# MCF3M – Grade 11 Functions and Applications Culminating Review

Thanks, Gagan!

MCF3M – Culminating REVIEW – Task # 1, 2 – DAY 1, Task # 3, 4, 5 – DAY 2, Task # 6 – DAY 3
Culminating Day One – REVIEW Date: ______________________________

Key Skills:

Create an equation from a graph
 Use factored form if zeros are given with a third point on the parabola
 Use vertex form if the coordinates of the vertex are specified along with another point on the parabola

Converting between forms of a quadratic function:
 vertex to standard form → expand and simplify
 factored to standard form → expand and simplify
 standard to vertex form → complete the square technique
 standard to factored form → factor fully to find zeros OR use the quadratic formula; solve

To find an optimum value (maximum or minimum) → find the vertex; optimum value is the y-coordinate of the vertex The x-coordinate of the vertex is:

On the axis of symmetry of the parabola and has equation x = h The midpoint of the zeros

To find the zeros:
 factor fully

To find initial value: determine the y-intercept

To sketch a graph, need to have 3 points:
 the zeros and then can find the vertex
 two points symmetric about the axis of symmetry and then can find the vertex.

To use quadratic functions to represent optimum revenue and interpret the meaning within the context of the question.

MCF3M – Culminating REVIEW – Task # 1, 2 – DAY 1, Task # 3, 4, 5 – DAY 2, Task # 6 – DAY 3

Review Questions – Day 1:

# 5 # 3, 6, 9ad, 12 # 5bd, 7be

Unit 1

Pg. 93

Pg. 110

Unit 2

Pg. 169

Unit 3

# 1b, 5a, 11

Unit 4

Pg. 57

Pg. 86

#7

Pg. 139

Pg. 203

Pg. 149

# 2b, 3b, 4c, 7d, 10

#6

Pg. 214

Pg. 100

#9

Pg. 163

# 11, 12

# 9, 10

Pg. 222

#5

Pg. 232

Pg. 115

Pg. 177

Pg. 240

Pg. 250

# 3

# 3. 6

# 2ace, 4ac # 3, 5 # 5, 9
# 6, 8

EXTRA QUESTION: Determine when a quadratic function reaches it maximum value.

Mr. McIntosh has 90 apple trees. He earns annual revenue of \$120 per tree. If he plants more trees they have less room to grow, resulting in fewer apples per tree. The annual revenue per tree is reduced by \$1 for each additional tree.

a) Determine the revenue equation, R(x), in dollars, where x is the number of additional trees planted.

The cost of maintaining each tree is \$8.

1. b)  Determine the cost equation, C(x) in dollars, where x is the number of additional trees planted.
2. c)  How many trees must Mr. McIntosh plant to maximize profit?

Note: PROFIT = REVENUE – COST
PROFIT = (# items sold)(price per item) – (cost per item)(# items)

P(x) = R(x) – C(x)
REVENUE = (# items sold)(price per item) COST = (cost per item)(# items)

# 5e # 3, 9ad # 9 # 7be
# 3. 6

# 10

Unit 1

Unit 2

Unit 3

Unit 4

Pg. 57

Pg. 93

# 6bd

Pg. 139

# 2b, 3b, 4c, 7d

Pg. 203

Pg. 100

Pg. 149

# 11

Pg. 214

Pg. 163

Pg. 222

Pg. 169

# 11, 12

MCF3M – Culminating REVIEW – Task # 1, 2 – DAY 1, Task # 3, 4, 5 – DAY 2, Task # 6 – DAY 3 Rubric for Mathematical Thinking

Level 1

Level 2

Level 3

Level 4

Making Inferences, conclusions and justifications
(c, d)

Justification of the answer presented has a limited connection to the problem solving process and models presented

Justification of the answer presented has some connection to the problem solving process and models presented

Justification of the answer presented has a direct connection to the problem solving process and models presented

Justification of the answer presented has a direct connection to the problem solving process and models presented, with evidence of reflection

Selection and application of

a variety of tools that manipulate the data or transform the model to solve the problem

(a, b, e, f, g)

Selects and applies appropriate tools, with major errors, omissions, or mis-sequencing

Selects and applies appropriate tools, with minor errors, omissions or mis-sequencing

Selects and applies appropriate tools, accurately, and logically sequenced

Selects and applies the most appropriate tools, accurately and logically sequenced

Ability to apply the processes of inquiry and problem solving, ie: reflecting, and revising and revisiting

(e)

Applies the processes to the assigned task with significant prompts

Applies the processes to the assigned task with minor prompts

Applies the processes to the assigned task without prompts

Creation of a model to represent the data
(a)

Creates a model that represents little of the range of data

Creates a model that represents some of the range of data

Creates a model that represents most of the range of data

Creates a model that represents the full range of data

Rubric for Mathematical Communication

Level 1

Level 2

Level 3

Level 4

Correct use of mathematical symbols, labels, and conventions
(throughout)

Sometimes uses mathematical symbols, labels, and conventions correctly

Usually uses mathematical symbols, labels, and conventions correctly

Consistently uses mathematical symbols, labels, and conventions correctly

Consistently and meticulously uses mathematical symbols, labels, and conventions

Appropriate use of

mathematical vocabulary

(throughout)

Sometimes uses mathematical vocabulary correctly when expected

Usually uses mathematical vocabulary correctly when expected

Consistently uses mathematical vocabulary correctly when expected

Consistently uses mathematical vocabulary, recognizing novel opportunities for its use

Degree of clarity in explanations and justifications in reporting (throughout)

Explanations and justifications are partially understandable

Explanations and justifications are understandable by the teacher, but would likely be unclear to others

Explanations and justifications are clear for a range of audiences

Explanations and justifications are particularly detailed and clear

MCF3M – Culminating REVIEW – Task # 1, 2 – DAY 1, Task # 3, 4, 5 – DAY 2, Task # 6 – DAY 3

Review Questions – Day 2 Culminating:

Date: ______________________________

In order to prepare for the culminating, complete the questions below. Additionally, it is highly recommended that you review all your notes,

tests, quizzes, and previous homework (listed in the order of importance).

Unit 5

Unit 6

Unit 7

Unit 8

Pg. 267

Ex 2

Pg. 337

Ex. 1, 2

Pg. 446

Pg. 203

Pg. 271

# 5ab, 8, 14

Pg. 339

# 1, 3, 6, 9

Pg. 276

Ex. 2, 3

Pg. 344

Ex. 1, 2, 3

Pg. 280

# 4, 6

Pg. 348

# 3, 4, 6

Pg. 286

Ex. 3

Pg. 365

Pg. 288

# 3, 8, 10

Pg. 299

# 1, 2a, 3b, 4, 7, 13

Pg. 309

#7

Review Questions – Day 3 Culminating:

Date: ______________________________

# 4, 6, 8, 10

# 1 – 7 # 1 – 10

Make sure you can log on to MyBluePrint. Explore and familiarize yourself with MyBluePrint and make searches based a different criteria (such as subject, strand etc.). Complete the introduction activities on MyBluePrint.

Question:

1. On MyBluePrint find how to become a veterinarian. Find one school you can go to, what are the required secondary and post-secondary courses you need, find what program you will need to go to, how long the program is etc.