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COWRA HIGH SCHOOLASSESSMENT TASK COVER SHEET

This sheet must be attached to the front of your Assessment Task and submitted to your class teacher on or before the due date.

Student’s Name: _________________________________________

Course: _________________________________________

Assessment Task: _________________________________________

Date Due: _______________

Date Received: _______________

Extension granted _____ days Other circumstances ~ documents attached

I certify:a) This assignment is entirely my own work and all borrowed material has been acknowledgedb) The material contained in this assignment has not previously been submitted for assessment in any

formal course of studyc) I retain in my possession a copy of this assignmentd) I understand that late assignments will be penalised unless an extension has been granted by Deputy

Principal - Curriculum

Student’s Signature: ____________________________

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COWRA HIGH SCHOOLAssessment Task (Student’s Copy)

Student’s Name: _________________________________________

Course: _________________________________________

Teacher: _________________________________________

Assessment Task received by: _________________________________________

Signature: _________________________________________

Date: ______________________ Time: ______________________

Please detach this if the Assessment Task has been handed in to the office and give to student to keep for their own records.

COWRA HIGH SCHOOL

Year 11 Assessment Task

NAME: Task 1 – Assignment/InvestigationCLASS: 11MAB / 11MAA

TEACHER: Mrs Yates / Mr Howard

COURSE: Mathematics Advanced TASK No: 1 Unit: Functions

DATE DUE: 9/4/2020 TIME DUE: 2 Weeks

MARK: 90 WEIGHT: 35% PRESENTATION: Word document

SYLLABUS OUTCOMES: A Student:Introduction to Functions MA-F1.2Linear, Quadratic and Cubic Functions MA-F1.3Further Functions and Relations MA-F1.4

DESCRIPTION OF TASK:

Students are to complete both parts of the task. The assignment is to be submitted digitally through either Google classroom or sent to teacher via email – [email protected].

MARKING CRITERIA:

Allocation of marks can be found throughout the task. Marks are awarded for correct mathematical reasoning and/or calculations.

mailto:[email protected]

COWRA HIGH SCHOOLAssessment Task Submission Policy

Submission of assessment tasks by students must follow faculty guidelines. There are basically four types of assessment tasks:

1. In Class Assessment Tasks ~ these tasks are supervised by the class teacher and collected by the class teacher at the conclusion of the assessment task. It is the responsible of the student who miss in class assessment tasks to contact the Head Teacher of that faculty.

2. Formal Examinations ~ at the conclusion of any formal examination the assessment task papers are to be collected and returned to the relevant faculty teacher.

3. Major Projects / Pieces of Work ~ these items, due to their size, are usually kept in the appropriate faculty location. Major works and projects should be kept in safe locations that minimises the risk of damage. Any assessment task would be submitted directly to the teacher. A receipt for the task will be issued to students.

4. Take Home Assessment Tasks ~ these are tasks that students are required to complete by a due date. Students should follow faculty submission guidelines regarding submission of these tasks.

Guidelines for the Submission of Assessment Tasks

1. When an assessment task is issued, the information provided to students will include: a clear statement of what the task involves and what the expectations of the student are an explanation of the marking criteria / outcomes to be assessed the due date of submission an assessment task submission cover sheet ~ see attached

2. Teachers should record the names of all students issued with the assessment task on a roll/class list and have the student acknowledge receipt of the assessment task by getting them to sign next to their name.

3. Students must take their assessment task to the class teacher. They must be signed in on the class roll and keep their receipt

4. All students must keep a copy of their assessment task.

Illness and Misadventure Appeals

If a student fails to submit an assessment task by the due date and has a legitimate reason than normal illness and misadventure procedures will apply.

REQUEST FOR ASSESSMENT EXTENSION PROCEDURE

Assessment extensions will only be granted in exceptional circumstances. All requests need to be made in writing using the extension request form. In seeking an extension discuss your request with your teacher/Head Teacher at least three (3) days before the due date with work already completed.

Forms for Illness/Misadventure and Extension can be accessed on the Cowra High School Website.

Part A – Investigating Graphs (80 Marks)

Using Geogebra, (https://www.geogebra.org/graphing), you will investigate a number of different types of graphs and their translations and dilations. You will also investigate how these variations impact on the domain and range of the graph.

Students are required to complete both parts of the task. Your screenshots, calculations and/or responses are to be placed/typed into the relevant section of the assignment.

How to Use Geogebra:

1. Go to https://www.geogebra.org/graphing. Alternatively, you can go to https://www.geogebra.org/download?lang=en-AU and download Geogebra onto your computer.

2. Type each equation in the input box provided and press ‘enter’.

For: Linear functions, type y=x Quadratic functions, type y=x^2 Cubic functions, type y=x^3 Hyperbolas, type y = 1/x Absolute value functions, type y=|x| Circles, type x^2+y^2=1. For the square root of a number, use the square root button

on the Geogebra keyboard.

3. A screenshot of your graph can be done using the snipping tool, or something similar.

Linear Functions: (13 Marks)

https://www.geogebra.org/download?lang=en-AU

https://www.geogebra.org/graphing

https://www.geogebra.org/graphing

y=mx+c

1. Using Geogebra, sketch the graph of y=x and place a screenshot of this graph in the empty space in the table below. Complete the required details (domain, range, x-intercept, y-intercept, odd/even/neither function) in the table below. 4

Equation: y=x

Domain:

Range:

x-intercept:

y-intercept:

Odd/Even/Neither:

Give a reason, either algebraically or graphically, for your decision.

2. Using Geogebra, sketch the following graphs in the form y=mx on the same number plane.

y=−2x, y=12x, y=4 x, y=−1.5x

Insert a screenshot of your graphs in the space below. 1

3. Explain how the value of m affects the shape, position, domain and range of the graph. 2

4. Using Geogebra, sketch the following graphs in the form of y=x+c on the same number plane.

y=x+3, y=x−4, y=x−14 , y=x+1.6


5. Explain how the value of c affects the shape, position, domain and range of the graph. 2

6. Using Geogebra, sketch the following graphs of the form y=c.

y=−4, y=2.5, y=−12 , y=1


7. a) Explain how these graphs, in the form y=c, differ from the original graph of y=x? 1

b) What affect does the value of c have in these cases? 1

Quadratic Functions: (13 Marks)

y=a ( x+h )2+c

1. Using Geogebra, sketch the graph of y=x2 and place a screenshot of this graph in the empty space in the table below. Complete the required details (domain, range, x-intercept, y-intercept, odd/even/neither function) in the table below. 4

Equation: y=x2

Domain:

Range:

x-intercept:

y-intercept:

Odd/Even/Neither:


2. Using Geogebra, sketch the following graphs in the form y=a x2 on the same number plane.

y=−2x2, y=12x2, y=4 x2, y=−1.5x2


3. Explain how the value of a affects the shape, position, domain and range of the graph. 2

4. Using Geogebra, sketch the following graphs in the form of y=x2+c on the same number plane.

y=x2+3, y=x2−4, y=x2−14 , y=x2+1.6



6. Using Geogebra, sketch the following graphs of the form y= (x+h )2.

y= (x−4 )2, y= (x+2.5 )2, y=(x−12 )2

, y= (x+1 )2


7. Explain how the value of h affects the shape, position, domain and range of the graph. 2

Cubic Functions: (13 Marks)

y=a ( x+h )3+c

1. Using Geogebra, sketch the graph of y=x3 and place a screenshot of this graph in the empty space in the table below. Complete the required details (domain, range, x-intercept, y-intercept, odd/even/neither function) in the table below. 4

Equation: y=x3

Domain:

Range:

x-intercept:

y-intercept:

Odd/Even/Neither:


2. Using Geogebra, sketch the following graphs in the form y=a x3 on the same number plane.

y=−2x3, y=12x3, y=4 x3, y=−1.5x3



4. Using Geogebra, sketch the following graphs in the form of y=x3+c on the same number plane.

y=x3+3, y=x3−4, y=x3−14 , y=x3+1.6



6. Using Geogebra, sketch the following graphs of the form y= (x+h )3.

y= (x−4 )3, y= (x+2.5 )3, y=(x−12 )3

, y= (x+1 )3



The Hyperbola: (15 Marks)

y= ax+h

+c

1. Using Geogebra, sketch the graph of y=1x and place a screenshot of this graph in the empty

space in the table below. Complete the required details (domain, range, x-intercept, y-intercept, odd/even/neither function) in the table below. 4

Equation: y=1x

Domain:

Range:

x-intercept:

y-intercept:

Odd/Even/Neither:


2. Using Geogebra, sketch the following graphs in the form y=ax on the same number plane.

y=−2x , y= 1

2 x , y= 4x , y=−1.5x



4. Using Geogebra, sketch the following graphs in the form of y=1x+c on the same number

plane.

y=1x+3, y=1x

−4, y=1x−14 , y=1x

+1.6


5. a) Explain how the value of c affects the shape, position, domain and range of the graph. 2

b) State the mathematical term that has the same meaning as y=c. 1

6. Using Geogebra, sketch the following graphs of the form y=1x+h .

y= 1x−4 , y= 1

x+2.5 , y= 1x−0.5 , y= 1

x+1


7. a) Explain how the value of h affects the shape, position, domain and range of the graph. 2

b) State the mathematical term that has the same meaning as x=h. 1

Absolute Value Function: (13 Marks)

y=a|x+h|+c

1. Using Geogebra, sketch the graph of y=|x| and place a screenshot of this graph in the empty space in the table below. Complete the required details (domain, range, x-intercept, y-intercept, odd/even/neither function) in the table below. 4

Equation: y=|x|

Domain:

Range:

x-intercept:

y-intercept:

Odd/Even/Neither:

Give a reason (graphically) for your decision.

2. Using Geogebra, sketch the following graphs in the form y=a|x| on the same number plane.

y=−2|x|, y=12|x|, y=4|x|, y=−1.5|x|



4. Using Geogebra, sketch the following graphs in the form of y=|x|+c on the same number plane.

y=|x|+3, y=|x|−4, y=|x|−14 , y=|x|+1.6



6. Using Geogebra, sketch the following graphs of the form y=|x+h|

y=|x−4|, y=|x+2.5|, y=|x−0.5|, y=|x+1|



The Circle: (13 Marks)

( x+h )2+( y+k )2=r2

1. Using Geogebra, sketch the graph of x2+ y2=1 and place a screenshot of this graph in the empty space in the table below. Complete the required details (domain, range, x-intercept, y-intercept, odd/even/neither function) in the table below. 4

Equation: x2+ y2=1

Domain:

Range:

x-intercept:

y-intercept:

Odd/Even/Neither:

Give a reason for your decision.

2. Using Geogebra, sketch the following graphs in the form x2+ y2=r2 on the same number plane:

x2+ y2=4, x2+ y2=√3, x2+ y2=36, x2+ y2=√14


3. Explain how the value of r affects the shape, position, domain and range of the graph. 2

4. Using Geogebra, sketch the following graphs in the form of x2+ ( y+k )2=1 on the same number plane.

x2+ ( y+3 )2=1, x2+ ( y−1 )2=1, x2+ ( y+5 )2=1, x2+ ( y−3 )2=1


5. Explain how the value of k affects the shape, position, domain and range of the graph. 2

6. Using Geogebra, sketch the following graphs of the form ( x+h )2+ y2=1, on the same number plane.

( x+3 )2+ y2=1, ( x−1 )2+ y2=1, ( x+5 )2+ y2=1 , ( x−3 )2+ y2=1



Part B: (10 Marks)

Answer the following questions using mathematical reasoning and your findings in Part A.

1. The value of m used in the Linear Graphs equation is very similar to the value of a used in the equations of the other graphs. Discuss whether or not the values of m and a have the same effect on each of the different graph types and provide reasoning for your decision. 3

2. Similarly, the values of h and k are used in many of the equations for the different graph types. Do they have the same effect on each of the graphs? Explain the reasoning for your decision. 3

3. State any other similarities or differences you have noticed between the graphs during your investigation in Part A. 4

cowra-h.schools.nsw.gov.au€¦ · web view2020. 3. 27. · circles, type x^2+y^2=1. for the...

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