Numeracy 2 (MAII3007) Coursework Portfolio

This is your Numeracy 2 e-portfolio for the semester commencing February 2018 (Spring 2018). It consists of two sections: Section 1 is worth 75% of the final mark and consists of 8 questions (70%) and periodic Skills Audit (carrying 5%). Section 2 consists of 3 tasks. Combined they are worth 25% of the final mark.

Student Name:
Student ID Number:
Tutor name:
This is your Numeracy 2 e-portfolio which you must submit by Wednesday 25th
April 2018 via the Student Portal.
Numeracy 2 (MAII3007) Coursework Portfolio
February 2018

Please read this carefully
This is your Numeracy 2 e-portfolio for the semester commencing February 2018 (Spring 2018). 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 you understand the policy and regulations about academic
misconduct. You must:
• Complete this work alone except where required or allowed by this 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’s 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.
This portfolio consists of two sections:
Section 1 is worth 75% of the final mark and consists of 8 questions (70%) and periodic Skills
Audit (carrying 5%).
Section 2 consists of 3 tasks. Combined they are worth 25% of the final mark.
Task 1 – Two Real life examples (8%)
Task 2 – Online Activity (10%)
Task 3 – Reflective log (7%)

Portfolio Contents
Week / Content Section 1
Question
Learning Outcome Page
Section 1
1. Recap numeracy 1. Introduction. Powers. Use of
calculator
1 * 1,2
2. Powers, root, logarithms. Use of calculator 2 * 1,2
3. Simple & compound interest 1 3,4 * 1,2
4. Linear relationships. Scatter plots. 5 * 1,2,3
5. Further linear relationships 5 * 1,2,3
6. The future value of money. Net present value. 6 * 1,2
7. Presentation of data. Histograms. 7 * 1,2,3
8. Probability. 8* 1,2
9. Revision None 1,2,3
Section 2
10. Real-Life Examples N/A 1,3
11. Online Activity N/A 1,2,3
12. Reflective Log N/A 1,2,3
* Also assessed in the online quiz, Section 2, Task 3

Section 1
This section should be filled in as you acquire the skills required for each question.
Answer all questions. Please show your workings and/or explain your results as required.
Marks will be awarded for good presentation. Please evaluate your progress using the skills
audits provided.
You may use your calculator as required.
You must show your working.
QUESTION 1 [6 marks]
Powers and Roots:
a) Simplify 75 x 72 (2 marks)
b) Simplify 103 ÷102 (2 marks)
c) Evaluate ( 123 )4 (2 marks)
Part a
75 x 72=72+ 5=77=823543
Part b
103 ÷102=103−2=101=10
Part c
( 123 )
4
=123+ 4=127=35831808

QUESTION 2 [8 marks]
a) Express the power 100 1/2 using the root notation and evaluate. (2 marks)
b) Evaluate 3
√ 1,000,000 (2 marks)
c) Simplify 7 3
√ 8−4 3
√ 8 (2 marks)
d) Scientific notation allows one to express large or small numbers in a simpler form.
Express the UK population of 65,648,000 in a scientific notation (2 marks)
Part a
1001 /2= √100=10
Part b
3
√ 1,000,000=10000001 /3=10 ( 6 ) 1
3 =102=100
Part c
7 3
√ 8−4 3
√ 8=7 ( 8
1
3 )−4 ( 8
1
3 ) =7 ( 23 ( 1
3 ))−4 ( 23 ( 1
3 )) =7 ( 2 ) −4 ( 2 ) =14−8=6
Part d
65,648,000 in scientific notation¿ 6.5648 ×107

SKILLS AUDIT: WEEKS 1 – 2
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
13. I understand what a power is ☒ ☐ ☐ ☐
14. I can perform calculations and
simplifications using power
☒ ☐ ☐ ☐
15. I understand what a root is ☒ ☐ ☐ ☐
16. I can perform calculations and
simplifications using roots, using a scientific
or financial calculator if required
☒ ☐ ☐ ☐
QUESTION 3 [10 marks]
Ann Miller invests £150,000 at an interest rate of 6% p.a.
Calculate the final balance after 5 years.
a) Using simple interest? (1 mark)
b) Using interest compounded annually? (3 marks)
c) Using interest compounded semi-annually? (3 marks)
d) Using interest compounded quarterly? (3 marks)
Part a

A=P+ PRT
100 =£ (150000+ 150000 × 6× 5
100 )=£ (150000+45000)=£ 195000
Part b
A=P(1+r )n=150000(1+0.06)5=£ 200,738.84
Part c
A=P(1+ r
2 )
nt
=150000(1+ 0.06
2 )
5× 2
=150000(1.03)10=£ 201587.46
Part d
A=P(1+ r
4 )
nt
=150000(1+ 0.06
4 )
5× 4
=150000(1.015)20=£ 202028.25

QUESTION 4 [10 marks]
a) Eliza invests £22,000 at a 2% interest rate annually.
Compounding the interest annually, how long will it take her
to receive the balance of £33,000?
(4 marks)
b) Using Rule 72, calculate how long will it take Eliza to double her investments?
(2 marks)
c) Mr Ramsbottom invests £32,000 in a bank savings account and after 10 years his
balance is £45,200.20.
Calculate the compound interest rate he received and round your answer to the
second decimal place.
(4 marks)
Part a
A=P(1+r )n
33000=22000(1+0.02)n
Dividing both sides of the equation by 22000 and simplifying we obtain
33000
22000 =22000
22000 (1.02)n
(1.02)n=1.5
Introducing logs on both sides of the equation we obtain
log(1.02)n=log1.5
nlog(1.02)=log 1.5
n= log1.5
log1.02 =20.475 years
Part b

At 2% interest, rule 72 confirms that it will take 36 years to double the investment.
Part c
A=P(1+r )n
45200.20=32000(1+r )10
Divide both sides by 32000 to obtain
45200.20
32000 = 32000
32000 ( 1+ r)10
45200.20
32000 =(1+ r)10
Introducing logs to both side of the equation we obtain
Log( 45200.20
32000 ¿=10 log (1+ r)
10 log ( 1+r ) =0.14999
log ( 1+r ) =0.014999
1+r =log−1 0.014999=1.4125
r =1.4125−1=0.4125=41.25 %
WEEKS 3 – 4

I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
17. I understand the idea of simple interest ☒ ☐ ☐ ☐
18. I can perform simple interest calculations ☒ ☐ ☐ ☐
19. I understand the idea of compound interest ☒ ☐ ☐ ☐
20. I can perform compound interest
calculations using a calculator if required
☒ ☐ ☐ ☐
21. I understand the Rule of 72 (or 69 or 70)
and can apply it.
☒ ☐ ☐ ☐
QUESTION 5 [8 marks]
a) Find the value of x if 15 x−10=50 (1 mark)
b) Solve the equation X + 20 = 70 (1 mark)
c) Solve the equation x−6
4 = 10 (1 marks)
d) To plot the linear graph of y = 3x + 10 complete the following table:
x - 8 -5 0 7 12 24
y -14 -5 10 31 46 82
(NO graph required)
(5
marks)
part a
15 x−10=50
15 x=50+10=60
x= 60
15 =4
Part b
x +20=70
x +20−20=70−20
x=50

Part c
x−6
4 = 10
x−6
4 × 4=10 × 4
x−6=40
x−6+ 6=40+6
x=46
WEEK 5
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
22. I understand the idea of a linear
relationship between two variables
☒ ☐ ☐ ☐
23. I can manipulate a linear equation to solve
for a variable
☒ ☐ ☐ ☐
24. I can construct a scatter plot from a set of
data (a linear relationship applies) and
apply a line of best fit.
☒ ☐ ☐ ☐
25. I understand the y-intercept and slope
(gradient) of a graph and their meaning to
real situations ( y=mx+c).
☒ ☐ ☐ ☐
26. I can use the scatter plot produced in part
(12) to derive a linear relationship between
two variables ( y=mx+c).
☒ ☐ ☐ ☐

27. I can use the relationship from part (14) to
extrapolate and interpolate
☒ ☐ ☐ ☐

Question 6 [10 marks]
Sarah Hair Saloon is considering an investment project to purchase and run a Hair Saloon
business. The initial cost is £55,000. The annual cash inflows (income) are projected to be as
follows:
Year 1 Year 2 Year 3 Year 4
£15,000 £25,000 £45,000 £15,000
The discount rate for this investment is 8% p.a., compounded annually.
a) Work out the Net Present Value (NPV) of this investment. (8 marks)
b) Should Sarah proceed with this project?
Explain your reasoning. (2 marks)
Part a
NPV =−C0+ C1
( 1+r ) 1 + C2
( 1+r )2 + C3
( 1+r ) 3 + C4
(1+r )4
NPV =−55000+ 15000
( 1+ 0.08 ) 1 + 25000
( 1+0.08 ) 2 + 45000
( 1+0.08 ) 3 + 15000
(1+0.08)4
¿−55000+ 15000
( 1.08 ) 1 + 25000
( 1.08 ) 2 + 45000
( 1.08 ) 3 + 15000
(1.08)4
¿−55000+13888.8889+21433.4705+35722.4509+11025.4478
¿−55000+82070.2580=27070.2580
NPV =£ 27070.26
Part b
Sarah should proceed with the project. The project is viable since the NPV is positive.

WEEK 6
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
28. I understand the idea of the future value of
money
☒ ☐ ☐ ☐
29. I understand the idea the net present value
(NPV) of a project
☒ ☐ ☐ ☐
30. I can complete a net present value
calculation, using a calculator if required
☒ ☐ ☐ ☐
Question 7 [10 marks]
A set of test scores, marked out of 100, is as follows:
66 93 75 58 68
53 65 92 94 62
63 74 93 92 95
58 94 62 78 96
62 64 87 66 57
a) Produce a tally of this data set suitable for the production of a histogram (3 marks)
b) Draw a histogram of this data set (6 marks)
c) Comment on the distribution of these marks. (1 marks)
Part a
We group the data in Excel using the data analysis function to obtain the table below
Range
Frequen
cy
50 0
55 1

60 3
65 6
70 3
75 2
80 1
85 0
90 1
95 7
100 1
Part b
Then, drawing the histogram we obtain
50 55 60 65 70 75 80 85 90 95 100
0
1
2
3
4
5
6
7
Histogram
Frequency
Score
Frequency
Part c
The histogram above shows that most of the scores lie between 60-74 implying that the median
lies there.
WEEK 7
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
31. I understand the idea of frequency
distribution
☒ ☐ ☐ ☐

32. I can read and interpret a histogram ☒ ☐ ☐ ☐
33. I can construct a histogram from a set of
data
☒ ☐ ☐ ☐
Question 8 [8 marks]
Probability is a measure of the likelihood and can be stated as a ratio, percentage or generally
as a number between zero and one.
a) What is the probability when the likelihood is impossible? (1 mark)
b) What is the probability when the likelihood is certain? (1 mark)
c) Express the probability of 0.06 as a % (2 marks)
d) Josiah tossed a coin and thrown a die at the same time (simultaneously). Work out the
probability of getting a head on the coin and a 5 on the die.
(4 marks)
Part a
The probability when the likelihood is impossible equals zero.
Part b
The probability when the likelihood is certain equals 1.
Part c
Probability of 0.06 as a percentage equals 0.06
1 × 100 %=6 %
Part d
Table 1 below shows the possible outcomes when tossing a coin and throwing a dice
simultaneously. H represents a head while T stands for the Tail. Also the numbers 1-6 represent
the number that appears on top when a dice is thrown.
Table 1: Total possible outcomes

1 2 3 4 5 6
H H1 H2 H3 H4 H5 H6
T T1 T2 T3 T4 T5 T6
Total possible outcomes=12
Probability ( Head∧a 5)=P( H 5)= 1
12
WEEK 8
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
34. I understand simple probabilities ☒ ☐ ☐ ☐
35. I can perform probability calculations, using
a calculator if required
☒ ☐ ☐ ☐
36. I understand and can perform exchange
rate calculations
☒ ☐ ☐ ☐

Section 2
Task 1 - Two Real life examples (100 words each) [8 marks]
Give two real-life situations or problems in businesses that involve the topics studied in
this module (e.g. powers and roots, simple and compound interests, linear
relationships, graphs, probabilities and Net Present values (NPV)).
[TYPE YOUR ANSWERS TO TASK 1 HERE]
(1) Net Present Value (4 marks)
NPV is a capital budgeting technique that takes into account the time value of
money when making calculations. Investors use the method as the basis for selecting
or rejecting a project. As a result, NPV can be positive, negative or zero. Positive
NPV implies that cash inflows are higher than cash outflows meaning that the
project is viable and should be accepted. A zero NPV denotes an equal amount of
cash inflows and cash outflows. A project may be considered to be acceptable when
it has zero NPV. On the other hand, a project with negative NPV should be ignored
since it brings losses.
(2) Linear relationships (4 marks)
Linear relations use one or more variables where one depends on another. Almost
every situation in life with an unknown quantity can be represented using linear
relationships. For instance, calculating mileage rates and predicting profit. Besides,
linear equations can be applied in calculating variable costs. For example, if a taxi
charges $8 to pick a person from a hotel and another $0.12 per kilometre travelled.
One can get a linear equation to find the total cost of the taxi over a given distance.
That is, setting x to represent distance covered and setting y to represent the total
cost. Therefore, the linear relationship will be y=0.12x+8
Task 2 - Online Activities [10 marks]
This relates to the quiz. Please complete and pass all three relevant quiz/activity;
screenshot and save the result’s screen ready to be pasted on the portfolio.
Ensure the followings are visible before the screenshot:
 Your full names on the top right-hand corner of the screen
 Your test result is any score from 40% to 100%

[PASTE YOUR SCREENSHOTS FOR TASK 2 HERE]
Task 3 - Reflective Log (150 words) [7 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. Start
your reflective log from week one by completing the skills audits and by writing
personal weekly notes after each topic. Please ask for your Tutor’s support if needed.
You may wish to consider the following points when providing your reflective
comments:
 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.)?
Reflective Log
Actually, before the semester I started I was clueless about how the semester could
unfold, bearing in mind of what I overheard from our predecessors. They could instil
fear in us that the course is tough. However, I was amazed to realize how simple and
informative the course was. Learning about powers, simple and compound interest,
probability and linear relationships in the first few classes of the semester was a bit
challenging. Particularly, probability. However, after concerted efforts through topical
tutorials, I was able to understand everything from the topic. This made me feel more
confident about the topic. Truly, I was amazed to know that these topics are applicable

in real life. Especially, the simple and compound interests which are crucial tools in
financial institutions.
Throughout the next couple of classes, I was thrilled to see how simpler the classes
became. I think this is attributed to the positive attitude and high self-esteem I
developed with time. I could perform calculations more easily and interpret real-life
word problems based on the understanding of the topics. However, I need to improve
my speed, especially when using a calculator to compute the calculations.