Description

I am looking for a tutor who has good foundation in the following topics (Polynomial and rational functions, Exponential logarithmic functions) to take of the following assignments using the rubric system provided.

10 attachmentsSlide 1 of 10attachment_1attachment_1attachment_2attachment_2attachment_3attachment_3attachment_4attachment_4attachment_5attachment_5attachment_6attachment_6attachment_7attachment_7attachment_8attachment_8attachment_9attachment_9attachment_10attachment_10

Unformatted Attachment Preview

TVO ILC

MHF4U – Unit 1

Unit 1 Assessment, Part 1

Unit 1 Assessment, Part 1

1. Fill in the tables below for each of the following polynomials: [K10]

a)

3

f( x)=− _14 x − 13 x 2+ 3x − 9

Degree

b) f(x)=6x 4

Degree

Type of

polynomial

Sign of leading

coefficient

End behaviours

Domain

Sign of leading

coefficient

End behaviours

Domain

+7x 2 − 8x + 9

Type of

polynomial

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

1

TVO ILC

MHF4U – Unit 1

Unit 1 Assessment, Part 1

2. Fill in the table below for the polynomial function: [K9]

f(x)= − (x− 4) (x+ 1) 2(x− 5)

x – intercepts

y − intercept

End behaviours

and behaviour of graph at

each x − intercept

Sketch:

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

2

TVO ILC

MHF4U – Unit 1

Unit 1 Assessment, Part 1

3. Solve the following equation algebraically. Explain your process. [A6], [C3]

0 = 18 x 4+ 87 x 3+ 3 x 2− 108x

4.

a) Describe the transformations on the cubic function below.

Explain your thinking process. [C4]

f(x)= 7 [1_2 (x− 5)] 3− 45

b) The point (-9, -2446) is on the transformed function f(x)= 7 [1_2(x− 5)] 3− 45use the

transformation statement the find the original point on the parent function. Justify your

answer. [T3], [C2]

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

3

TVO ILC

MHF4U – Unit 1

Unit 1 Assessment, Part 1

5. Determine the values of mand n for f(x)= mx 3+ 20x 2+ nx− 35given that

(x+ 1) gives a remainder of zero, and when divided by (x− 2)the remainder is 45. [T5],

[C3]

6. Use algebra to determine whether the following function is even, odd or neither. [A6]

a)

f(x)= 55 x 4−x 2− 78

b)

f(x)=37×3+93x

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

4

MHF4U – Unit 1

TVO ILC

Unit 1 Assessment, Part 2

Unit 1 Assessment, Part 2

1. Use the characteristics of the given function to graph the function and it’s reciprocal on

the same set of axes, either using online graphing technology or by hand. State the

intercepts and identify any maximum or minimum points, where possible. Explain

your thinking process. [K6] [C2]

f(x) = − x 2+ 7x – 6

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

1

MHF4U – Unit 1

TVO ILC

Unit 1 Assessment, Part 2

2. a. Fill in the table and sketch the graph of the following equation. [A10], [C2]

-2x – 5

f( x) = _

3x + 18

Vertical

asymptotes

Horizontal

asymptotes

x − intercept

y− intercept

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

Domain

2

MHF4U – Unit 1

TVO ILC

Unit 1 Assessment, Part 2

2x− 5 [K2]

2 b. State positive and negative intervals for f(x)=

−

____________

3x+ 18

Positive interval:

Negative intervals:

3. Find the real roots of the following rational equations. [K8] [C2]

_

− 7x

a. 9x

+ 11 − 12= x_1

b.

___

x–1 = ____

3x+8

x+2 5x–1

4. Solve the following inequality algebraically. Explain your process. [A4] [C2]

8x − 3 ≤ 2x + 1 ≤ 17x – 8

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

3

MHF4U – Unit 1

TVO ILC

Unit 1 Assessment, Part 2

5. S

olve the following inequality algebraically. Include an interval chart in your solution.

[A6] [C2]

____

5x+4

< ____
5x–7
x–11 x+13
6. T
he dimensions of a box are 3 cm × 5 cm × 7 cm. The width, length, and height of the
box must be increased by the same amount xin order for the box to have a volume of
693 cm cubed. Determine the value of x that will produce a box with a volume of
693 cm 3. [T4] [C2]
Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.
4
TVO ILC
MHF4U – Unit 1
Unit 1 Assessment, Part 2
7. T
he specifications for a storage container state that the length is 1 metre more than triple
the width and the height is 5 metres less than double the width. Find the range of possible
dimensions for a volume of at least 8436 m 3 using the algebraic method. [T6] [C2]
Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.
5
MHF4U – Unit 2
TVO ILC
Unit 2 Assessment
Unit 2 Assessment
Knowledge: /14
Application: /20
Thinking: /12
Communication: /16
1. Fill in the table. [K2]
Exponential Form
Logarithmic Form
2401 = 7 4
a = log bc
2. Solve for x . Give answer to three decimal places where applicable.
a. x
= log 37
b. x
= log 10 000
Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.
[K2]
1
MHF4U – Unit 2
TVO ILC
Unit 2 Assessment
3. Convert each of the following to exponential form and solve.
a. n = log 416384
[K6]
b. 6 = log b46656
4. Use the special properties of logarithms to solve the following equations.
[K4]
a. M = log 1111 21
b. 4 log 57 = x
4
c. x
= log 2378
Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.
2
MHF4U – Unit 2
TVO ILC
Unit 2 Assessment
5. Evaluate the following using a method of your choice.
a. log 9729
[A4]
=
b. log 67776− log 6 36 =
6. Solve for the unknown variable using a method of your choice. [A4] [C2]
a. 5 11x+ 23 = 125 7x
b. 2 n = 123
7. Solve for the unknown variable using a method of your choice. [T4] [C2]
3 x+ 5 +
3 x = 177 876
Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.
3
TVO ILC
MHF4U – Unit 2
Unit 2 Assessment
8. Describe the transformations on the given logarithmic function. [C6]
g( x) = − 1_6 log 10[− _61(x− 7)]− 85
9. W
rite the equation of a logarithmic function that has been vertically stretched by 5,
reflected in the x − axis, horizontally compressed by 1/3, moved 11 units left and 8 units
down. Justify your answer. [A5] [C2]
10. The point (− 23, − 13) is on the transformed function: y = − 2log 10[− 5(x + 3)]− 9.
Find the original point on the parent function f(x) = log 10 x. Justify your answer. [T4] [C2]
Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.
4
TVO ILC
MHF4U – Unit 2
Unit 2 Assessment
11. Ethan bought new car worth $60 000. After 5 years, the car was worth $35 429.40.
Calculate the depreciation rate of the Ethan’s car. [T4] [C2]
12. The hydrogen ion concentration of a lemon is about 0.01. What is its pH? [A3]
13. H
ow does an earthquake of magnitude 8.4 compare to an earthquake of magnitude 3.7?
Round answer to the nearest whole number. [A4]
Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved.
5
Rubric Name: MHF4U Rubric - 1.11 Polynomial and Rational Functions - Part 1
Knowledge and Understanding
Level 4
Level 3
Level 2
Level 1
Below Level 1
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Demonstrates understanding of the
characteristics of a polynomial
function (degree; type, sign of
leading coefficient, end behaviours
and domain)
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Calculates x and y-intercepts,
describes end behaviours and
creates a sketch of a polynomial
function
Thinking
Level 4
Level 3
Level 2
Level 1
Below Level 1
Below level 1
Calculates the coordinates of a
point on a parent function, given
coordinates of a transformed point
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Determines the coefficients of the
fourth and third-order terms of a
quartic function
Communication
Level 4
Level 3
Level 2
Level 1
Below Level 1
Below level 1
Expresses and organizes
mathematical thinking
With a high degree of
effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Uses mathematical conventions,
vocabulary, and terminology
With a high degree of
effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Application
Level 4
Level 3
Level 2
Level 1
Below Level 1
Solves a polynomial equation
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Uses algebraic method to classify a
polynomial function as even, odd or
neither
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Rubric Name: MHF4U Rubric - 2.6 Exponential and Logarithmic Functions
Knowledge and Understanding
Level 4
Level 3
Level 2
Level 1
Below Level 1
Below level 1
Converts between exponential and
logarithmic forms
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Determines, with technology, the
approximate common logarithm of a
number
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Solves simple logarithmic equations
in one variable algebraically
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Recognizes equivalent algebraic
expressions involving logarithms
and exponents, and solves
equations involving expressions of
these type
Rubric Name: MHF4U Rubric - 2.6 Exponential and Logarithmic Functions
Knowledge and Understanding
Level 4
Level 3
Level 2
Level 1
Below Level 1
Below level 1
Converts between exponential and
logarithmic forms
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Determines, with technology, the
approximate common logarithm of a
number
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Solves simple logarithmic equations
in one variable algebraically
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Recognizes equivalent algebraic
expressions involving logarithms
and exponents, and solves
equations involving expressions of
these type
Rubric Name: MHF4U Rubric - 2.6 Exponential and Logarithmic Functions
Knowledge and Understanding
Level 4
Level 3
Level 2
Level 1
Below Level 1
Below level 1
Converts between exponential and
logarithmic forms
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Determines, with technology, the
approximate common logarithm of a
number
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Solves simple logarithmic equations
in one variable algebraically
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Recognizes equivalent algebraic
expressions involving logarithms
and exponents, and solves
equations involving expressions of
these type
Thinking
Level 4
Level 3
Level 2
Level 1
Below Level 1
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
Calculates the coordinates of a
point on a parent function, given
coordinates of a transformed point
With some
effectiveness
With limited
effectiveness
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Solves problems arising from real-
world applications involving
exponential and logarithmic
equations algebraically
Communication
Level 4
Level 3
Level 2
Level 1
Below Level 1
Below level 1
Expresses and organizes
mathematical thinking
With a high degree of
effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Uses mathematical conventions,
vocabulary, and terminology
With a high degree of
effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Application
Level 4
Level 3
Level 2
Level 1
Below Level 1
Evaluates logarithmic expressions
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Solves exponential equations
Below level 1
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Writes the equation of a
transformed logarithmic function
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Below level 1
Answers questions arising from
real-world applications involving
logarithmic equations
With a high degree
of effectiveness
With considerable
effectiveness
With some
effectiveness
With limited
effectiveness
Purchase answer to see full
attachment
Tags:
Logarithmic Form
Exponential Form
Vertically compressed
Horizontally stretched
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

## Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.