Numeracy 2 (MAII3007) Coursework Portfolio Autumn2018

Numeracy 2 e-portfolio for the semester commencing October 2018 (Autumn 2018) with solved questions on powers, roots, simple and compound interest, linear equations, scatter plot, histogram, and NPV. Submit by Tuesday 18.12.2018 via the Student Portal.

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
3

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
5
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.
7
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.
8

x -2 0 1
y
TYPE YOUR ANSWER TO QUESTION 5 HERE]
9

-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:
11
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]
12

A:
Range No. of Orders
20-30 35
30-50 90
50-70 100
70-90 130
90-110 85
110-130 40
130-150 15
Total 495
B: Right Skewed Distribution
C: Orders sold below £ 70 are 225
D: Total items sold = 495
Items sold in a range price between £90 – 150 = 140
percent of all sold items are in a range price between £90 – 150 = 140/225 = 62.22%
QUESTION 8 [ 7 marks]
The owner of a bakery is considering an investment project to purchase new kitchen
equipment. The initial cost is £18,000. The annual cash inflows (income) are projected to be as
follows:
Year 1 Year 2 Year 3 Year 4
£1200 £1500 £900 £600
13
Week 8 – NPV

After 4 years the equipment will be disposed off. The discount rate for this investment is 5%
p.a., compounded annually.
a) Work out the Net Present Value (NPV) of this investment. (5marks)
b) Should the bakery proceed with this project?
Explain your reasoning. (2 marks)
TYPE YOUR ANSWER TO QUESTION 8 HERE]
A:
Year Cash Flows PVF @ 5% PV
0 -£ 18,000.00 1.000 -£ 18,000.00
1 £ 1,200.00 0.952 £ 1,142.86
2 £ 1,500.00 0.907 £ 1,360.54
3 £ 900.00 0.864 £ 777.45
4 £ 600.00 0.823 £ 493.62
NPV -£ 14,225.52
B: Bakery should not proceed with the project as it has negative net present value. When the
project has negative NPV it means cash inflows from the project will be lower than the net
investment in the project.
QUESTION 9 [7marks]
A box contains 2 red pens and 6 blue pens. One pen is taken at random and its colour noted
before being replaced. A second pen is taken.
a) Find the probability that both pens are red (3 marks)
b) Find the probability that that first pen is green and the second one is red. (4 marks)
TYPE YOUR ANSWER TO QUESTION 9 HERE]
A: Total pens = 8 pens
Red Pens = 2 pens
Probability that both pens are red = 2/8 or ¼ or 0.25 or 25 %
B: The first pen is green has zero probability and second one red is also 25%
14
Week 9 – Probability

P(Green) = 0 and P(Red) = 2/8 = 25% therefore P(Green) + P(Red) = 0+ 25% is equal to 25%
QUESTION 10 [4 marks]
The probability that Julie picks a winning ticket in a lottery is 0.3.
How many losing tickets are in the lottery if there are 390 tickets in total?
TYPE YOUR ANSWER TO QUESTION 10 HERE]
Total Tickets = 390
Tickets that has wining tickets = 30%
Number of wining tickets = 30% * 390 = 117
Number of Losing Tickets = 390-117 = 273
15

Section 2
In – class activity 25 marks
TASK 1 – Reflective log [5 marks]
This reflective log should develop as the course proceeds andcan 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.
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]
Skills audit I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
1. I understand what a power is ☐ ☐ ☐ ☐
2. I can perform calculations and
simplifications using power
☐ ☐ ☐ ☐
3. I understand what a root is ☐ ☐ ☐ ☐
4. I can perform calculations and
simplifications using roots, using a scientific
or financial calculator if required
☐ ☐ ☐ ☐
5. I understand the idea of simple interest ☐ ☐ ☐ ☐
6. I can perform simple interest calculations ☐ ☐ ☐ ☐
7. I understand the idea of compound interest ☐ ☐ ☐ ☐
8. I can perform compound interest ☐ ☐ ☐ ☐
16

calculations using a calculator if required
9. I understand the Rule of 72 (or 69 or 70)
and can apply it.
☐ ☐ ☐ ☐
10. I understand the idea of a linear
relationship between two variables
☐ ☐ ☐ ☐
11. I can manipulate a linear equation to
calculate a variable
☐ ☐ ☐ ☐
12. I can construct a scatter plot from a set of
data (a linear relationship applies) and
apply a line of best fit.
☐ ☐ ☐ ☐
13. I understand the y-intercept and slope
(gradient) of a graph and their relevance to
real situations ( y=mx+c).
☐ ☐ ☐ ☐
14. I can use the scatter plot produced in part
(12) to derive a linear relationship between
two variables ( y=mx+c).
☐ ☐ ☐ ☐
15. I can use the relationship from part (14) to
extrapolate and interpolate
☐ ☐ ☐ ☐
16. I understand the idea of the future value of
money
☐ ☐ ☐ ☐
17. I understand the idea the net present value
(NPV) of a project
☐ ☐ ☐ ☐
18. I can complete a net present value
calculation, using a calculator if required
☐ ☐ ☐ ☐
19. I understand the idea of frequency
distribution
☐ ☐ ☐ ☐
20. I can read and interpret a histogram ☐ ☐ ☐ ☐
21. I can construct a histogram from a set of
data
☐ ☐ ☐ ☐
22. I understand simple probabilities ☐ ☐ ☐ ☐
23. I can perform probability calculations, using
a calculator if required
☐ ☐ ☐ ☐
24. I understand and can perform exchange
rate calculations
☐ ☐ ☐ ☐
TASK 2 [8 marks]
17

a) Explain the difference between a bar chart and a histogram. Point at least two
characteristics. (4 marks)
b) Create one real – life example that involves simple or compound interest. Support your
example with appropriate calculations. (4 marks)
TYPE YOUR ANSWER TO TASK 2 HERE] A)A Bar chart is an illustrative picture of data that are
used to compare various types of data. A characteristic of Bar chart includes discrete variables
that present categorical data. Bar charts do not touch each other and so has spaces between
each bar. On the other hand, histogram is the graphical representation that shows data in form
of a bar to illustrate numerical data frequency and quantitative data. The characteristics of
Histogram and are connected to each other, so has no space and the delivery of non-discrete
variables, and histograms are grouped together in elements which are said to be ranges.
B:
Example: Mr. Rex has invested £ 250,000 for 10 years in bank giving simple interest of 12%. Now Mr. Rex
wants some money for new project in next 4 years. The question is that how much money Mr. Rex will
receive in next 4 years.
Amount Invested = £ 250,000
Time = 4 years
Interest R = 12%
Simple Interest = (£ 250,000 * 12 * 4) /100 = £ 120,000
Amount received in next 4 years = £ 250,000 + £ 120,000 = £ 370,000
TASK 3 [12 marks]
This section covers the online quiz. You must complete and pass all 3 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%
TYPE YOUR ANSWER TO TASK 3 HERE]
18

19

20