Numeracy 2 (MAII3007) Coursework Portfolio Solution Autumn 2018

This Numeracy 2 (MAII3007) coursework portfolio from Autumn 2018 covers topics such as powers, roots, logarithms, simple and compound interest, linear relationships, scatter plots, histograms, net present value, exchange rates, and probability. The portfolio includes calculations and explanations for each question, demonstrating the application of these concepts. It also contains a reflective log, real-life examples, and online tasks. The solutions provided detail the steps taken to solve problems related to interest calculations, linear equations, statistical analysis, and investment appraisal. The student's work showcases their understanding of financial mathematics and its practical applications. Desklib provides access to this and other solved assignments to aid students in their studies.

Numeracy 2 (MAII3007) Coursework
Portfolio
Autumn2018
Student Name
Student ID
Tutor
This is your Numeracy 2 e-portfolio which you must submit by Tuesday
18.12.2018 via the Student Portal.
1

Please read carefully
This is your Numeracy 2 e-portfolio for the semester commencing October 2018 (Autumn
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 that 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 peoples’ 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.
2

The portfolio’s structure
Section 1 - is worth 75% of the final mark and consists of 10 questions.
Section 2 - is worth 25 % of the final mark and consist of three tasks.
Portfolio Contents
Week / Content Section 1
Question
Learning Outcome Page
Section 1
1. Recap numeracy 1.
Introduction, powers and use of calculator
1,2
2. Powers, root, logarithms. Use of calculator 1 1,2 4
3. Simple & compound interest 2,3 1,2 5
4. Simple & compound interest 2,3 1,2 5
5. Linear relationships 4,5 1,2,3 6 - 7
6. Further linear relationships 4,5 1,2,3 6 - 7
7. Scatter plots and Histogram 6,7 1,2,3 8 - 9
8. Net present value. Exchange rates. 8 1,2 8 - 9
9. Probability. 9, 10 1,2 10
10. Revision and in-class task 1,2,3
Section 2
11. Reflective Log N/A 1,3 11
12. Real-Life Examples N/A 1,2,3 13
13. Online tasks N/A 1,2,3 13
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Section 1
10 questions 75 marks
You are required to complete this section immediately after completing the class sessions
related to each question. Answer all questions and show your workings and/or explain your
results. Marks will be awarded for good presentation.
You must show your workings.
QUESTION 1 [11 marks]
a) Put these in order starting with the smallest. (6 marks)
A.(2¿¿−2)2 ¿
B. 43 ×4− 4
C. 108 ÷ 109
b) Anna says that 3 √8 is the same as3
√8. (3 marks)
Show that Anna is wrong.
c) Write the number in standard form.(2 marks)
0.00000000375
[TYPE YOUR ANSWER TO QUESTION 1 HERE]
Answer to question a)
Here we have to arrange in ascending order:
A: (2-2 )2 ]= (1/4)2 = 12 /42 = 1/16 = 0.0625
B: . 43 ×4− 4 = 43/44 = ¼ = 0.25
C: 108 ÷ 109 = 108/109= 1/10 = 0.10
So the right answer is A than C and than B.
4
Week 1 and 2 – Powers and roots

Answer to question b)
Value of 3 √8 = 3* square root of 8 = 3*2.828 = 8.484
Value of 3
√8 = cube root of 8 = 2
It shows that both values are not same. It proves that Anna is wrong.
Answer to question c)
The number 0.00000000375 is already in standard form
QUESTION 2 [9marks]
A. Anna deposited £3800 in a bank paying 3% simple interest rate. (3 marks)
Find out how much interest she will receive after 1 year and 3 months.
B.Amanda wants to invest £13,500. Two different institutions have offered her different
investment propositions. Showing your calculations, decide which investment option is more
beneficial for her. (6 marks)
Option 1
£13500 is deposited for 6 years in a bank paying 4% interest compounded annually.
Option 2
£13500 is deposited for 6 years in a bank paying 3.5% interest compounded semi - annually.
[TYPE YOUR ANSWER TO QUESTION 2 HERE]
Answer to Question A
Formula of interest= (Principle*Time*Interest Rate)/100
= £3800* 15 months * 3%/12
= £142.5
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Week 3 and 4– Simple and compound interest

Answer to Question B
Formula of future value using the compound interest rate is A = P[1+r/100]^T
Option 1: Future value will be = £13500* [1+0.04]^ 6 = £17081.81
Option 2: Future value will = £3500*[1+0.0175]^12 = £16624.43
Option 2 will be beneficial for Amanda
QUESTION 3 [6marks]
A. Sara invests £6850 at a 4.5% interest rate annually. How long would it take for Sara
to reach the balance of £8920.48 with annually compounding interest?(3 marks)
B. Matilda invests £8500 in a bank savings account and after 8 years her balance is
£13547.78.
Calculate the compound interest rate she received and round your answer to two
decimal places (2dp). (3 marks)
[TYPE YOUR ANSWER TO QUESTION 3 HERE]
Solution to A:
Principal = £6,850
Interest = 4.5%
Balance = £8920.48
£8920.48 = £6,850 (1+ 0.045/1)1*T
1.30226 = 1.045T
Using Log we get
Log 1.30226 = log 1.045T
Log 1.30226 = T * log 1.045
Dividing the both side by log 1.045 , we get
Log 1.30226/ log 1.045 = T
6

0.11469770 / 0.01911629
T = 6 years
Solution B:
Applying the given value in compound interest formula we get:
£13547.78 = £8500 * [1+ R/1] 8
Dividing £8500 by both side, we get
1.593856 = (1+R)8
8
√ 1.593856 = 8
√ (1+ R)8
1+R = 1.060000698
R = 0.060000698 or 6.00 %
QUESTION 4 [7 marks]
b) Calculate the intersect point for line y = 7x – 10 and y = 5x + 2 (4 marks)
b) Solve the inequality and choose a correct graphical representation for your result. (3 marks)
6t – 6 ≤ 8t – 12
A. B. C.
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Week 5 and 6 – Linear equations
-3
3-33
-3 3

D. E. F.
TYPE YOUR ANSWER TO QUESTION 4 HERE]
A: Intercept Point of y = 7x – 10 and y = 5x + 2
7x – 10 = 5x + 2
7x-5x = 10+2
2x= 12
X= 6
Y = 7(6)-10 = 32
Intersect point is (6,32)
B:
6t – 6 ≤ 8t – 12
6t -8t ≤ 6-12
-2t ≤ -6
t ≥ 3
The correct graphical representation will be C
QUESTION 5 [5 marks]
Draw a line representing the given linear inequalitiesy > 3x + 1 and shade the region that
satisfies this inequality.
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x -2 0 1
y
TYPE YOUR ANSWER TO QUESTION 5 HERE]
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-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5
-6
-4
-2
0
2
4
6
-5
1
4
Series2
Linear (Series2)
QUESTION 6 [10 marks]
The scatter plot presents the correlation between monthly expenses spent on advertising a
newly launched product and monthly profit from its sale. Knowing that the line of the best fit
crosses points (4000, 13057) and (6000, 17057) calculate the expected profit when company
invests £8000 for an advert.
10
Week 7 – Scatter plot and Histogram

2500 3000 3500 4000 4500 5000 5500 6000 6500 7000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
expenses
profit
Your calculation should including steps such as:
a) Calculate slope (m) (3 marks)
b) Calculate y – intercept (c) (3 marks)
c) Create the linear equation for the line of the best fit (y = mx + c) (2 marks)
d) Calculate the future profit (2 marks)
TYPE YOUR ANSWER TO QUESTION 6 HERE]
A) Slope(m) =
Intercept point of line of best fit are (4000, 13057) and (6000, 17057)
Therefore m = (17057-13057)/(6000-4000) = 2
B) y- intercept ( c )
y = mx + c
for intercept (4000,13057)
13057 = 2 *4000 + c
C = 5057
C:
Linear equation :
Y = mx + c
Y = 2 x + 5057
D:
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Expenses Profit
3000 11000
3500 11600
4000 12500
4500 13800
5000 14500
5500 16100
6000 16950
6500 18000

Value of x: 8000
Y = 2*8000+ 5057
Y = 21057
So the future profit will be £21057
QUESTION 7 [9 marks]
The histogram shows weekly customers’ orders in one of the online clothing shop.
20 - 30 30 -50 50 - 70 70 - 90 90 - 110 110 - 130 130 - 150
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Online order per purchase price
Order price [£]
Number of orders
a) How many orders were sold in total? (2 mark)
b) How you describe the shape of the histogram? (2 mark)
c) How many orders were sold below£70? (2 marks)
d) What percent of all sold items are in a range price between £90 – 150? (3 marks)
TYPE YOUR ANSWER TO QUESTION 7 HERE]
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