Numeracy 2 E-portfolio: Semester Commencing February 2018

• 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.)?

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.

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

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 must show your working.

QUESTION 1        [6 marks]

Powers and Roots:

1. a) Simplify  using the indices rule, we add the power when there is multiplication

= 823543

1. b) Simplify 

when there is division, we subtract the powers using the rule of indices.

1. c) Evaluate (2 marks)

In this case, the powers are multiplied as they are within a bracket.

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

1. b) Evaluate (2 marks)
2. c) Simplify 7 (2 marks)

1. 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

This can be represented in scientific notation as 6.5648

SKILLS AUDIT: WEEKS 1 – 2

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	?	?	?	?

Ann Miller invests £150,000 at an interest rate of 6% p.a.

1. 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

1. b) Using interest compounded annually? (3 marks)

A = P (1 + r)^t

= 150000(1+0.06)⁵

= 150000(1.06)⁵

1. 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

1. 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

1. 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 =  years

I will take approximately  years for the amount to be £33,000

1. 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 = years                                                                                             

200. 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. 

A = P (1 + r)^t_,

45200.20 = 32000(1+r)¹⁰

 = (1+r)¹⁰

1 + r =  =

r = 0.03514

r = 3.514%                                                                                                                      

I know how to….	I can do well	I need practice	I’m not sure	I can’t do
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 calculations using a calculator if required	?	?	?	?
9. I understand the Rule of 72 (or 69 or 70) and can apply it.	?	?	?	?

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

add 10 both sides

Portfolio Contents

15x -10 + 10 = 50 + 10

15 x = 60

Divide both sides by 15

16x/15 = 60/15

X = 4

1. 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

1. c) Solve the equation = 10 (1 marks)

1. d)           To plot the linear graph of y = 3x + 10complete the following table:                        

x	- 8	-5	0	7	12	24
y	-14	-5	10	31	46	82

 

I know how to….	I can do well	I need practice	I’m not sure	I can’t do
10. I understand the idea of a linear relationship between two variables	?	?	?	?
11. I can manipulate a linear equation to solve for 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 meaning to real situations ().	?	?	?	?
14. I can use the scatter plot produced in part (12) to derive a linear relationship between two variables ().	?	?	?	?
15. I can use the relationship from part (14) to extrapolate and interpolate	?	?	?	?

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.

1. 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

1. 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.

WEEK 6

I know how to….	I can do well	I need practice	I’m not sure	I can’t do
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	?	?	?	?

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

1. a) Produce a tally of this data set suitable for the production of a histogram (3 marks)  

lower		upper	frequency
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

1. b) Draw a histogram of this data set (6 marks)

1. c) Comment on the distribution of these marks. (1 marks)

the chart shows that there are fewer observations on the upper side of the chart which deviate from other data points. Thus, in this case, it means that the data have a relative longer tail to the right. Thus, it can be concluded that the data are positively skewed.

I know how to….	I can do well	I need practice	I’m not sure	I can’t do
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	?	?	?	?

Probability is a measure of the likelihood and can be stated as a ratio, percentage or generally as a number between zero and one.

1. a)  What is the probability when the likelihood is impossible?

the probability when the likelihood is impossible is zero. This means that out of all the possible outcome, the one selected cannot happen.

1. b)  What is the probability when the likelihood is certain?

The probability of a certain event is 1. In other words, there is 100% certainty that an event will occur. However, these events are rare. S

1. c)   Express the probability of 0.06 as a % (2 marks)  

to convert a decimal number to a percentage, we just need to multiply that number by 100.

0.06  100 = 6%                                     

1. 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.

In this case, the sample space is: {H1, H2, H3, H4, H, 5, H6, T1, T2, T3, T4, T5, T6}

Thus, there is only one chance out of 12 of getting a head on the coin and a 5 on the die.

The probability is, therefore,

I know how to….	I can do well	I need practice	I’m not sure	I can’t do
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 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)).

Week / Content

First, application of mathematics in real life is almost in each aspect. Compound interest rate is the most pronoun form of interest in which the interest rate is earned on a cumulative basis. This is mostly used to calculate the interest rates of loans, as they yield a higher revenue on loans as compared to the simple interest rate. A good example is a case where the interest rate is 10% and one borrows 10,000 for a period of two years. The interest earned in first years will be  = , the interest rate of the second-year amount will be calculated on this new amount. Therefore, loans are given on the basis of compound interest.

Graphs have a lot of uses in real life. First, plots such as bar graph are used in illustrating the trend of some factors over time. This is because they depict the trend clearer. The longer the column in the plot the higher the value associated with that category. Also, a plot such as scatter plot are used to determine whether two factors of variables are associated. The plot shows the strength and direction of the association. A good example is trying to understand the behaviour of sales using the amount invested on the advertisement. One can plot a scatter plot using sales as the dependent variable and advertising amount as the independent variable. The plot is used to determine whether there is a plausible relationship between the two variables.

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.

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

[PASTE YOUR SCREENSHOTS FOR TASK 2 HERE]

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.

[I have confidence in square root, solving equations and indices. Those I except the get quite good grade. Working with powers was quite interesting although I had some issues initially especially when working with either division of multiplication of numbers with equal base but different powers. In particular, understanding that when one is doing division, the powers should be subtracted, and when multiplying the powers should be added. However, I would like some improvement in the future values of investment and compound interest especially those that are computed either monthly or continuously. I have come across such a problem and finding the interest rate was quite hectic. Although this can be improved over time, I will try and do lots or research and practice on these areas.  I had a lot of headache understanding those concepts.  My contribution was quite well in class and discussions, and I did all the test with high integrity.]