Numeracy 2 (MAII3007) Coursework Portfolio, Spring 2018, University

This Numeracy 2 portfolio assignment, submitted in April 2018, covers a range of financial and mathematical concepts. Section 1 includes detailed solutions and explanations for questions on powers, roots, simple and compound interest calculations, linear relationships, net present value, histograms, and probability. The portfolio demonstrates the application of these concepts through calculations and problem-solving. Section 2 requires the student to provide real-life examples related to the module's topics. The assignment also includes skills audits to self-assess understanding of the concepts. The student demonstrates proficiency in calculating powers, roots, interest (simple and compound), solving linear equations, working with NPV, creating histograms, and calculating probabilities.

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.
Please read this carefully
Numeracy 2 (MAII3007) Coursework Portfolio
February 2018

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.
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)
using the indices rule, we add the power when there is multiplication
= 75 +2=77
= 823543
b) Simplify 103 ÷102 (2 marks)
when there is division, we subtract the powers using the rule of indices.
= 103−2=101 = 10
c) Evaluate ( 123 )4 (2 marks)
In this case, the powers are multiplied as they are within a bracket.
= 123 ×4 =1212 = 8916100448256
[TYPE YOUR ANSWER HERE]

QUESTION 2 [8
marks]
a) Express the power 100 1/2 using the root notation and evaluate. (2 marks)
10 0
1
2 =¿ √ 100
= √10 ×10=10
b) Evaluate 3
√ 1,000,000 (2
marks)
c) Simplify 7 3
√ 8−4 3
√ 8 (2
marks)
7 3
√ 8−4 3
√ 8=7 3
√ 23 −4 3
√ 23
= 7 ×2−4 × 2 = 14 – 8
= 6
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)
This can be represented in scientific notation as 6.5648 ×107
[TYPE YOUR ANSWER TO QUESTION 2 HERE]

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)
A = p × r × t
P = £150,000, r = 6%, and t = 5 years.
A = 150000 × 6/100 × 5
= 150000 × 0.06 × 5
= £45,000
A = I +P
150000+45000
= £195,000

b) Using interest compounded annually? (3 marks)
A = P (1 + r)t
= 150000(1+0.06)5
= 150000(1.06)5
= £ 200733.8 4
c) Using interest compounded semi-annually? (3 marks)
A = P (1 + r/n)t, t = 2
= 150000(1+0.06/2)5×2
= 150000(1.03)10
= £ 201587.46
d) Using interest compounded quarterly? (3 marks)
A = P (1 + r/n)t, t = 2
= 150000(1+0.06/4)5×4
= 150000(1.015)20
= 202028.25098250841
[TYPE YOUR ANSWER TO QUESTION 3 HERE]

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)
A = P (1 + r)t,
33000=22000(1+0.02)t
t=log1.02 ( 3
2 )
t = 20.4753188576339 years
I will take approximately 20.5 years for the amount to be £33,000
b) Using Rule 72, calculate how long will it take Eliza to double her investments?
(2 marks)
The time required for the amount to double is;
= 72/r
72/2 = 36years
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)
A = P (1 + r)t,
45200.20 = 32000(1+r)10
1.41250625 = (1+r)10
1 + r = 10
√ 1.41250625 = 1.0351398733097
r = 0.03514
r = 3.514%
[TYPE YOUR ANSWER TO QUESTION 4 HERE]

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)
add 10 both sides
15x -10 + 10 = 50 + 10
15 x = 60
Divide both sides by 15
16x/15 = 60/15
X = 4
b) Solve the equation X + 20 = 70 (1 mark)
we subtract 20 on both sides of the equation.
X + 20 – 20 = 70 – 20
X = 50

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)
[TYPE YOUR ANSWER TO QUESTION 5 HERE]
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)
NPV = (C for Period 1 / (1 + R)1) + (C for Period 2 / (1 + R)2) ... (C for Period x / (1 + R)x) -
Initial Investment
= (15000/(1+0.08)1 + (25000/(1+0.08)2 + (45000/(1+0.08)3 + (15000/(1+0.08)4 – 55000
= £ 27070.2 6
b) Should Sarah proceed with this project?
Explain your reasoning. (2 marks)
Sara should proceed with the investment. This is because the Net present value of the investment
is more that the initial invested amount. In other words, the net worth is positive.
[TYPE YOUR ANSWER TO QUESTION 6 HERE]
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)
low
er upper
frequenc
y
50 < 54.99 1
55 < 59.99 3
60 < 64.99 5
65 < 69.99 4
70 < 74.99 1
75 < 79.99 2
80 < 84.99 0
85 < 89.99 1
90 < 94.99 6
95 < 99.99 2
25
b) Draw a histogram of this data set (6 marks)