4 and 106−50
4−1 = 56
4 and 56
3 = 14 and 18.67. Therefore, the width of the class must
be between 14 and 18.67. For our simplicity purpose, we take 16 as the class width.
a) Therefore the tally dataset is as follows:-
Class Tally Frequency
50 – 65 || 2
66 – 81 |||| |||| | 11
82 – 97 || 2
98 – 113 | 1
10

b) Histogram
50 – 65 66 – 81 82 – 97 98 – 113
0
2
4
6
8
10
12
Frequency
c ) Analysing the Histogram above, we can say that the data is highly constricted towards the
class interval 66 – 81, i.e. almost 75% of people have a monthly average expenditure between
66 to 81 on clothes.
11

QUESTION 7
[11 marks]
The company producing kitchen equipment has received an order for 780 cooking pots.
The scatter plot presents the production of cooking pots in time. Knowing that the line of the
best fit crosses points (4.5, 233.5) and (6, 313) calculate the time needed to fulfil the order.
Your calculation should include steps such as:
a) Calculate the slope (m)
(2 marks)
b) Calculate y – intercept (c)
(2 marks)
c) Create the linear equation for the line of the best fit (y = mx + c)
(2 marks)
d) Calculate the time needed to fulfil the order.
(2 marks)
12
Scatter plot

e) What type of correlation is presented in this question. Justify your answer.
(3 marks)
TYPE YOUR ANSWER TO QUESTION 7 HERE]
a) Since the line of best fit crosses points - A (4.5, 233.5) and B (313, 6), therefore we can say
that after 4.5 days the production of cooking pots reaches 233.5 units and after 6 days the
production of cooking pots reaches 313 units.
Again when we analyse the graph, we see that on Day 0(zero) there is no production, i.e. 0
units.
Therefore, Production per day can be calculated as 233.5
4.5 = 51.89 units as per Point A, and
313
6 = 52.17 units as per Point B.
Since, there are two values of per day production, we take the arithmetic mean of the two as
our Rate of Production per day which becomes our slope in this case. Therefore, Slope (m) =
51.89+ 52.17
2 = 52.03.
b) Since the line passes through the point (0, 0) [discussed in (a)], therefore y-intercept is
zero.
c) Equation of the line: Y = mx + c
Here, Slope(m) = 52.03 and c (y-intercept) = 0,
Therefore, the equation of this line is: Y = 52.03x
d) Order for Cooking Pots (Y) = 780
Therefore total time required = 780
52.03 = 14.99 ≈ 15 days.
e) This question represents a positive correlation wherein one variable increases with the
increase of the other, i.e. with increasing number of days, the production of cooking pots also
increase and vice-versa.
13

QUESTION 8
[3 marks]
Give three examples which present: positive, negative and no correlation, respectively one
example for each.
TYPE YOUR ANSWER TO QUESTION 8 HERE]
The examples of a positive, negative and no or zero correlation are as follows:-
Positive Correlation: Profit and Revenue – With the increase in Profits, it can be presumed
that there is an increase in Revenue but the reverse may not always hold.
Negative Correlation: Velocity and Time – A vehicle moving at a higher velocity will tend to
cover a distance at a lesser time against the vehicle moving at a lesser velocity for the same
distance.
No or zero correlation: Rotation of the Earth with respect to a Person’s Height.
QUESTION 9
[12 marks]
14
Probability

The cinema’s box office sells tickets for three movies: A, B and C for a Saturday evening. The
capacity of each screening room is 70 seats. The cinema expects 170 customers that evening.
The probability that the customer will buy a ticket for movie A is 0.45 and for Movie B is 0.35.
Prices for tickets
a) Calculate the expected number of customers who will buy the ticket for movie A.
(2 marks)
b) Calculate the probability of buying a ticket for the movie C.
(2 marks)
c) Assuming that every one in five people will spend £10 on beverages and sweets, calculate the
total cash inflow that day for the cinema. (tickets plus beverages and sweets)
(4 marks)
d) If the number of the sold tickets is lower than 45% of the screening room capacity the movie
will not be shown again. Which movie accordingly will not be shown again?
(4 marks)
TYPE YOUR ANSWER TO QUESTION 9 HERE]
15
Movie A Movie B Movie C
£8.50 £12.00 £10.50

Section 2
In – class activity 15 marks
This section covers in – class task. The task consists of 8 questions. Students have 1 hour to
answer all questions. The task is worth 15% of the final mark.
You must complete the task in the class. The picture of the answer box from the in-class task
must be pasted on the portfolio. Ensure the followings are visible before taking a picture:
 Your full name
 Your test results
 Tutor’s signature
 Date
PASTE HERE THE SCREEN SHOT OF THE ANSWER SHEET OF THE IN – CLASS TASK]
Section 3
20 marks
Task 1 [5 marks]
This reflective log should develop as the course proceeds and may be the last part to be
completed. Reflect honestly on your experiences throughout the semester. For this reason, you
can use the skills audits to summarise all topics covered during the ten weeks.
Words limit is approx. 100 - 150 words.
In your reflection you must comment on the following points:
 Which topics do you feel most confident about?
(e.g. powers and roots, interest rates, NPV etc.)
 Are there areas for improvement?
(e.g. in probability, I need do practice more or research etc.)?
 How would you evaluate your participation on the module?
(e.g. contribution to classes, independent study etc.)?
TYPE YOUR ANSWER TO TASK 1 HERE

Summarizing the above work done by me, I must say that the exercise covered almost all the
topics taught throughout the semester. Questions were conceptual based and I had a better
understanding of the various applications of these concepts. The topics that I felt most
confident were NPV and powers and roots as well as Linear equation problems. However,
Probability was a bit tricky and I think I need to concentrate more on this topic to have a
clear, better and in-depth understanding. It was a brain-teasing session which I enjoyed a lot
while reviving my past learning.
Apart from this, I explored how to use symbols and make equations in Word which added to
my skill development. Tally was another perfect exercise for mental ability. I learnt how
analyse, interpret and use data. This assignment helped me to assess my mental ability where
I found out my Strengths and Weaknesses
Overall it was really a challenging session for me and most importantly it reminded me of my
golden period- my School Days.
Task 2 [5 marks]
Do lines y = -5x + 3 and y = 5x + 2 have an intersect point? Justify your answer.
TYPE YOUR ANSWER TO TASK 2 HERE]
Let us solve the two linear equations simultaneously.
y=−5 x +3 → equation (1) y=5 x +2 → equation (2)
Or, 5 x+ y=3 or, −5 x+ y=2
5 x+ y=3
−5 x+ y=2
-----------------------
2 y=5, or, y=2.5
Putting the value of ‘y’ in equation (2), we have: y=5 x +2
Or, 2.5=5 x +2
Or, 0.5=5 x
∴ x= 0.5
5 ¿ 0.1
Therefore, solving the two linear equations we find that both the lines intersect at
point (0.1, 2.5) and hence the answer is justified.
Task 3 [10 marks]

This section covers an online quiz. You must complete and pass all three-relevant
quiz/activities; screenshot and save the result’s screen ready to be pasted on the portfolio.
Ensure the followings are visible before the screenshot:
 Your full name on the top right-hand corner of the screen
 Your test result is any score from 40% to 100%
[PASTE YOUR SCREENSHOT FOR TASK 3 HERE]