Preliminary Mathematics General - Data and Financial Mathematics
Outcomes Assessed:
MGP-1 uses mathematics and statistics to compare alternative solutions to contextual problems
MGP-2 represents information in symbolic, graphical and tabular form
MGP-6 models financial situations relevant to the student’s current life using appropriate tools
MGP-7 determines an appropriate form of organisation and representation of collected data
MGP-8 performs simple calculations in relation to the likelihood of familiar events
MGP-10 justifies a response to a given problem using appropriate mathematical terminology
Topics Assessed
· Relative Frequency and Probability
· Mobile phones and plans
· Financial Mathematics
Task
Part A
You will prepare one A4 double-sided handwritten summary sheet of, what you consider to be, important formulae, definitions and notes on the three topic areas to be assessed. You will hand this in to your teacher insert date (day before in-class task)
Part B
Attached is a list of terms relevant to the three topic areas (Relative Frequency and Probability, Mobile phones and plans and Financial Mathematics). You will choose 15 terms from the list, five for each topic and prepare a handwritten glossary. You will hand this in to your teacher insert date (day of in-class task). For each word chosen, you are to write its meaning and provide an example of its application to Mathematics.
Part C
You will sit a written in-class task in four sections in class on insert date. The task will address each of the topic areas (Relative Frequency and Probability, Mobile phones and plans and Financial Mathematics).
In the first section of the written in-class task, you will be required to generate data from your calculator, using the random number generator. On the attached sheet you will find instructions on how to use this function on your calculator.
Word List for Part B
Frequency
Taxable Income
Leave Loading
Commission
Probability
Postpaid plan
Deductions
Prepaid plan
Experiment
Royalty
Overtime
Medicare Levy
Call rate
Relative Frequency
Outcomes
Retainer
Allowable Deductions
Flag fall
Download
Multistage Events
Wage
Double time
Call charge
Monthly Access Fee
Impossible
Complementary Events
GST
Bonus
Salary
Allowance
Equally Likely Outcomes
Gross pay
Time-and-a-half
Likely
Piecework
Budgeting
Unlikely
Sample Space
Net Pay
Tax Payable
Event
Certain
Random
Random Number generator instructions
Generating random numbers between to intervals on a Casio fx-82AU Plus calculator
Your calculator should now look like this
Section One – Relative Frequency and Probability
Question 1
a) Using your calculator, you are to model rolling a 10 sided die (numbered 1 -10 inclusive) 50 times using the random number generator function. Place your raw data in the space below.
(1 mark)
b) Complete the following frequency distribution table. (2 marks)
Score / tally / frequency / relative frequency1
2
3
4
5
6
7
8
9
10
Question 2 / Marks
a) Using your results, what is the relative frequency of obtaining a:
i. 5
ii. 7 or 10
iii. number greater than 4 / 1
1
1
b) Using your results, what is the expected frequency of obtaining a 2 if you were to roll a die 700 times? / 2
c) (i) What is the theoretical probability of rolling a 1 on a 10 sided die?
(ii) How does this compare to your experimental probability? / 1
1
Section Two – focus study “Maths and communication”
Basic / Big / Super / Mega
Monthly access fee / 29.00 / 49.00 / 79.00 / 99.00
Free calls / $120 / $300 / $600 / $800
Connection fee – Flag fall / 0.30 / 0.30 / 0.30 / 0.30
Call rates (per 30 sec) / 0.44 / 0.40 / 0.40 / 0.35
Messaging / SMS / 0.25 / 0.25 / 0.25 / 0.25
MMS / 0.50 / 0.50 / 0.50 / 0.50
The table above shows four mobile phone plans. Use it to answer the questions that follow.
(a) (i) Jack uses the Basic plan. What is his monthly access fee?
(ii) What is the charge for a two minute call? / 1
1
(b) Lauren used the Big plan last month and was charged $20.00 in addition to the monthly access fee. How many SMS messages did she send? / 2
Question 2 - On the next page is a mobile phone bill. Use it to answer the questions below.
(a) What is the mobile phone number? / 1
(b) How long is the plan to pay off the mobile phone? / 1
(c) What is the total cost of purchasing the phone? / 1
(d) What is the total due on this bill? / 1
Account 1234567890
/ Issued 22 April 2015
MobileNet 0432 123 456
Item / Service summary / Incl GST $
Call charges
411 / National direct dialled / to 13 april / 88 calls / 159.45
413 / Mobile originated SMS / to 13 april / 54 calls / 13.51
414 / Calls forwarded / to 13 april / 19 calls / 1.38
415 / MessageBank / to 13 april / 8 calls / 2.39
416 / Packet data sessions / to 13 april / 0.00
417 / Mobile enhanced SMS / to 13 april / 0.99
407 / Calls to Sensis / to 13 april / 1 calls / 1.75
408 / Included allowance / to 13 april / (cr)176.72
Services and Equipment Rental
439 / 1 Business Cap Plan Mro Bonus @ 20.00 per month rental credit / 14 April to 13 May / (cr)20.00
436 / 1 Business Mobile Cap Plan $49 @ 48.99 per month / 14 April to 13 May / 48.99
437 / 1 24 month mobile repayment option @ 32.45 per month / 32.45
Total for 0432 123 456 / 64.19
Section Three - Financial Mathematics
Below are three job advertisements. Use these to answer the questions on the following page.
Job A: Office Manager
The office manager is paid a salary in fortnightly instalments of $3 154. A bonus of 25% of a week’s pay is provided to the office manager if, at the end of the year, they meet the company’s targets.
Job B: Sales assistant at a retail store
This job pays a retainer of $12 per hour in addition to a commission on the following scale
Sales (per day) / Commission (%)First $200 / 5
Next $300 / 6.5
Thereafter / 8
Job C: Palm Tree maintainer on a tropical island
This job pays a wage of $10.50 per hour. There is a ‘height’ allowance of $2.50 per hour along with a $20 allowance per day if there is wet weather.
Question 1 / MarksUse the information on the previous page, regarding the job descriptions, to answer the following questions.
a) Find the yearly salary of the office manager if they meet the company’s targets. / 2
b) If the office manager was to take 4 weeks annual leave, calculate their pay for the 4 weeks assuming they receive 17.5% leave loading. (note: do not include the bonus) / 2
c) Calculate the weekly pay of the sales assistant given the following information. (Assume this is an average weekly pay.)
Day / Hours worked / Sales
Monday / 6 / $200
Tuesday / 6 / $350
Wednesday / 6 / $500
Thursday / 9 / $800
Friday / 6 / $400
Saturday / 3 / $75
Sunday / 0 / 0
/ 2
d) What is the average monthly pay of the palm tree maintainer if he works an average of 40 hours per week with 8 days in the month deemed as wet weather? (Assume this is the average monthly pay) / 2
e) Justify which job has the highest yearly pay. (Use the assumptions from the previous questions.) / 2
Section Four - Cloze passage (10 marks)
Complete each sentence using the most appropriate term.
1. A ______is a payment made to musicians, authors or others who create works for mass production for the general public to purchase.
2. A ______plan requires money to be paid monthly, for an agreed minimum time period, for network usage and costs incurred for calls, SMS and data downloads.
3. A fixed amount paid to employees per year is called a ______.
4. The conversion process between a ______and a megabyte is to multiply by 2 to the power 10.
5. Another term for experimental probability is ______.
6. ______is an extra payment made to employees when taking annual leave and is usually paid at a rate of 17.5% of a normal four weeks pay.
7. Regardless of the length of a phone call, each is charged a connection fee or
______.
8. Income based on the number of hours worked is called a ______.
9. In a ______event, P (E) = P (A) x P (B) .
10. The health care tax paid annually by employees is called the ______
______.
End of examination!