Introduction Math 11 Pre-Calculus MEC MathEduCurriculum Copyright 2019

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New BC Curriculum Mathematics 11 Pre-Calculus

Page 1 General Information

Page 2 Record Chart

Page 3 - 5 Unit 6 Guided Outline Page 6 - 15 Workbook Samples

Page 16 - 23 Test Page Samples

Textbook This course uses the textbook “Pre-Calculus 11” ISBN -13: 978-0-07-073873-7 by McGraw-Hill Ryerson at 1-800-565-5758. Cost about $ 95.

It also uses workbooks as indicated below.

Curriculum Outline

1. Real Numbers, Workbook, 16 pages 6. Quadratic Functions, Textbook 2. Powers, Workbook, 28 pages 7. Quadratic Equations, Textbook 3. Radicals Textbook 8. Inequalities, Textbook 4. Factoring, Workbook, 21 pages 9. Trigonometry, Textbook 5. Rationals Textbook 10.Financial Literacy, Workbook, 68 pages

Structure This course is generally designed with the self-paced student in mind. It is based on a mastery system in which the student must obtain an 80% on the tests. Each unit test has two versions

in which the student has a chance to reach and or exceed the 80% mastery level.

Evaluation There are 10 unit tests which account for 60% of the final mark. There are 4 cumulative tests which account for 40% of the final mark.

Composition This paper course is made up of: 10 Unit Outlines

Workbooks with Solution keys where needed

10 Unit Tests each with an A and a B version (20 tests), Plus (20 tests) Answer Keys

4 Cumulative Tests, Plus (4 Cumulative Tests) Answer Keys,

All Answer Keys have a suggested marking scheme,

All files are put on a CD disk in pdf and MS Word,

A perpetual license for your school.

The entire paper course is placed in a binder along with the disk and shipped as one unit.

Cost: $ 495.00. See Ordering.

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Mathematics 11 Pre-Calculus Record Chart

Name Start Date:

Unit Topic Test A Test B Average Date

1 Real Numbers

2 Powers

3 Radicals

Cumulative Test 1

4 Factoring

5 Rationals

Cumulative Test 2

6 Quadratic Functions

7 Quadratic Equations

Cumulative Test 3

8 Inequalities

9 Trigonometry

Cumulative Test 4

10 Financial Literacy

Course Evaluation

Course Evaluation Total Marks Percent Value Result Unit Tests (10) 60%

Cumulative Tests (4) 40%

Final Mark

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Math 11 Pre-Calculus

Textbook: Pre-Calculus 11 by McGraw-Hill Ryerson

Unit 6 Quadratic Functions

Goal: The goal of this unit is to investigate the nature of quadratic

functions/equations and how they can be applied to real-world

situations.

Objectives: In order to achieve the above goal you will:

* Investigate quadratic functions in vertex form.

* Investigate quadratic functions in standard form.

* Investigate completing the square.

What Needs to be Done:

Unit 6 has 3 sections: 3.1, 3.2, and 3.3. Each section in unit 6 has an

accompanied video to enhance your understanding of the section material. There

may be more than one video for a section. Unit 6 corresponds to chapter 3 in the

textbook. Use the section-numbered videos below as they correspond in the

Unit 6 - Chapter 3 Practice Guide below to help you with your understanding.

Video Selections:

3.1 https://www.youtube.com/watch?v=BMyV6j0EH3I Parabolas7of8 All parabolas have the same shape. (3:02 min).

3.1 https://www.youtube.com/watch?v=eFZOnAcuVLM

Graphing Parabolas w/ vertex & intercepts (15:00 min)

3.1 https://www.youtube.com/watch?v=ZJDM4TE6I30 How to Graph Parabolas (7:00 min)

3.1 https://www.youtube.com/watch?v=vAPPYoBV2Ow

Find the Equation of a Quadratic Function from a Graph (4:55 min)

3.2 https://www.youtube.com/watch?v=Ev5eCg65WXg

Properties of Quadratic Functions in Standard Form (11:39 min)

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Page

138-139

Write out definitions for all new terms as you discover them.

Read over these pages. 140-141 Read "Quadratic Functions" and then glance over "Career Link". 142 Read over this page. 143-144 Watch video " Parabolas7of 8 All parabolas have the same shape."

(3:03 min). Use technology in "Investigate Graphs of Quadratic

Functions in Vertex Form"

144-145 Go over "Link the Ideas" and define the new terms. Watch video " Graphing Parabolas w/ vertex & intercepts" (15:00 min) but just the first 7: 30 min.

146-147 Go over these two pages. 148-150 Go over Example 1. Watch video "How to Graph Parabolas" (7:00 min).

151-154 Go over Example 2. Watch video " Find the Equation of a Quadratic Function from a Graph" (4:55 min).

154-156 Go over Example 3. Read over “Key Ideas”.

157-162 Under "Check Your Understanding" try # 1, 2ac, 3ac, 4ac, 5a, 6, 7ac, 8, 9, 10, 13, 14, 16, 18, 20, 22, and 24.

163-164 Read P. 163 and define the new term on P. 164. Watch video " Properties of Quadratic Functions in Standard Form " (11:39 min).

165-166 Read over "Link the Ideas". Note how to determine the x-coordinate.

166-168 Go over Example 1. 168- 172 Go over Examples 2-3. 173 Read over "Key Ideas".

3.3 https://www.youtube.com/watch?v=xGOQYTo9AKY

Completing the Square - Solving Quadratic Equations (4:36 min)

3.3 https://www.youtube.com/watch?v=TV5kDqiJ1Os Example 3: Completing the square | Quadratic equations (5:43 min)

3.3 https://www.youtube.com/watch?v=LMApqDGjOr4

Quadratic Equation Word Problems, part 1 070-25a (8:39 min)

Quadratic Functions

Unit 6 - Chapter 3 Practice Guide

(Check Mark as You Complete)

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174-179 Under "Check Your Understanding" try # 1, 2ab, 3, 4ac, 5bd, 6ac, 7, 9, 11,

12, 13, 15, 17, 20, 21, and 23.

180 Read over. Watch video "

183 Go over "Link the Ideas". Define the new term and write out the new

formula. Watch video "Completing the Square - Solving

Quadratic Equations (5:43 min).

184-186 Go over Example 1.

187-188 Go over Example 2.

188-191 Go over Examples 3 and 4. Watch video " Quadratic Equation Word

Problems, part 1 070-25a" (8:38 min).

192 Read over "Key Ideas".

192-197 Under "Check Your Understanding" try # 1,

2ac, 3ac, 4ac, 5bd, 6bd, 7ace, 8b, 9, 11, 12ac, 13, 14, 17, 19, 21, 23, 28

and 31.

198-200 Under "Chapter Review" try # 1ac, 2a, 3ad, 4ad, 5a, 7, 9b, 11, 12, 14ac,

and 17.

201-203 Under "Chapter 3 Practice Test" try # 1-6, 7b, 9a, 10, 13, and 15.

Since this course is based on the mastery system, you need to reach 80% in the test before

you can proceed to the next chapter, so review your problems and when you are ready,

ask your instructor for the test.

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Real Numbers

Watch video "Classifying Numbers" (8:48 min) https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-irrational-

numbers/v/categorizing-numbers

Assigning real numbers to each group of numbers

Let N = Natural numbers,

W = Whole numbers,

I = Integer numbers,

R = Rational numbers,

IR = Irrational numbers.

Examples:

7 N,W,I,R

√𝟏𝟏 IR

-8 I, R 0.2222… R

√𝟏𝟔 N, W, I, R

√𝟐𝟏𝟔𝟑

N, W I, R,

- √𝟖𝟑

I, R

1 / 9 R 0.101001000100001…

IR

Your Turn

11

√𝟖𝟏 -1.4 0.212212221…

√𝟏𝟑

√𝟑𝟒𝟑𝟑

- √𝟔𝟒𝟑

2 / 3 0.21021002100021000021…

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(a) 5.73232323232…

Let x = 5.73232323232… Multiply by ten to isolate the repeating numbers.

Let 10x = 57.32323232...

It will not work to subtract x and 10x

Multiply 57.323232… by 100 because there are two repeating numbers.

Therefore (10x x 100) 1000x = 5732.323232…

Subtract Left Side 1000 x -10x = 990x and

Right Side 5732.32323232… - 57.32323232… = 5675

Therefore, 990x = 5675

x = 5675

990

Therefore, 5.73232323232… = 5675

990 =

1135

198

Try the following.

Can the following repeating decimals be expressed in the form 𝑚

𝑛 ? Reduce to lowest terms if possible.

_ __ ___ ___ __

(a) 0.3 (b) 0.13 (c) 0.163 (d) 2. 127 (e) 6.743

_

(a) 0.3

__

(b) 0.13

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Powers - Laws of Exponents 1. Review

1. Meanings of exponents

Powers with exponent 1 are always equal to the base. b1 = b

Powers with exponent 0 are always equal to 1. b0 = 1

Negative whole exponents represent fractions. b–n

= nb

1

If you have a non-whole-number exponent, for now, evaluate on the calculator.

2. Exponent calculation properties

Multiplying powers with the same base: add the exponents. am · a

n = a

m+n

Dividing powers with the same base: subtract the exponents. nm

n

m

aa

a -=

Power of a power: multiply the exponents. (am)n = a

mn

Multiplying powers with the same exponent: an · b

n = (ab)

n

Dividing powers with the same exponent:

n

n

n

b

a

b

a÷ø

öçè

æ=

Examples

61 = 6

70 = 1

4–2

= 1

16

62 · 6

3 = 6

3+2 = 6

5

(53) / (52) = 53−2

= 51 = 5

(34)2 = 3

4x2 = 38

65 · 4

5 (6x4)

5 = 24

5

42

/ 52 = (

4

5)2

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3. Part A. Simplify each of these integral exponent expressions as much as possible.

1. -2-2

2. (-2)-2

3. 6-1 +

4-1

4. 𝒙𝟐𝒙𝟒 + 𝒙𝟑𝒙𝟑

5. x3 x

5 + x

4

6. −𝟐𝒙𝟐(𝟑𝒙𝟑) + 𝟓𝒙𝟑(−𝟑𝒙𝟐)

7. a2 b

2 (ab)

3

8. r4 r – s

2 s

3

9. (x2 y

4 z

5) · (x

5 y

3 z)

10. a3 b

-3 (ab)

2

11. 50

12. 05

13. ( )2

43-

14. 4

3

2

2-

15. 12 · x

4

16. x4 x

7

17. (x4)7

18. x · x2 · x

3

19. (x2)3 · (x

5)4

20. a4 b

3 a

5 b

2

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Polynomials and Factoring

Review

A polynomial is made up of several monomials (including the sum or difference of monomials).

A monomial is made up of a coefficient and one or more variables.

The monomial 7𝑥3 has a coefficient of 7 and the variable is 𝑥3 . The exponent of the variable

must be a positive integer in the numerator of the monomial.

The monomial 4𝑥2𝑦 has a coefficient of 4 and two variables 𝑥2 and y.

In a polynomial each monomial is called a term of the polynomial

Terms are separated by addition signs and subtraction signs, but never by multiplication signs.

Watch video " Identifying degree and name of Polynomials" (3:57 min)

https://www.youtube.com/watch?v=l_kY3sHViSA

A polynomial with one term is called a monomial

A polynomial with two terms is called a binomial

A polynomial with three terms is called a trinomial

Examples of polynomials:

Polynomial Number of terms Some examples

Monomial 1 3, x, 7x3

Binomial 2 3x + 7, x2 - x, x - 9

Trinomial 3 x2 + 8x + 6, x

5 - 3x + 12

The degree of a polynomial is the highest degree of its monomials with non-zero coefficients.

The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a

non-negative integer.

Example 1, The degree of the monomial 4𝑥3𝑦2 is 5.

Example 2, The degree of the polynomial 7𝑥4 + 7𝑥3 is 4.

Example 3, The degree of the polynomial 7𝑦𝑥4 + 7𝑥2 + 55𝑥3 is 5. (7𝑦𝑥4 = 1 + 4 = 5)

Adding and Subtracting Polynomial Expressions

Like terms are those that have the same variable raised to the same exponent. 7𝑥3, 1/37𝑥3,

-27𝑥3, 57𝑥3,

Unlike terms are those that have different variables (6x, 5y) or the same variable but raised to

different exponents. 6x, 5𝑥2, 𝑥5

Like terms can be added or subtracted to make a single term. (2a + 3b - 4c) - (a - 4b -17c). This

results in (a + 7b + 13c).

Part A: Multiplying Polynomials

In order to multiply a monomial by a polynomial, you multiply each polynomial term by the

monomial.

4𝑥2 ( 2𝑥2 + 3x - 7) = 8𝑥4 + 12𝑥3 - 28𝑥2

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In order to multiply a binomial by a binomial, you multiply each binomial term by each

binomial.

(2x + 8) (6x -3) = 12𝑥2 - 6x + 48x - 24.

Collect like terms. = 12𝑥2 + 42x - 24

Simplify with a common factor. = 6 (2𝑥2 + 7x - 4)

In order to multiply a binomial by a trinomial, you multiply each binomial term by each

trinomial.

(2x + 8) ( 2𝑥2 + 3x - 7) = ( 4𝑥3 + 6𝑥2 - 14x + 16𝑥2 + 24x - 56)

Collect like terms. = (4𝑥3 + 18𝑥2 + 10x - 56)

Simplify with a common factor. = 2(2𝑥3 + 9𝑥2 + 5x - 28)

Part A: Problems

1. The degree of the following polynomial, 5𝑥5 + 22𝑥2 - 17𝑦𝑥2𝑥3, is (a) 5 (b) 6 (c) 7 (d) 8

2. Expand and simplify. (9x + 2) (12x -3)

3.Expand and simplify. (5x + 6) ( 3𝑥2 + 6x - 7)

4. Expand and simplify. (x + 3) (𝑥2 - 3x + 4 )

Expand and simplify the following.

5. (3a - 4) (5𝑎2 - 3a - 9 )

6. (5a + 6 ) ( - 2𝑎2 + 4a + 1 )

7. ( 4a + 7b ) ( 2a - 5b - 3 )

8. 2(4𝑎2 - 3a + 7 ) - (𝑎2 + 6a)

9. (3a + 2) (8𝑎2 - 5a - 3)

10. 2a (𝑎2 - 2a + 4) - [𝑎2 - 3a (2 - a ) ]

11. (4a + 6) (3𝑎2 - 7a - 9)

12. 3a (𝑎2 - 7a + 8) - [𝑎2 - 4a (8 - a ) ]

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Part A: Answers

1. (b) 6 2. 3(36𝑥2 - x - 2) 3. 5𝑥3 48𝑥2 + x - 42 4. 𝑥3 -5x + 12 5. 15𝑥3 -29𝑎2 -15a

+ 36 6. - 10𝑎3 + 8𝑎2 + 29a + 6 7. 2a(4a - 6a - 3b) - 7b(5b + 3) 8. 7𝑎2 - 12a + 14

9. 24𝑎3 + 𝑎2 - 19a - 6 10. 2a(𝑎2 - a + 1) 11. 2(6𝑎3 - 5𝑎2 - 39a - 27)

12. a(3𝑎2 - 26a + 56)

Part B: Factoring Trinomials

Multiplying two binomials will make a trinomial.

(a + 2) (a + 4) = 𝑎2 + 4a + 2a + 8 = 𝑎2 + 6a + 8

Example 1 Watch video "Factoring Trinomials" (5:07 min)

https://www.youtube.com/watch?v=U7n6B0aIQh0 You can also manipulate a trinomial into two binomials.

Given 𝑎2 + 6a + 8, ask yourself what two numbers multiply to 8 (1 x 8 = 8) but add to the middle

number 6? Only two numbers will do this, 2 and 4. (2 x4 = 8 and 2 + 4 = 6).

You can re-write the polynomial as 𝑎2 + 2a + 4a + 8.

Find a common factor for the first two terms and a common factor tor the last two terms.

a ( a + 2) + 4(a + 2)

Collect like terms ( a + 2 ) and use the Distributive Property = (a + 4) ( a + 2 )

𝐄𝐱𝐚𝐦𝐩𝐥𝐞 𝟐

𝑎2 - 8a + 15 What two numbers multiply to 15 (1 x 15 = 15) but add to -11?

Only two numbers will do this, -5 and -3.

Re-write the polynomial as 𝑎2 - 5a - 3a + 15.

Find a common factor for the first two terms and a common factor tor the last two terms.

a (a - 5) - 3(a - 5)

Collect like terms ( a - 5 ) and use the Distributive Property = (a - 5) ( a - 3 )

𝐄𝐱𝐚𝐦𝐩𝐥𝐞 𝟑 −2𝑎2 + 13a + 7 What two numbers multiply to -14 (-2 x 7 = -14) but add to 13?

Only two numbers will do this, 14 and -1.

Re-write the polynomial as −2𝑎2 + 14a - 1a + 7.

Find a common factor for the first two terms and a common factor tor the last two terms.

-2a (a - 7) - 1(a - 7)

Collect like terms (a - 7) and use the Distributive Property = (a - 7) ( -2a - 1 )

This can also be written as -1(2a + 1) (a - 7) or - (2a + 1) (a - 7)

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Investments and Loans with Compound Interest The compound interest formula can be used to calculate the final amount or the future value of an

investment or loan using a scientific calculator. Where 'A' is the final amount of the investment or loan. It

can also be called the future value.

The letter 'P' is the principal of the starting investment or loan. The letter 'r' is the interest in decimal form.

The letter 't' is the number years. The letter 'n' is the number of compounding periods per year.

When the compound interest is paid yearly, ‘n’ = 1.

When the compound interest is paid semi-annually, 'n' = 2.

When the compounding interest is paid quarterly, 'n' = 4.

When the compound interest is paid monthly, 'n' = 12.

When the compound interest is paid bi-weekly ‘n’ = 26.

When the compound interest is paid weekly, ‘n’ = 52.

When the compound interest is paid daily, 'n' = 365.

Watch video "Compound Interest" (6:31) https://www.youtube.com/watch?v=OQ9Mv2jwQWo

Example 1:

If $2000.00 is invested at a banking institution at 8% for 4 years, what is the amount of money in the

account in each of the following.

(a) compounded annually

(b) compounded semi-annually

(c) compounded quarterly

(d) compounded monthly

(e) compounded daily

Solution 1:

(a) A = 2000 ( 1+ 0.08 ) 4 , A = $ 2720.98

(b) A = 2000 (1 + .08

2)2𝑥4 , A = $ 2737.14

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(c) A = 2000 (1 + .08

4)4𝑥4 , A = $ 2745.57

(d) A = 2000 (1 + .08

12)12𝑥4 , A = $ 2751.33

(e) A = 2000 (1 + .08

365)365𝑥4 , A = $ 2760.20

Problem 8:

At 6% over 7 years an amount of $ 7500.00 is invested at the local bank. Determine the amount of money

that will be in the account for the following conditions.

(a) compounded annually

(b) compounded semi-annually

(c) compounded quarterly

(d) compounded monthly

(e) compounded daily

TMV stands for Time Value of Money

To use this application, you must be able to input all field except

for the one that you are solving. To solve, place cursor in the unknown field,

FV = 0, and press ALPHA ENTER (solve).

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Future Value is defined as the amount of the total investment which includes the initial principle plus the

interest earned on the investment.

Example 1: Determine the future value of an investment of $400 placed in a Canada Savings Bond that

earns 4.3% compounded quarterly for 10 years.

Solution 1: Access the TMV solver financial application in your calculator

N = 4 x 10 (number of payment per year times 10 years)

I% = 4.3% (compound interest rate)

PV = -400 (400 principle investment)

PMT = 0 (no regular payments

FV = 0 (unknown – you will solve this last)

P/Y = 4

C/Y = 4 (compounded quarterly)

Place cursor on FV then press ALPHA SOLVE for future value calculation.

If no additional payments (P/Y) are made to an investment or loan, then enter the value that is equal to

the C/Y value. The Ti will not accept zero for P/Y and so for problems with no payments, make P/Y the

same value as C/Y.

Example 2: If 700 is invested at 8% compounded monthly, how much will there be in the account after 10 years?

Solution 2: There will be $1553.75

N = 10 x 12 = 120

I = 8%

PV = -700 (negative sign)

FV = 0

P/Y = 12

C/Y = 12

PMT = End Begin

Future Value is $613.49

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Math 11 Pre-calculus: Unit 1 – Real Numbers Test A

Name: ____________________________ Date: ________________ Total Mark = / 50 Part A: True or False. Circle your answer = 5 Marks 1. True / False. All whole numbers are also natural numbers. 2. True / False. All integers are whole numbers. 3. True / False. All rational numbers are also integers. 4. True / False. All natural numbers are also whole, integer, and rational numbers. 5. True / False. Adding a rational number to an irrational one makes it rational. 6. True / False. Some real numbers can be both rational and irrational. 7. True / False. Squaring an irrational number makes it rational. 8. True / False. The addition of a rational and an irrational number is always irrational. 9. True / False. The multiplication of two rational numbers is always rational. 10. True / False. The multiplication of two different irrational numbers makes it rational.

Math 11 Pre-calculus: Unit 2 – Powers Test A

Name: ____________________________ Date: ________________ Total Mark = ____ / 50

Part A Multiple Choice. 1. Simplify 492/2 x 3431/3

(a) 75 (b) 3434/2 (c) 494/4 (d) 74

2. Simplify 491/2 x 3433/3

(a) 75 (b) 3434/2 (c) 494/4 (d) 74

3. Simplify 91/2 x 3−3/3

(a) 31 (b) 3−3/6 (c) 27−3/6 (d) 30

4. Simplify 41/2 x 45/2

(a) 45/4 (b) 43 (c) 45/2 (d) 12

5. Simplify 31/3 x 37/2

(a) 38/5 (b) 323/36 (c) 323/6 (d) 37/6

6. Simplify 253/2 ÷ 1252/2

(a) 51 (b) 56/4 (c) 53/2 (d) 50

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Math 11 PC Unit 3 Test A: Radical Expressions and

Equations

Name___________________ Date __________ ________

Marks 40

1. Simplify the following expression. 2.5 √2 + 12 √2 - 7

1

2. Simplify the following expression and identify any restrictions on the values for the variables

4√2𝑥 + 3√8𝑥 - √32𝑥

2

3. Simplify the following expression.

1 √2433

+ √11253

- 7 √99 - 3√11

3 4

4

Math 11 Pre-calculus: Unit 4 – Factoring Polynomials Test A

Name: ____________________________ Date: ________________ Total Mark = / 40

Circle the letter of your answer

1. What is the greatest common factor for 14𝑎4 and 56𝑎7

(a) 14𝑎3 (b) 56𝑎4 (c) 784𝑎3 (d) 14𝑎4

2. What is the greatest common factor for 3𝑎4𝑏7 and 24𝑎2 𝑏6

(a) b + 8 (b) 𝑎2𝑏6 (c) 3𝑎2𝑏6 (d) 3𝑎6𝑏2

3. Factor by grouping 2a - 18 + ab - 9b

(a) (a - 9b)(2 + b) (b) (a - 9)(2 + b) (c) (b - 9)(a + 2) (d) (b - 9)(2a + b)

4. Factor by grouping 12𝑎3+ 15𝑎2𝑏 + 8𝑎𝑏2 + 10𝑏3 (a) (4𝑎2 + 2𝑏2)(3a + 5b)

(b) (3𝑎2 − 2𝑏2)(4a - 5b) (c) (12𝑎2 + 2𝑏2)(a + 5b) (d) (3𝑎2 + 2𝑏2)(4a + 5b)

5. Which expression is equivalent to 9a² - 16?

(a) (3a + 4)(3a - 4) (b) (3a - 4)(3a - 4) (c) (3a + 8)(3a - 8) d (3a - 8)(3a - 8)

6. Select the expression that is equivalent to 2b² + 12b - 54.

(a) 2(b + 9)(b - 3) (b) 2(b - 3)(b - 9) (c) (b + 6)(2b - 9) (d) (2b + 6)(b - 9)

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7. Select the expression that is equivalent to 16c² - 25d²

(a) (8c - 5d) (8c - 5d) (b) (8c - 5d) (8c + 5d) (c) (4c - 5d) (4c - 5d) (d) (4c - 5d) (4c + 5d)

8. Select the expression that is a factor of c² + 2c -15.

(a) (c + 15) (b) (c + 3) (c) (c - 5) (d) (c - 3)

9. Select the factors of a² - 2a - 24

(a) (a + 6)(a - 4) (b) (a + 2)(a - 12) (c) (a + 12)(a - 2) (d) (a + 4)(a - 6)

10. One factor of 21ab³ - 15a²b² is 3ab². What is the other factor?

(a) 7a² - 5b (b) 7a² - 5b² (c) 7ab - 5a² (d) 7a - 5b

11. Factor the following but if it cannot be factored, circle "prime" a² - a - 30.

(a) (a + 1)(a - 30) (b) (a + 5)(a - 6) (c) (a + 6)(a - 5) (d) prime

12. Factor the following but if it cannot be factored, circle "prime" c² + c - 18.

(a) (c + 2)(c + 1) (b) (c - 2)(c + 9) (c) (c + 2)(c + 9) (d) prime

Math 11 PC Unit 5 Test A: Rational Expressions

and Equations

Name____________________ Date _________ ________

Marks 40

1. Determine the non-permissible value(s) for the following rational expression.

-5(a – 1)

(a – 1)(a + 3)

1

2. Write a rational expression in simplest form. State any non-permissible values for the variables.

4b² + 22b + 30

8b²- 4b – 60

3

3. Write an expression with restrictions in simplest form for the time required to travel 100 miles at a rate

of 2c miles per hour.

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Math 11 PC Unit 6 Test A : Quadratic Functions

Name__________________ Date ___________ ________

Marks 40

1. Sketch the graph of the following function. Identify the vertex, axis of symmetry, direction of

opening, maximum or minimum value, domain, range, and intercepts.

Y = 0.20 (x + 3)² + 1

5

2. Determine the quadratic function in vertex form for the following parabola.

3

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Math 11 PC Unit 7 Test A : Quadratic Equations

Name____________________ Date _________ ________

Marks 40

1. Solve the following equation algebraically.

16 = -k² - 8k

2

2. Determine the roots of the following quadratic equation algebraically.

n² + 5n = -4

2

3. A rollerblader jumps off a bank at a skateboard centre. Her direction can be followed by the

function h(d) = - .85d² + .8d + 2.5, where h is the height above ground and d is the horizontal

distance the rollerblader travels from the bank. Both variables are in m.

(a) Write out a quadratic equation to illustrate the situation when the rollerblader lands.

(b) Determine the distance from the bank that the rollerblader will land to 2 decimals.

2

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Math 11PC Unit 8 Test B: Linear and Quadratic

Inequalities

Name_____________________ Date_________ ________

Marks 40

1. Graph the following inequality using a table of values. 3x – 12y < 30 Show your use of a test point in each region to confirm the region.

3

2. With the aid of technology graph the following. x + 5y < 25

Math 11 PC Unit 9 Test B: Trigonometry

Name_____________________ Date ________ ________

Marks 40

1. Sketch an angle in standard position when the angle is 235°.

1

2. What is the reference angle for a 345° angle in standard position?

1

3. Determine the measure of the angle in standard position given its reference angle, 35°, and its

location, the fourth quadrant.

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1

4. The London Eye Ferris Wheel contains 32 capsules. When it opened to then public in the year

2000, it was the largest in the world. If the height and radius of the Ferris wheel are 135 m and

66.5 m respectively, how high up is the capsule located at 55° in the diagram?

3

1

Math 11 Pre-calculus: Unit 10 – Financial Literacy Test B

Name: ____________________________ Date: ________________ Total Mark = ___ / 50

Part A: Multiple Choice = 30 Marks

1. Determine the interest earned on a simple interest investment with a 5-year term at 5.3% on a deposit of $2000. A. $530 B. $789 C. $1700 D. $2530 2. Laura borrowed $7 000 from a financial institution. Which compounding period will result in the greatest amount of interest owed? A. annually B. quarterly C. monthly D. daily 3. Cameron invests $5000 in a GIC at a rate of 3.2% interest compounded annually for 5 years. What is the future value of this investment? A. $5781.05 B. $5800.00 C. $5850.16 D. $5852.86

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4. Patrick invested $6500 for 5 years into a GIC. At the investment’s maturity, its value was $10 000. What was the interest rate if it was compounded quarterly? A. 5.8% B. 7.8% C. 8.7% D. 11.3% 5. Jenny invested $1200 into a high interest e-savings account that offered 2.7% interest compounded weekly. Today his money has grown to $1400. How long was the money invested? A. 5 years B. 6 years C. 7 years D. 8 years

6. Determine the present value of a 5-year GIC with an interest rate of 3.3%, compounded monthly, if the future value is $3525.75. A. $3900.45 B. $1299.14 C. $2990.14 D. $3000.00

1