YEAR 11 Mathematics Standard

Assessment 1: Research Assignment 1

Name: …………………………………………………………………………. Class / Teacher: ……………………………………..

Due Date: Thursday 21st May 2020 (Term 2 Wk 4B) Assessment Name: Research Assignment 1

Mark: /65 Weighting: 30 %

SYLLABUS OUTCOMES TO BE ASSESSED:MS11-1 A student uses algebraic and graphical techniques to compare alternative solutions to contextual problems. MS11-2 A student represents information in symbolic, graphical and tabular form. MS11-3 A student solves problems involving quantity measurement, including accuracy and the choice of relevant units. MS11-5 A student models relevant financial situations using appropriate tools. MS11-6 A student makes predictions about everyday situations based on simple mathematical models. MS11-9 A student uses appropriate technology to investigate, organise and interpret information in a range of contextsMS11-10 A student justifies a response to a given problem using appropriate mathematical terminology and/or calculationsDIRECTIVES TO BE ASSESSED:Compare: To estimate, measure, or note the similarity or dissimilarity between.Model: To give a representation of mathematical problem obtained.Predict: To make an educated guess about future events. Represent: To show a general relationship that expresses similarities between objects.Solve: To manipulate something for a particular purpose to find the answer for mathematical problems.Use: Apply, utilize or employ in a particular situation.

TASK DESCRIPTION:

PART A (21 marks) – Finding a job and calculating taxPART B (25 marks) – Formulas in everyday lifePART C (19 marks) – Measurement at home

As this task must be all your own work, your teacher will not help you with the questions. However, they may help you with similar questions from the textbook or other resources.

The topics assessed are:• Earning and Managing Money: F1.2 (NCM Ch 3)• Formulae and Equations: A1 (NCM Ch 2; Ch 12: 12.01, 12.03, 12.04)• Units of Measurement: M1.1 (NCM Ch 5: 5.01 - 5.04; Ch 6: 6.3, 6.4, 6.5)

Recommended Equipment: NESA-approved scientific calculator Pens, paper Internet-connected device An ordinary 6 sided die (web-based simulators can be used as an alternative, or use spreadsheet activity

p160-1 from the textbook)

STUDENT CHECKLIST:Have you:

o Revised the above topics, ensuring you have referenced syllabus documents?o Completed ALL relevant chapters in the textbook?o Asked your teacher or SLSO for clarification or help with any related class work, via email or Google

Classroom?

Marks by topic/outcome:

● Earning and Managing Money: F1.2 (MS11-5) /21

● Formulae and Equations: A1 (MS11-1) /25

● Units of Measurement: M1.1 (MS11-3) /19

TOTAL = /65

Markers’ Comments:

Student Reflection

Part A: Earning and Managing Money (F1.2) (21 marks)

1. Research and choose an occupation that you have an interest in (assume you have just finished Year 12, TAFE or University). (1 mark)

2. Find an online job advertisement describing the position and the rate of pay. (2 marks)

3. Calculate the fortnightly gross pay and the hourly rate of pay based on an average 40 hour week. (2 marks)

4. Using the current PAYG rate of tax from the ATO, calculate the tax payable on your gross income per

fortnight and per year. (2 marks)

5. Calculate the net fortnightly pay after tax. (2 marks)

6. Research and list some of the possible deductions associated with your chosen occupation. For your final calculations, research and estimate possible values for these deductions. (E.g. union and professional fees, $676 per year). (2 marks)

7. Calculate the taxable income for your occupation after deductions. (2 marks)

8. Calculate the Medicare levy payable. (3 marks)

9. Calculate the total tax payable on your salary. (3 marks)

10. State whether you will receive a refund or a debt statement from the ATO and how much is it worth (based on your PAYG calculations in part 4 and actual tax payable in question 9) (2 marks)

Relevant websitesJobseeker: https://www.jobseeker.org.auSeek: https://www.seek.com.au/Australian Tax Office: https://www.ato.gov.au/

See marking criteria at the end of this task for mark allocation.

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Part B: Formulas and Equations (A1) (25 marks)

Part 1 – A Drinking Scenario (4 marks)Arthur and his wife went to a BBQ. He had two glasses of white wine and she had three full strength beers. They both believe they are okay to drive home. What other factors would influence their BAC and thus their ability to drive home? Include at least 4 contributing factors.

Part 2 - Calculating BAC (6 marks)

Use the correct formula to calculate the BAC for the following situation:

BAC - Blood Alcohol contentN - Number of standard drinks consumedH - Hours drinkingM - Mass in kilograms

Using a random name and random number generator in Google, (or use a pair of dice, or make a spinner), complete the table below for 2 random people (1 male, 1 female) weighing between 61kg and 86kg*, drinking for between 1 and 6 hours, consuming between 1 and 6 standard drinks. Calculate BAC to 3 significant figures.

Name Sex N H M (kg) Working (substitution) BAC (3 s.f.)

M

F

*To calculate the weight with dice, roll two dice (or one twice) and add the product to 60kg. eg Rolling a 2 and a 3 would give a product of 2x3=6 and a total weight of 60 + 6 = 66kg.

Use a single die to produce numbers between 1 and 6 for N and H

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You could also create a spreadsheet as demonstrated in page 160-161 of the textbook (Chapter 4: Probability)Part 3 - Children’s Pain Relief Medication (10 marks)

Look at the packaging image for recommended dose of paracetamol below.

1. Panadol claims to be effective in the temporary relief of fever and pain associated with which of the following (circle ALL correct answers): (1 mark)

snake bite cold and flu teething burns headache sprains immunisation

2. When determining a dose, should you use the child’s age or weight? Justify your answer. (1 mark)

3. Roll two dice. Use the sum to represent the age of the child in years. What is the age and dose of Panadol required? (1 mark)

….. + ….. = ………. Years. Therefore, dose = …………..mL

4. Use Young’s formula to calculate the adult dose of Panadol based on the child dose in Q3: (2 marks)

child dosage= age∈ yearsage∈ years+12

×adult dosage

5

5. Roll two dice and calculate the product. Now add 5kg to find the weight of the child in kg. What is the weight and dose of Nurofen required? (to the nearest mL) (2 marks)

….. x ….. + 5 = ……….kg Therefore dose = ……….mL

6. Use Clark’s formula to calculate the adult dose of Nurofen based on the child dose in Q5: (2 marks)

child dosage=weight∈kg×adult dosage70

7. What relationship do you notice about the weight and dose on the Nurofen package? (1 mark)

Part 4 – Stopping Distance (5 marks)

1. You are driving a car down the road and suddenly see a kangaroo up ahead. a. Roll a die to determine your reaction time. (0 marks)

Reaction time = …….. seconds

b. Roll a die to determine your speed by multiplying it by 20. (Roll again in you roll a 1)

Speed = 20 x …… = …………….km/h (1 mark)

c. Calculate the distance you travel at this speed during your reaction time. (2 marks)

2. Now you apply the brakes.a. Calculate your braking coefficient (k) by rolling the die 3 times and adding the scores after the

last digit, eg a roll of 2, 3, 4 would give k = 0.004234: (0 marks)

K = 0.004 ... ... …

b. Use the formula below to calculate the braking distance d in metres, given the value for k above and v is the speed in km/h from Q1b: (1 mark)

d=k v2

3. Calculate the total stopping distance, using your answers to Q1 and Q2 above. (1 mark)

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Part C: Measurement at Home – Solar Energy (M1.1) (19 marks)

1. Using Google Earth or Google Maps, locate your home (we won’t check if it is really your home, just make sure it is not the same as someone else’s submission).

a. Solar panels should face North in Australia. Use the “Measure Distance” tool (right click for menu) to find the perimeter and area of the largest roof face which is closest to facing North on your roof. Paste screenshot below, showing perimeter and area. (2 marks)

Eg

b. In order to operate effectively, the solar panel installer has informed you that there must be a 5cm space between each row of panels, as shown below. Given this new information, draw a scale diagram of the layout of your panels, and determine how many full panels can actually fit on the roof section you have chosen. (2 marks)

(Hints: Measure the perpendicular height of the roof section. Use the scale 1cm=1m. Grid paper will help too - search for some on the internet if you don’t have your own. Make a cut-out solar panel)

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2. Each panel in the previous question is 330W panel. a. Calculate the total Watt rating of the system, according to your answer to Q1b. (1 mark)

b. Covert previous answer to kW. (1 mark)

c. Using the table below, predict how many kWh this system will produce each day for a building located in Sydney. (1 mark)

Average Daily Production table reproduced with permission from Clean Energy Council (http://www.solaraccreditation.com.au/consumers/purchasing-your-solar-pv-system/how-solar-pv-works.html)

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3. Use the Distance Measuring Tool to measure the length and breadth of your yard or block:a. Paste a screenshot for each below (2 marks)

b. What is the precision of the tool (according to the measurements you made)? (1 mark)

c. Calculate the absolute error (answer in metres) (1 mark)

d. Calculate the percentage error of the greatest measurement. (1 mark)

e. Calculate the lower limit and the upper limit of each measurement (2 marks)

f. Hence, find the maximum and minimum possible perimeters of your yard or block (2 marks)

g. Convert your maximum perimeter from m to mm (1 mark)

h. Re-write your answer to Q3g in scientific notation, with 2 significant figures (2 marks)

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END of TASK – check that you have completed each question.

Before submitting to Google Classroom, make sure your file name identifies you and the task

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Marking Rubric for Part A - Earning and Managing Money: F1.2 (MS11-5) /21

Question Marks Description1 0

1Occupation is not realistic for a new graduate (e.g. CEO of Australia post)Occupation is realistic and at an appropriate level of entry

2 012

Occupation stated with no evidence of researchOccupation stated with evidence and without a salaryOccupation and salary stated with evidence presented

3 012

Not attemptedOnly one of the calculations is correctBoth fortnightly and hourly rates are correct

4 012

P.A.Y.G. not calculatedP.A.Y.G. stated with no evidence of researchP.A.Y.G. calculated correctly and evidence is attached

5 012

Incorrect responsePartially correct working out and answerCorrect working out and answer

6 012

No deductions listed Possible deductions listed with no research proofPossible deductions listed with evidence of research

7 012

Incorrect or non attemptPartially correct working out and answerAll working out and answer are correct

8 0123

Incorrect or non attemptPartially correct working out and answerAll working out and answer are correctAll working out and answer are correct with evidence of Medicare Levi rates attached

9 0123

Incorrect or non attemptPartially correct working out and answerAll working out and answer are correctAll working out and answer are correct with evidence of Tax rates attached

10 012

Incorrect responseCorrect response with no explanationCorrect response with an explanation

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Marking Rubric for Part B - Formulae and Equations: A1 (MS11-1) /25

Question Marks CriteriaPart 1 0

1234

1 mark per factor mentioned from: license type, size and strength of beverage, weight, sex, time drinking, liver function, food consumption

Part 2 0123456

Male: (3 marks)1 mark for completing Name, N, H, M 1 mark for working (substitution)1 mark for BAC answer (to 3 significant figures)

Female: as per Male (3 marks)

Part 3Q1

01

Any mistake = 0Circle ONLY: cold and flu, teething, headache, immunisation

Part 3Q2

01

MUST JUSTIFY: Weight – because children of the same age can have a big range of weights so weight is safer. Also, the packaging states to use weight unless it is unknown.

Part 3Q3

01

Incomplete = 0Must fill all blanks – sum correct AND dose correct for age.

Part 3Q4

012

Answer only or incorrect substitution = 0Substitution but not solved = 1Correct substitution and solved to find answer = 2

Part 3Q5

012

No answer or dose onlyBlanks filled to find weight but no dose or incorrect doseBlanks filled to find weight and correct dose

Part 3Q6

012

No answer or answer only with no workingCorrect substitution but no answer or incorrect answerCorrect substitution and correct answer with working to solve equation

Part 3Q7

01

No answer or incorrect / irrelevant Relationship is linear / half a mL per kg of weight

Part 4Q1a

0 No mark for just rolling a die – this question is just for scaffolding and differentiation data

Part 4Q1b

01

Blank or incorrectMultiply above score by 20 correctly

Part 4Q1c

012

Blank or entirely incorrect workingConvert km/h to m/s with workingCalculate distance to nearest metre with working

Part 4Q2a

0 No mark for just rolling a die – this question is just for scaffolding and differentiation data

Part 4Q2b

01

Blank or entirely incorrect workingCorrect substitution and calculation of distance in metres

Part 4Q3

01

Blank or entirely incorrect workingCorrect answer, with working showing reference to previous answers

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Marking Rubric for Part C - Units of Measurement: M1.1 (MS11-3) /19

Question Marks Description1a 0

12

BlankScreenshot or measurements onlyScreenshot with perimeter and area clearly shown, as in example

1b 012

Blank Scale diagram correct but no panels or panels incorrectScale diagram correct and panels clearly drawn and counted

2a 01

Blank or incorrectWorking showing correct answer using previous answer

2b 01

Blank or incorrectCorrect answer using previous answer

2c 01

Blank or incorrectWorking showing correct answer using previous answer

3a 012

Blank or incorrect1 Screenshot showing either length or breadth1 Screenshot showing length AND 1 Screenshot showing breadth

3b 01

Blank or incorrectCorrect answer using previous answer

3c 01

Blank or incorrectCorrect answer using previous answer

3d 01

Blank or incorrectCorrect answer using previous answer

3e 012

Blank or incorrectCorrect answer for either lower or upper limits, using previous answersCorrect answer for both lower and upper limits, using previous answers

3f 012

Blank or incorrectCorrect answer for either maximum or minimum, using previous answers, with workingCorrect answer for both maximum and minimum, using previous answers, with working

3g 01

Blank or incorrectCorrect answer using previous answer

3h 012

Blank or entirely incorrectCorrect with either scientific notation or significant figuresCorrect with both scientific notation and significant figures

13

14

15