MATI3006 E18 Brief Only Main 2 1

Numeracy 1 (MATI3006) Portfolio

Autumn 2018 (E18)

Submission Deadline:2PM, 19th December 2018

Student Name

Student ID

Tutor

Section #1- Skills Audit [30%]

Task Instructions

You are required to answer each topic, providing clear and concise answers. Where

required, supply examples showing use of the said topics in real world problems. You should

also provide answers to the examples you write below. The suggested word count for this

section is 500 words.

Choose any number between 30 and 100. Can you create at least two different number sentences

that equal to this number? (for example :   󰇛  󰇜          󰇜

You must use at least three separate operations.

I have chosen 60

  󰇛 󰇜  

󰇛    󰇜 󰇛  󰇜  

Choose any two fractions with different denominators (e.g 

 

󰇜.Which one is larger? Show

your calculations, do not convert them as decimals or percentages.

I have chosen the following fractions 

  



To find out which fraction is larger we will write the two fractions to have the same denominator

The common denominator will be     





  







  



When the two fractions are expressed using common denominator, it is evident that 

 is larger

than 

 because it has a larger numerator.

Convert both fractions you have used above into decimal and percentages.



  

    



 

   

Provide one real life example for each of the following

>Percentage increase

>Percentage decrease

Show step by step calculations for each of your examples(questions)

Percentage Increase.

Peter scored 5 marks more in this term’s Mathematics quiz than he did in the previous

examination. In the previous mathematics exams he scored 30 marks. Calculate the percentage

increase in his scores.

  

 



  

Percentage Decrease.

A retail shop decide to give discounts to the clients during the thanksgiving period. The owner of

the shop reduce the price of a microwave from $90 to $81. Calculate the percentage decrease on

the microwave.

    

    

  

 



  

Give one real- world example(question) of reverse percentages and show your calculations to find

the answer?

The price of the imported phone increase will the decrease in the exchange rates. Last year the

price of the phone was $150, but this year, the price increased by 20% due to the changes in the

foreign exchange rates. Calculate the new price of the phone.

    󰇛  󰇜

 󰇛 󰇜 

Give one real- world examples each (question) of Direct and Indirect Proportions and show your

calculations to find the answer?

Direct Proportion.

When baking a bake the chef adds 4 cups of flour for every 1.5 cups of sugar. How much sugar will

be needed in case he uses 10 cups of flour?

Solution

If for 4 cups of flours he uses 1.5 cups of sugar then for 10 cups of flour he will use



  

Indirect Proportion.

In a factory, an increase in the number of workers decreases the time it takes to complete the

work. One the first day, the manager employed four people to work on the production section.

These individuals completed the work in 3 hours. On the next day, he hired two more workers since

he wanted the production to be completed faster. How long did the employees take to complete

the production on the second day assuming that all of them work at the same rate?

Solution

To calculate the time it take for the 6 workers to complete the work, the following formula will be

used.

  󰇛󰇜



The constant of proportionality will be determined using the first scenario.

      

The time taken by the 6 workers would then be:

Section #2- Online Test with Evidence [10%]

Paste your screenshots here, please try and keep them within this box:

  

 

Section #3- Reflection [15%]

Write a short reflection (approximately 100-150 words) about your personal learning experience of the

topics covered in this section. You may write about your learning style, lessons learnt, working in

groups, and about your skills you have developed studying this module

You can use the Skills Audit above to facilitate your answer.

I have learned a lot of concepts from the topics covered so far. I have learned how to

express a number in different ways using the various operations available. Before this

lesson, I never thought a number could be expressed using three different operators. I have

also learned how to determine which fraction is larger by putting the fractions to have a

common denominator. During class time, I didn’t know it was possible to determine a

larger fraction without using percentage or decimal. However, using the practical session

and groups work, I understood how the concept of common denominator could be used

instead of decimals or percentage.

Furthermore, during the group session, I learned how to find a percentage increase or

decrease and inverse percentage. This lessons stuck in mind because we did a lot of

examples and each group member solved at least one problem during the group work.

Finally, I learned how to solve indirect proportion questions which I could not previously. I

was excited and went ahead to help my other classmates who had problem-solving these

questions.

Section #4 [45 %]

4.1 Fill the data in the below table, follow these set of instructions:

a. Input total count of student numbers at random from the following range [200-650]

b. Calculate 2018 predicted numbers using following method: 12% increase from the mean

student numbers for all three previous years.

c. Calculate the Range for the number of enrolled students for all 4 years.

d. Draw an appropriate graph and comment on the data, highlighting any significant changes.

e. The number of students enrolled in the ‘Under 25’ category has increased by 15% between

2014 and 2015. Calculate how many students were in the ‘Under 25’ category in 2014.

f. Calculate the percentage change for the ‘Over 35’ category between 2016 and 2017.

g. There were 20% more females than males in 2016 under ’25-35’ category. How many male

students were enrolled in the same year and category?

h. What is the ratio of total students in ‘Under 25’ category to the total population for 2017?

Write your answer in a simplest form.

Student Count

2015

2016

2017

2018 (Predicted)

Under 25

400

550

560

25-35

300

420

480

448

Over 35

240

280

380

336

Show your calculations below, including drawing of the appropriate graph.

b) Under 25

󰇛  󰇜

 

25-35

󰇛  󰇜

 

Over 35

󰇛  󰇜

 

c) Range

  

Most of the students enrolled are under 25 years. There are very few students who are above 35

years. In 2015 the school enrolled few students while in 2018, the school predicts to enrol the

highest number of students.

    󰇛  󰇜



  

100

200

300

400

500

600

2015 2016 2017 2018 (Predicted)

Students Count

Year

The number of students enrolled per year.

Under 25 25-35 Over 35

  

 

    



  

g) Let the number of the males be x, then the number of the females will be 1.2x. To find the

number of males, we will solve the following equation

    

  

 

The number of males is 190.

h) Ratio

󰇛   󰇜

    

The ratio of the total students in ‘Under 25’ category to the total population for 2017 is   

4.2 You are required to provide a brief, between 100-200 words, summary of the information from

these two graphs below. Comment on changes in student population between years 2004-2014. You

may separate UG/PG students, comment on any changes and visible trends.

Undergraduate Students.

Most of the undergraduate students are 20 years and below. The total number of

undergraduate students enrolled increased gradually from 2005 to 2010. In late 2010,

however, the numbers decreased slightly. The decrease was felt in all the age groups

except in the age group of 21 to 24 years. From this observation, it could be concluded

that most of the students graduating from high school at that time were between 21 to 24

years. In 2012, the number of students who are 20 and below increased slightly then

flatten. However, the number of students between 25 to 4o years continued to decrease.

The decrease was because most of the students in this age brackets had already completed

their undergraduate courses in their earlier years.

Postgraduate Students

The number of students enrolling for postgraduate studies is increasing from one year to

the next. Most of the postgraduate students are between 21 to 24 years. This is fresh

graduates who have decided to further their studies. Although the number of students is

generally increasing, there is a slight decrease in the number of students in all the

categories in the year 2007 and 2012.

4.3 You decided to record number of times the bus was late during your morning commute. The

table below shows the time (t) the bus you usually take, was late over the 20-day period. You are

required to fill in the frequency and the calculate following:

TIME (T) IN MINUTES

FREQUENCY

0 ≤ t< 5

5 ≤ t < 10

10 ≤ t < 15

15 ≤ t < 20

a) Fill in the frequency information, make sure frequency adds up to the total recorded

experiment(n=20).

b) Estimate average number of minutes your bus was late.

c) Estimate what would be the Median for the above data.

Interval

Frequency(f)

Midpoint(m)

Product(mf)

0 ≤ t < 5

2.5

22.5

5 ≤ t < 10

7.5

10 ≤ t < 15

12.5

15 ≤ t < 20

17.5

Sum

135

Average



 

 

c) Median

Interval

Frequency(f)

Cumulative

frequency

0 ≤ t < 5

5 ≤ t < 10

10 ≤ t < 15

15 ≤ t < 20

   



  

  

 



 

   

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