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Im looking for a tutor who has foundation in the following topics trigomertic functions and characteristics functions, and can use the provided rubrics to solve the provided assignment.

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TVO ILC

MHF4U – Unit 2

Culminating Task: Making the World a Better Place

Culminating Task: Making the World a Better Place

Part of the evaluation of this course will be in the form of a Culminating Task, worth 15% of

your final course work.

In this activity you will explore connections between the concepts learned in this course

and environmental issues. Specifically, you will create a mathematical model and visual

representations to provide evidence to convince investors that a way to improve an

environmental issue of your choice would be a worthy project in which to invest.

Overview

You have decided that you are going to make a pitch to the hosts of a reality TV show where

entrepreneurs request funding for projects, or products, designed to reduce the damage to

the environment caused by human activity.

Your pitch must combine a compelling reason why your initiative should be supported, with

evidence that justifies the need for action. You will research and collect secondary data,

use the data to create graphical and algebraic models, make predictions based on your

algebraic model and create a visual presentation using the media/ platform of your choice

(PowerPoint, WordPress, Prezi, Weebly, iMovie, Show Me, Blogger, Tumblr, YouTube, etc.).

The function used to create your algebraic model must be one of the types of functions

(polynomial of degree 3 or higher, exponential, logarithmic or trigonometric) covered in this

course.

Step 1:

Identify and describe an environmental issue and a proposed way to reduce impact and

improve outcomes. The proposal could be as simple as a campaign to convince people to

change daily habits that are harmful to the environment or as complex as developing a new

environmentally friendly product or process.

Step 2:

Research secondary data from a reliable source and create a mathematical model to predict

outcomes if no action to reduce harmful effects is taken.

Step 3:

Create algebraic and graphic representations of your model and provide a brief, but

convincing, description of the benefits of your proposal.

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

1

TVO ILC

MHF4U – Unit 2

Culminating Task: Making the World a Better Place

Task Checklist

This assessment is out of 60 marks and is worth 15% of your final mark. You will submit

your Culminating Task upon completion of Unit 4 where you will be prompted at the end of

the final learning activity to submit your assessment for feedback and a grade by selecting

the “Assignments” link and following the submission directions.

Your proposal should contain the following elements:

Task Checklist Item

Weight

(No. of marks)

A description of the environmental issue that needs to be addressed. 2

A description of the product or change in behaviour that could

reduce the damage caused by the environmental issue, with

justification.

5

A set of secondary data from a reliable source, in table form,

pertaining to the environmental issue. It must be appropriate for

modeling with one of the types of functions studied in this course:

polynomial of degree 3 or higher; exponential; logarithmic or

trigonometric. A spreadsheet (Excel, Google Sheets etc.) could be

used to create the table and would facilitate graphing the data.

8

The APA reference for the data set.

2

5

A scatter plot of the data including appropriate titles, scales and

units, created with the graphing technology of your choice.

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

2

TVO ILC

MHF4U – Unit 2

Culminating Task: Making the World a Better Place

An algebraic model that fits the data. The model can feature one

of the functions mentioned above or could be a combination or

composite of two of those functions. The choice of model should be

based on visual inspection of data trends observed and does not

need to be supported by statistical analysis, which is beyond the

scope of this course.

5

An explanation of how the algebraic model was determined,

including justification for the choice of parent function (or combined

or composite function) and any transformations used to model the

data.

5

restrictions on the domain of your function and a description,

including justification, of potential limitations of the algebraic model

as it applies to correlation with the data and the ‘real world’ context.

5

A graph of the algebraic model, including appropriate titles, scales,

units, and restrictions on the domain, created with graphing

technology, and superimposed on the scatter plot.

5

At least one calculation using the algebraic model to make a

prediction, or for emphasis.

3

A brief sales pitch, using the graph as evidence, and calculations

involving the algebraic model to make predictions to convince the

reality TV show panel that your proposal deserves support.

10

Correct use of mathematical terminology and conventions

throughout.

5

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

3

TVO ILC

MHF4U – Unit 2

Culminating Task: Making the World a Better Place

The teacher will assess your work using the following rubric. Before submitting your

assessment, review the rubric to ensure that you are meeting the success criteria to the best

of your ability.

Categories

Knowledge and

Understanding

Level 4

Level 3

Level 2

Level 1

(80 – 100%)

A data table is

created with a

high degree of

effectiveness.

(70 – 79%)

A data table is

created with

considerable

effectiveness.

(60 – 69%)

A data table

is created

with some

effectiveness.

(50 – 59%)

A data table

is created

with limited

effectiveness.

Graphing

technology is

used to create

the required

graphs with a

high degree of

effectiveness.

Graphing

technology is

used to create

the required

graphs with

considerable

effectiveness.

Graphing

technology is

used to create

the required

graphs with some

effectiveness.

Graphing

technology

is used to

create the

required graphs

with limited

effectiveness.

Calculations

using the

algebraic model

are carried

out with a

high degree of

effectiveness.

Calculations

using the

algebraic model

are carried out

with considerable

effectiveness.

Calculations

using the

algebraic model

are carried

out with some

effectiveness.

Calculations

using the

algebraic model

are carried out

with limited

effectiveness.

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

4

TVO ILC

MHF4U – Unit 2

Culminating Task: Making the World a Better Place

Thinking

A clear link

between the

environmental

issue, and

the product or

initiative being

proposed to

mitigate it, is

established with

a high degree of

effectiveness.

A clear link

between the

environmental

issue, and

the product or

initiative being

proposed to

mitigate it, is

established with

considerable

effectiveness.

A clear link

between the

environmental

issue, and

the product or

initiative being

proposed to

mitigate it, is

established

with some

effectiveness.

A clear link

between the

environmental

issue, and

the product or

initiative being

proposed to

mitigate it, is

established

with limited

effectiveness.

The algebraic

model represents

the data with a

high degree of

effectiveness.

The algebraic

model represents

the data with

considerable

effectiveness.

The algebraic

model represents

the data

with some

effectiveness.

The algebraic

model represents

the data

with limited

effectiveness.

Restrictions on

the domain and

limitations of

the model suit

the context, and

they take into

consideration

the correlation

between the

algebraic

model and the

data, with a

high degree of

effectiveness.

Restrictions on

the domain and

limitations of

the model suit

the context, and

they take into

consideration

the correlation

between the

algebraic model

and the data,

with considerable

effectiveness.

Restrictions on

the domain and

limitations of

the model suit

the context, and

they take into

consideration

the correlation

between the

algebraic model

and the data,

with some

effectiveness.

Restrictions on

the domain and

limitations of

the model suit

the context, and

they take into

consideration

the correlation

between the

algebraic model

and the data,

with limited

effectiveness.

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

5

TVO ILC

MHF4U – Unit 2

Culminating Task: Making the World a Better Place

Application

Appropriate

secondary data

is selected with

a high degree of

effectiveness.

Appropriate

secondary data

is selected with

considerable

effectiveness.

Appropriate

secondary data

is selected

with some

effectiveness.

Appropriate

secondary data

is selected

with limited

effectiveness.

The process

used to

determine the

algebraic model

is described with

a high degree of

effectiveness.

The process

used to

determine the

algebraic model

is described with

considerable

effectiveness.

The process

used to

determine the

algebraic model

is described

with some

effectiveness.

The process

used to

determine the

algebraic model

is described

with limited

effectiveness.

Transformations

applied to the

chosen parent

function(s) are

appropriate and

are justified with

a high degree of

effectiveness.

Transformations

applied to the

chosen parent

function(s) are

appropriate and

are justified with

considerable

effectiveness.

Transformations

applied to the

chosen parent

function(s) are

appropriate and

are justified

with some

effectiveness.

Transformations

applied to the

chosen parent

function(s) are

appropriate and

are justified

with limited

effectiveness.

The algebraic

model is used

to support a

point or make

a prediction

within the

presentation with

a high degree of

effectiveness.

The algebraic

model is used

to support a

point or make a

prediction within

the presentation

with considerable

effectiveness.

The algebraic

model is used

to support a

point or make a

prediction within

the presentation

with some

effectiveness.

The algebraic

model is used

to support a

point or make a

prediction within

the presentation

with limited

effectiveness.

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

6

TVO ILC

MHF4U – Unit 2

Culminating Task: Making the World a Better Place

Communication

Mathematical

language

and notation,

throughout the

activity, are used

Mathematical

language

and notation,

throughout the

activity, are used

Mathematical

language

and notation,

throughout the

activity, are used

with a high

degree of

effectiveness.

with considerable with some

effectiveness.

effectiveness.

with limited

effectiveness.

The

environmental

issue is

described with a

high degree of

effectiveness.

The

environmental

issue is

described with

considerable

effectiveness.

The

environmental

issue is

described

with some

effectiveness.

The

environmental

issue is

described

with limited

effectiveness.

The reference

for the data

set is stated in

APA style with a

high degree of

effectiveness

The reference

for the data

set is stated in

APA style with

considerable

effectiveness.

The reference

for the data set

is stated in APA

style with some

effectiveness

The reference

for the data set

is stated in APA

style with limited

effectiveness.

Elements of the

activity that are

pertinent to the

presentation

are synthesized

to create a

convincing bid

for support with

a high degree of

effectiveness.

Elements of the

activity that are

pertinent to the

presentation

are synthesized

to create a

convincing

presentation

Elements of the

activity that are

pertinent to the

presentation

are synthesized

to create a

convincing

presentation

with considerable with some

effectiveness.

effectiveness.

Elements of the

activity that are

pertinent to the

presentation

are synthesized

to create a

convincing

presentation

with limited

effectiveness.

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

Mathematical

language

and notation,

throughout the

activity, are used

7

TVO ILC

MHF4U

Unit 3 Assessment

Unit 3 Assessment

1.

Determine the following: [K4]

a. Given a sector with an arc length of 4.5 cm and a radius of 3 cm, find the angle

subtended by the arc.

b. Given a sector with an angle of 13 radians and a radius of 7 m, find the arc length.

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

1

TVO ILC

MHF4U

Unit 3 Assessment

2. Fill in the table. Show your work and keep answers exact. [K4]

Degrees

Radians

_

2π

45

2 30

0

3. Determine the values of θif 0

your process. [K4], [C2]

4. Determine exact values of θif

your process. [K4], [C2]

≤ θ ≤ 2π given that cosx = − 0.3178. Explain

0 ≤ θ ≤ 2π given that tanθ =

_

− √

3 . Explain

5. Describe the transformations on the given cosine function. [C4]

f(x) = 0.5cos

[0.5(x− π)]− 12

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

2

TVO ILC

MHF4U

Unit 3 Assessment

6. Find an equation for each function and explain your thought process.

a. A sinusoidal function with an amplitude of 15 units, a period of

radians to the right, axis at

y = 33

, a phase shift of

[A4] [C2]

b. [A4] [C2]

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

3

TVO ILC

MHF4U

Unit 3 Assessment

7.

Determine the exact value of tan

. [T4]

8. Determine a value of x for each of the following. Give answers in simplest exact form.

[A6]

a.

_ = sinx

b. c

os 11π

31

c.

tan π_8 = cotx

9. Prove the following identity. Explain your thought process. [T3] [C2]

cos x

cot 2 x = _

1 − cos 2 x

2

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

4

TVO ILC

MHF4U

Unit 3 Assessment

10.Solve the following trigonometric equation for 0

[A4] [C2]

cos 2 x

−

≤ x ≤ 2π. Explain your process.

1 = 0

11.The depth of water in a harbour varies as a function of time. The maximum depth is

9 feet and the minimum depth is 1 foot. The depth can be modelled with a sinusoidal

function that has a period of 12 hours. If the depth is 5 feet at 12 midnight, and is

increasing,

a. C

reate an algebraic model to predict the depth of the water as a function of time.

Justify your reasoning. [T4] [C2]

b. The water must be at least 7 feet for Annie’s fishing boat to safely navigate the

harbour. She wants to enter the harbour during the afternoon.

i. Create a graph of this function using technology. [T2]

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

5

TVO ILC

MHF4U

Unit 3 Assessment

ii. What is the earliest time she can enter the harbour? [T2]

iii. How long can she safely stay in the harbour? [T2]

Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.

6

TVO ILC

MHF4U 4.8

Unit 4 Assignment

Unit 4 Assignment

1. Given that f( x) = { (1,3), ( 5,7), (9, 11), ( 13, -5)} and g(x)= { (-2,33), ( 1,-1), (5, 9)}.

Determine the following: [K3]

a.

f(x) + g(x) =

b.

g(x) − f(x) =

c.

f(x) ∙ g(x) =

2. Given that f(x) = 2x− 3and g (x) = 9

x 2− 5x+ 11, determine the following:

a.

b.

c.

d.

g(x) − f(x) =

[K2]

f(x) ∙ g(x) =

[K2]

=

[K1]

f(x)

_

g(x)

g ∘ f(x)

[K2]

3. Use the given graphs to sketch the graph of f(x) + g(x). Explain your process. [A3] [C2]

f(x)

g(x)

Copyright © 2018 The Ontario Educational Communications Authority. All rights reserved.

f(x) + g(x)

1

TVO ILC

MHF4U 4.8

Unit 4 Assignment

4. State the domain and range of each function below. Explain your process.

Function

[A4] [C2]

Reasoning

_

f( x) = 13 √ − 4x

+ 16 + 19

1

f(x) = _

6x + 81− 99

5. Calculate the average rate of change for the function f( t) = 2

x 3+ 5 over the interval

− 1 ≤ x ≤ 2.

[K3]

6. a.Use an x− interval of 0.0001 to determine the instantaneous range of change of the

function f(x)= x 4+ 8 x 3 + 19 x 2+ 12xat x = − 2.

Give answer to the nearest tenth.

b.

[A3]

Determine whether the function f(x)= x 4+ 8 x 3 + 19 x 2+ 12x at x = − 2

has a maximum or minimum at the point wherex = − 2. Justify your answer.

[A5] [C2]

7. Use algebra to determine whether each function is even, odd or neither.

a.

f(x) = xcosx+ 1

b.

tanx

f(x) = _

x

[A6] [C2]

3

Copyright © 2018 The Ontario Educational Communications Authority. All rights reserved.

2

TVO ILC

MHF4U 4.8

Unit 4 Assignment

8. A marine biologist measures the presence of a pollutant in an ocean and concludes that

the concentration, C, in parts per million (ppm), as a function of the population, P, of the

people who visit the beach is given by C( P) = 1.38P+ 97.4. The population of people

visiting the beach, in thousands, can be modeled by P( t) = 12 (1.078) t where t is the

time in years since the first measurement.

a.

Determine an equation, in simplified form, for the concentration of pollutant as a

function of the number of years since the first measurement.

b.

[T2]

How long (to the nearest year) will it take for the concentration to reach 180 ppm?

[T3]

9. You are designing a water slide. Your first step is to create an algebraic model to

describe the slide’s profile, as shown.

a.

Use graphing technology to determine an equation for the algebraic model.

Consider the shape only; do not worry about scale. Describe how you arrived at

your design. [T3] [C2]

b.

Because of safety concerns, you want to make the slide less steep, and with smaller

bumps. Suggest changes to your algebraic model and an include a graph that

shows your original design and the one that has the improved safety features.

[T2] [C2]

Copyright © 2018 The Ontario Educational Communications Authority. All rights reserved.

3

Knowledge & Understanding: /16

Level 4

80-100%

Level 3

70-79%

Level 2

60-69%

Level 1

50-59%

Uses the

Uses the

Uses the

Uses the

relationship between relationship between relationship between relationship between

radian measure, arc radian measure, arc radian measure, arc radian measure, arc

length and angle at length and angle at length and angle at length and angle at

the centre with a the centre with the centre with the centre with

high degree of considerable

some effectiveness limited effectiveness

effectiveness

effectiveness

Converts between

exact values in

radian measure and

degrees with a high

degree of

effectiveness

Converts between

exact values in

radian measure and

degrees with

considerable

effectiveness

Converts between

exact values in

radian measure and

degrees with some

effectiveness

Converts between

exact values in

radian measure and

degrees with limited

effectiveness

Solve linear

trigonometric

equations, for the

domain of real

values from 0 to 21

with a high degree

of effectiveness

Solve linear

trigonometric

equations, for the

domain of real

values from 0 to 2TT

with considerable

effectiveness

Solve linear

trigonometric

equations, for the

domain of real

values from 0 to 2TT

with some

effectiveness

Solve linear

trigonometric

equations, for the

domain of real

values from 0 to 2T

with limited

effectiveness

Thinking: /17

Level 4

80-100%

Level 3

70-79%

Level 2

60-69%

Level 1

50-59%

Uses compound

angle formulas to

determine exact

values of

trigonometric ratios

with a high degree

of effectiveness

Uses compound

angle formulas to

determine exact

values of

trigonometric ratios

with considerable

effectiveness

Uses compound

angle formulas to

determine exact

values of

trigonometric ratios

with some

effectiveness

Uses compound

angle formulas to

determine exact

values of

trigonometric ratios

with limited

effectiveness

Prove trigonometric

identities through

the application of

reasoning skills,

using a variety of

relationships with a

high degree of

effectiveness

Prove trigonometric

identities through

the application of

reasoning skills,

using a variety of

relationships with

considerable

effectiveness

Prove trigonometric

identities through

the application of

reasoning skills,

using a variety of

relationships with

some effectiveness

Prove trigonometric

identities through

the application of

reasoning skills,

using a variety of

relationships with

limited effectiveness

Solves problems

based on

applications

involving a

trigonometric

function using a

graph generated

with technology with

a high degree of

effectiveness

Solves problems

based on

applications

involving a

trigonometric

function using a

graph generated

with technology

considerable

effectiveness

Solves problems

based on

applications

involving a

trigonometric

function using a

graph generated

with technology

some effectiveness

Solves problems

based on

applications

involving a

trigonometric

function using a

graph generated

with technology

limited effectiveness

Application: /18

Level 4

80-100%

Level 3

70-79%

Level 2

60-69%

Level 1

50-59%

Represents a Represents a Represents a Represents a

sinusoidal function sinusoidal function sinusoidal function sinusoidal function

with an equation, with an equation, with an equation, with an equation,

given its graph or its given its graph or its given its graph or its given its graph or its

properties, with properties, with properties, with properties, with

angles expressed in angles expressed in angles expressed in angles expressed in

radians with a high radians

radians some

radians limited

degree of

considerable

effectiveness

effectiveness

effectiveness

effectiveness

Solves equations

using equivalent

trigonometric

expressions with a

high degree of

effectiveness

Solves equations

using equivalent

trigonometric

expressions with

considerable

effectiveness

Solves equations

using equivalent

trigonometric

expressions with

some effectiveness

Solves equations

using equivalent

trigonometric

expressions with

limited effectiveness

Solves quadratic

trigonometric

equations for the

domain of real

values from 0 to 2TT

with a high degree

of effectiveness

Solves quadratic

trigonometric

equations for the

domain of real

values from 0 to 2TT

with considerable

effectiveness

Solves quadratic

trigonometric

equations for the

domain of real

values from 0 to 2TT

with some

effectiveness

Solves quadratic

trigonometric

equations for the

domain of real

values from 0 to 2TT

with limited

effectiveness

Communication: /18

Level 4

80-100%

Level 3

70-79%

Level 2

60-69%

Level 1

50-59%

Expresses and

organizes

mathematical

thinking with a high

degree of

effectiveness

Expresses and

organizes

mathematical

thinking with

considerable

effectiveness

Expresses and

organizes

mathematical

thinking with some

effectiveness

Expresses and

organizes

mathematical

thinking with limited

effectiveness

Uses mathematical

conventions,

vocabulary, and

terminology with a

high degree of

effectiveness

Uses mathematical

conventions,

vocabulary, and

terminology with

considerable

effectiveness

Uses mathematical

conventions,

vocabulary, and

terminology with

some effectiveness

Uses mathematical

conventions,

vocabulary, and

terminology with

limited effectiveness

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