## Question

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.

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.

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%)

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 (2 marks)

b) Simplify (2 marks)

c) Evaluate (2 marks)

QUESTION 2 [8 marks]

a) Express the power 100 1/2 using the root notation and evaluate. (2 marks)

b) Evaluate (2 marks)

c) Simplify 7 (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)

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)

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?

b) Using Rule 72, calculate how long will it take Eliza to double her investments?

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.

Dividing both sides of the equation by 22000 and simplifying we obtain

Introducing logs on both sides of the equation we obtain

Divide both sides by 32000 to obtain

Introducing logs to both side of the equation we obtain

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

## Answer

a) Find the value of x if (1 mark)

b) Solve the equation X + 20 = 70 (1 mark)

c) Solve the equation = 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

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 (). ? ? ? ?

26.I can use the scatter plot produced in part (12) to derive a linear relationship between two variables (). ? ? ? ?

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)

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

Part b

Then, drawing the histogram we obtain

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.

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

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

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%

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:

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.