Numeracy 2 E-Portfolio: Questions And Answers

Section 1 - 10 Questions

1. Anna deposited £3800 in a bank paying 3% simple interest rate.

 Find out how much interest she will receive after 1 year and 3 months.

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.

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.

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.

Your calculation should including steps such as:

1. a) Calculate slope (m)
2. b) Calculate y – intercept (c)
3. c) Create the linear equation for the line of the best fit (y = mx + c)
4. d) Calculate the future profit

The histogram shows weekly customers’ orders in one of the online clothing shop.

a)How many orders were sold in total?

b)How you describe the shape of the histogram?

c)How many orders were sold below £70?

d)What percent of all sold items are in a range price between £90 – 150?

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:

1. a) Work out the Net Present Value (NPV) of this investment.
2. b) Should the bakery proceed with this project?

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.

1. a) Find the probability that both pens are red
2. b) Find the probability that that first pen is green and the second one is red.

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?    

This reflective log should develop as the course proceeds and can 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?
• Are there areas for improvement?  
• How would you evaluate your participation on the module?

a)Explain the difference between a bar chart and a histogram. Point at least two characteristics.       

b)Create one real – life example that involves simple or compound interest. Support your example with appropriate calculations.

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 characteristics of Bar chart includes discrete variables that presents categorical data. Bar charts do not touch each other and so has spaces between each bar. whereas the 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.

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%

Section 1 - 10 Questions

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

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

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.

QUESTION 1

1. Put these in order starting with the smallest. 
2. b) Anna says that  is the same as. 

Show that Anna is wrong.

1. c) Write the number in standard form.

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: .  = 4³/4⁴ = ¼ = 0.25

C:  10⁸ ÷ 10⁹ = 10⁸/10⁹= 1/10 = 0.10

So the right answer is A than C and than B.

Answer to question b)

Value of  = 3* square root of 8 = 3*2.828 = 8.484

Value of  = 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

1. Anna deposited £3800 in a bank paying 3% simple interest rate.

 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.

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

Answer to Question B

Formula of future value using the compound interest rate is A = P[1+r/100]^T

Question 1

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

4. 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?

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). 

[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 = 1.045^T

Using Log we get

Log 1.30226 = log 1.045^T

Log 1.30226 = T * log 1.045

Dividing the both side by log 1.045 , we get

Log 1.30226/ log 1.045 = T

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

1+R = 1.060000698

R = 0.060000698 or 6.00

QUESTION 4

1. Calculate the intersect point for line y = 7x – 10 and y = 5x + 2 

1. b) Solve the inequality and choose a correct graphical representation for your result. 

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)

QUESTION 5 [5 marks]

Draw a line representing the given linear inequalitiesy > 3x + 1 and shade the region that satisfies this inequality.

x	-2	0	1
y

QUESTION 6 

The scatter plot presents the correation 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.

Your calculation should including steps such as:

1. a) Calculate slope (m)
2. b) Calculate y – intercept (c)

1. c) Create the linear equation for the line of the best fit (y = mx + c) 
2. d) Calculate the future profit 

TYPE YOUR ANSWER TO QUESTION

1. A)  Slope(m) =

Intercept point of line of best fit are (4000, 13057) and (6000, 17057)

Therefore m = (17057-13057)/(6000-4000) = 2

1. 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

Value of x: 8000

Y = 2*8000+ 5057

Y = 21057

So the future profit will be £21057

QUESTION 7

The histogram shows weekly customers’ orders in one of the online clothing shop.

1. How many orders were sold in total? 
2. How you describe the shape of the histogram? 
3. How many orders were sold below£70? 
4. What percent of all sold items are in a range price between £90 – 150? 

TYPE YOUR ANSWER TO QUESTION 7 HERE]

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

Question 2

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

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

After 4 years the equipment will be disposed off. The discount rate for this investment is 5% p.a., compounded annually.

1. a) Work out the Net Present Value (NPV) of this investment.
2. b) Should the bakery proceed with this project?

Explain your reasoning.

TYPE YOUR ANSWER TO QUESTION 8 HERE]

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.

1. a) Find the probability that both pens are red 
2. b) Find the probability that that first pen is green and the second one is red.

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%

P(Green) = 0 and P(Red) = 2/8 = 25% therefore P(Green) + P(Red) = 0+ 25% is equal to 25%

QUESTION 10

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

Section 2
In – class activity	25 marks

TASK 1 – Reflective log 

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
I understand what a power is	?	?	?	?
I can perform calculations and simplifications using power	?	?	?	?
I understand what a root is	?	?	?	?
I can perform calculations and simplifications using roots, using a scientific or financial calculator if required	?	?	?	?
I understand the idea of simple interest	?	?	?	?
I can perform simple interest calculations	?	?	?	?
I understand the idea of compound interest	?	?	?	?
I can perform compound interest calculations using a calculator if required	?	?	?	?
I understand the Rule of 72 (or 69 or 70) and can apply it.	?	?	?	?
I understand the idea of a linear relationship between two variables	?	?	?	?
I can manipulate a linear equation to calculate a variable	?	?	?	?
I can construct a scatter plot from a set of data (a linear relationship applies) and apply a line of best fit.	?	?	?	?
I understand the y-intercept and slope (gradient) of a graph and their relevance to real situations ().	?	?	?	?
I can use the scatter plot produced in part (12) to derive a linear relationship between two variables ().	?	?	?	?
I can use the relationship from part (14) to extrapolate and interpolate	?	?	?	?
I understand the idea of the future value of money	?	?	?	?
I understand the idea the net present value (NPV) of a project	?	?	?	?
I can complete a net present value calculation, using a calculator if required	?	?	?	?
I understand the idea of frequency distribution	?	?	?	?
I can read and interpret a histogram	?	?	?	?
I can construct a histogram from a set of data	?	?	?	?
I understand simple probabilities	?	?	?	?
I can perform probability calculations, using a calculator if required	?	?	?	?
I understand and can perform exchange rate calculations	?	?	?	?

TASK 2 [8 marks]

1. Explain the difference between a bar chart and a histogram. Point at least two characteristics. 
2. Create one real – life example that involves simple or compound interest. Support your example with appropriate calculations.

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.

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 = £ 370,00

TASK 3 

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 nameson the top right-hand corner of the screen
• Your test result is any score from 40% to 100