Notice of Assessment Task MATHEMATICS Stage …...1 Notice of Assessment Task MATHEMATICS Stage 5, Year 10 5.1/5.2 - 2020 Date of initial notification: Week 5 – Thursday (27/02/2020)

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Notice of Assessment Task

MATHEMATICS Stage 5, Year 10 5.1/5.2 - 2020

Date of initial notification: Week 5 – Thursday (27/02/2020)

Due Date of Task: Week 8 – Monday (16/03/2020)

Course component/Focus area/Topic/Module: Linear Relationships and Surface Area Topics included are: • Solve and analyse a variety of problems involving linear patterns. • Solve a variety of problems involving surface area.

Task Description: This task is an assignment to be completed in your own time. This assignment consists of 2 parts. The first part will assess your skills in Linear Relationships and the second part will assess your skills in Surface Area.

- In Part 1, you will be using your skills in linear relationships to analyse everyday scenarios that consist of linear patterns. In the first two questions, you will be given two everyday scenarios where you will answer questions to analyse the linear pattern and in the last question you will come up with your own scenario that represents a linear pattern.

- In Part 2, you will be using your skills in surface area to calculate the cost of painting your house and water tank with a waterproof paint. Question 1 will require you to build a house and a water tank using the prisms you have learned in class. Question 2 will require you to draw the surface area of your house and water tank and then calculate the surface area. In question 3, you will research a brand of waterproof paint and calculate the cost of painting your house and water tank.

Outcomes to be assessed in this task:

MA5.2-9NA, MA5.2-12MG

Marking Criteria: See Rubric at the back.

Task Number: 1 Time Allowed: 2 weeks Weighting of task: 20%

Mark Allocations: Part 1 (LR): /50

- Question 1: /17 - Question 2: /18 - Question 3 /15

Part 2 (SA): /25

- Question 1: /4 - Question 2: /9 - Question 3: /12

Total : /75

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Year 10 5.1/5.2 Assessment Task 1

Part 1: Linear relationships

In Part 1, you will be using your skills in linear relationships to analyse everyday scenarios that consist of linear patterns. In the first two questions, you will be given two everyday scenarios where you will answer questions to analyse the linear pattern and in the last question you will come up with your own scenario that represents a linear pattern. Question 1: The cost to hire an uber taxi is as follows:

• A base fare of $2.50 • $1.50 per kilometre travelled.

Let 𝑥 = the number of kilometers travelled, and 𝑦 = the amount of money spent in dollars ($). 1ai) How much will it cost (y) to travel 5km

Working: 𝑦 = 2.50 + (1.50 ×________) Answer: ________

1 mark

1aii) How much will it cost (y) to travel 10km Working: 𝑦 = 2.50 + (_______ × _______) Answer: ________

1 mark

1aiii) How much will it cost (y) to travel 15km Working: 𝑦 = ________ + (_______ × ________) Answer: ________

1 mark

1b) Complete the following table that represents the linear relationship of hiring an uber taxi.

𝑥 0 5 10 15 20 25

𝑦

3 marks

4

1c) Graph this linear relationship on the grid below. Make sure you label the axes.

3 marks

1d) Calculate the gradient using the rise/run method. Gradient = /012

/34 =

2 marks

1e) What is the y-intercept?

1 mark

1f) Come up with a formula that represents this linear relationship. [Hint: use the gradient-intercept form for an equation of a line]

2 marks

5

1g) If you have $40 to spend, how many km can you travel? [Hint: use the formula you created from part 1e]

3 marks

Question 2: You receive and inheritance of $20,000 from a relative who passed away. That money is kept in a bank account and the conditions of your inheritance only gives you access to $160 per week. Assume that each week you will spend the full $160. 2a) If 𝑥 = the number of week passed since receiving the inheritance

𝑦 = _________________________________________________________________

1 mark

2bi) How much will it money will be left in the inheritance account (𝑦) after 5 weeks? Working: 𝑦 = 20,000 − (160 ×________) Answer: ________

1 mark

2bii) How much will it money will be left in the inheritance account (𝑦) after 10 weeks? Working: 𝑦 = 20,000 − (________ × ________) Answer: ________

1 mark

2biii) How much will it money will be left in the inheritance account (𝑦) after 15 weeks? Working: 𝑦 = __________ − (________ × ________) Answer: ________

1 mark

2c) Complete the following table that represents this linear relationship.

𝑥 0 5 10 15 20 25

𝑦

3 marks

6

2d) Graph this linear relationship on the grid below. Make sure you label the axes.

3 marks

2e) Calculate the gradient using the rise/run method. Gradient = /012

/34 =

2 marks

2f) What is the y-intercept?

1 mark

2g) Come up with a formula that represents this linear relationship. [Hint: use the gradient-intercept form for an equation of a line]

2 marks

7

2h) How many years will this $20,000 last you?

3 marks

Question 3: Come up with your own scenario that represents a linear relationship, similar to the scenarios in question 1 and 2. 3a) Give a description of your scenario below 2 mark

3bi) 3bii)

Write down the variables: Let 𝑥 = __________________________________________________________ Let 𝑦 = ___________________________________________________________

1 mark 1 mark

3c) Complete the following table that represents this linear relationship.

𝑥 0

𝑦

3 marks

8

3d) Graph this linear relationship on the grid below. Make sure you draw and label the axis.

3 marks

3e) Calculate the gradient using the rise/run method. Gradient = /012

/34 =

2 marks

3f) What is the y-intercept?

1 mark

3g) Come up with a formula that represents this linear relationship. [Hint: use the gradient-intercept form for an equation of a line]

2 marks

9

Part 2: Surface Area In Part 2 you will be using your skills in surface area to calculate the cost of painting your house and water tank with a waterproof paint. Question 1 will require you to build a house and a water tank using the prisms you have learned in class. Question 2 will require you to draw the surface area of your house and water tank and then calculate the surface area. In question 3, you will research 2 brands of waterproof paint and use your mathematical skills to d You will first build a house and water tank, calculate the surface area of them and the determine the cost of paint required to paint all the inside walls on the house and water tank with waterproof paint. Question 1: 1a) Draw a 3D sketch of your house and include the appropriate dimensions.

[Hint: Most houses consist of a rectangular prism base and a triangular prism roof]

2 mark

1b) Draw a 3D sketch of your water tank and include the appropriate dimensions. [Hint: Most water tanks are designed in the shape of a cylinder]

2 mark

10

Question 2: 2a) Draw a net diagram of your house. Make sure you include all the dimensions.

[Hint: you can draw a separate net diagram for each prism part of your house)

3 mark

11

2b) Calculate the surface area of your house. Show all working below. ‘

3 mark

2c) Calculate the surface area of your water tank. Show all working below and round your answer to the nearest meter.

3 mark

12

Question 3: 3a) Research a brand of waterproof paint for the exterior of your house.

Record the following details below: Name of paint: ________________________ Website: _____________________________________________________________ How many litres of paint in one can: _______________ Cost of one can: _______________

2 marks

3bi) 3bii)

If 1 litre of paint covers an area of 15m2, how many litres do you need to cover the entire exterior of your house? How many cans to you need to purchase?

2 mark 2 marks

13

3ci) 3cii)

To waterproof your tank, you need to purchase a waterproofing membrane. It costs $49.50 for 4 litres of this waterproofing membrane. If 1 litre of this membrane covers an area of 10m2, how many litres do you need to cover the entire interior of your water tank? How many cans to you need to purchase?

2 marks 2 marks

3d) Calculate the cost of buying all the cans of paint.

2 marks

Year 10 5.1/5.2 Assessment Task 1 – Marking Rubric

Marks 1 2 3 Total Part 1 Linear Relationships

Question 1: Uber Taxi Question

1ai - Correct substitution and calculation

/1

1aii - Correct substitution and calculation

/1

1aiii - Correct substitution and calculation

/1

1b - Correct substitution of ‘0’ value - Correct substitution of ‘0’ value - some correct values

- correctly completed table of values

/3

1c - Correct labelling of axes and scale

- Correct labelling of axes and scale - Some points plotted correctly

- Correct labelling of axes and scale - All points plotted correctly

/3

1d - Correctly identifying either the rise OR the run

- Correctly identifying the rise AND the run

/2

1e - Correct y-intercept /1

1f - Attempt to come up with

formula with relevant numerical values

- Correct formula /2

1g - Correctly identifying that y=40 - Correctly identifying that y=40 - Attempt to solve equation

- Correctly identifying that y=40 - Solves the equations

/3

Total /17 Feedback: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Feedback: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Question 2: Inheritance Question 2a - Correctly defines y /1

2bi - Correct substitution and calculation

/1

2bii - Correct substitution and calculation

/1

2biii - Correct substitution and calculation

/1

2c - Correct substitution of ‘0’ value - Correct substitution of ‘0’ value - Some correct values

- Correctly completed table of values

/3

2d - Correct labelling of axes and scale



/3

2e - Correctly identifying either the rise OR the run


/2

2f - Correct y-intercept /1

2g - Attempt to come up with



2h

- Correctly identifying that y=0 - Correctly identifying that y=0 - Solves the equation

- Correctly identifying that y=0 - Solves the equations - Converts the values of months to

years

/3

Total /18

Feedback: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Question 3: Own Scenario Question

3a - Gives a vague description of scenario

- Gives a detailed description of the scenario

/2

3bi - Correctly defines the x variable /1 3bii - Correctly identifies the y variable /1

3c - Correct substitution of ‘0’ value

OR - Chooses appropriate x values

- Correct substitution of ‘0’ value - Some correct values

- Correctly completed table of values

/3

3d - Correct labelling of axes and scale



/3

3e - Correctly identifying either the rise OR the run


/2

3f - Correct y-intercept /1

3g - Attempt to come up with



Total /15

Marks 1 2 3 Total Part 2 Surface Area

Question 1: Drawing your house

1ai

- Drawing of rectangular prism and triangular prism of a house

- Drawing of rectangular prism and triangular prism of a house

- Write appropriate dimensions at all sides

/2

1aii - Drawing of a water tank in the

shape of a cylinder - Draw water tank as a cylinder - Write appropriate dimensions of

height and radius/diameter

/2

Total /4 Question 2: Calculating Surface Area

2a - Attempt to draw surface area diagram

- Correct surface area diagram - Correct surface area diagram - Correct labelling of dimensions

/3

2b - Attempt to calculate surface area

of house - Correct calculation for surface

area of most surfaces of the house.

- Correct calculation of the entire surface area of the house (roof and body).

/3

2c

- Identifies the formula for calculating the surface area of a cylinder and attempts to substitute the values in

- Correct calculation of surface area of a cylinder

- Correct calculation of surface area of a cylinder

- Correctly rounds answer to the nearest meter

/3

Total /9 Feedback: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________

Marks 1 2 3 Total

Part 2 Surface Area Question 3: Cost of Painting House

3a - Incomplete answers. - Completes all information about brand of paint

/2

3bi - Attempts calculation to find the amount of litres required

- Correct calculation /2

3bii - Recognises that you use answer

from previous part and attempts the calculation

- Correct calculation AND rounds to the nearest whole number

/2

3ci - Attempts calculation to find the amount of litres required


3cii - Recognises that you use answer

from previous part and attempts the calculation

- Correct calculation AND rounds to the nearest whole number

/2

3d - Recognises that you use answers

from previous 2 parts and attempts calculation


Total /12 Feedback: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Overall Feedback: Overall Mark: /75 ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Documents

Notice of Assessment Task MATHEMATICS Stage …...1 Notice of Assessment Task MATHEMATICS Stage 5, Year 10 5.1/5.2 - 2020 Date of initial notification: Week 5 – Thursday (27/02/2020)