foundations of mathematics 11 - matheducurriculum - foundations of... · 2019. 3. 31. · math 11...

Math 11 Foundations: Introduction MEC MathEduCurriculum Copyright 2019

Page 1 of 16

Foundations of Mathematics 11 Page 1 General Information

Page 2 Record Chart

Page 3 - 6 Outline Example of Unit 4 Quadratics

Page 7 - 11 Test Sample Unit 4 Quadratics

Page 12 - 16 Workbook Example Financial Lit.

Textbook and Workbooks This course uses a combination of Workbooks and a Textbook “Foundations of Mathematics 11”

ISBN-13: 978-0-17-650270-6

by Nelson Education Ltd. 1- 800-268-2222. Price is about $ 95.

Curriculum Outline

*Unit 1 Angle Relationships Textbook *Unit 2 Systems of Equations Workbook 43 Pages

*Unit 3 Linear Inequalities / Optimization Textbook

*Unit 4 Quadratic Functions / Equations Textbook

*Unit 5 Scale Models Workbook 45 Pages

*Unit 6 Statistical Reasoning Textbook

*Unit 7 Mathematical Reasoning Textbook

*Unit 8 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 has two versions in

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

Evaluation There are 8 unit tests which account for 70% of the final mark. There are 3 cumulative tests

which account for 30% of the final mark.

Composition The course is made up of a paper copy of:

8 Chapters Outlines,

8 Chapter Tests each with an A and a B version (16 tests), Plus (16 tests) Answer Keys

3 Cumulative Tests, Plus (3 Cumulative Tests) Answer Keys,

All Answer Keys have a suggested marking scheme,

Computer files of Outlines,Tests and Workbooks are put on 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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Record Chart

Mathematics 11: Foundations of Mathematics

Record Chart

Name: Start Date:

Unit Topic Test A Test B Average Date

1 Angle Relationships

2 Systems of Equations

Cumulative Test 1

3 Linear Inequalities / Optimization

4 Quadratic Functions / Equations

Cumulative Test 2

5 Scale Models

6 Statistical Reasoning

7 Mathematical Reasoning

Cumulative Test 3

8 Financial Literacy

Course Evaluation

Course Evaluation Total Marks Out of Percent Value Result

Tests (8) 70%

Cumulative Tests (3) 30%

Final Mark


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Math 11 Foundations of Mathematics Textbook: Foundations of Mathematics 11 by Nelson

Unit 4 Quadratic Functions & Equations - Chapter 7 Goal: The goal of this chapter is to further develop algebraic and

graphical reasoning.

Objectives: In order to achieve the above goal you will model and solve

problems algebraically and graphically by using:

(a) quadratic functions.

(b) solve quadratic functions by graphing, factoring, and using the

quadratic formula.

(c) solve problems modeled on quadratic functions and equations,

What Needs to be Done:

Unit 4 has 8 sections: 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, and 7.8. Each section in unit

4 has an accompanied video to for a section.

Use the section-numbered videos below as they correspond in the Unit Practice

Guide below to help you with your understanding.

Video Selections:

7.1 https://www.youtube.com/watch?v=fDj0u2CNSoc Exploring Quadratic Relations (4:49 min)

7.2 https://www.youtube.com/watch?v=yzzHMhzFbzA

Properties of Graphs of Quadratic Functions (4:36 min)

7.2 https://www.youtube.com/watch?v=xAnTbbxSLnY

Graphs of Quadratic Functions (5:26 min)

7.3 https://www.youtube.com/watch?v=hcng4zEpSVg Solving Quadratic Equations by Graphing (12:53 min)

https://www.youtube.com/watch?v=fDj0u2CNSochttps://www.youtube.com/watch?v=yzzHMhzFbzAhttps://www.youtube.com/watch?v=xAnTbbxSLnYhttps://www.youtube.com/watch?v=hcng4zEpSVg


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7.4 https://www.youtube.com/watch?v=C8YcqPLAz3A Quadratic Relations of the Form y = a(x r)(x s) (7:41 min)

7.4 https://www.youtube.com/watch?v=2K9Wf3FznVU Factored Form of Quadratic Function.mp4 (9:20 min)

7.5 https://www.youtube.com/watch?v=1RknGmFnJiU

Solving Quadratic Equations Using the TI-83 Calculator (3:11 min)

7.5 https://www.youtube.com/watch?v=SDe-1lGeS0U

Solving Quadratic Equations by Factoring - Basic Examples (7:18min)

7.6 https://www.youtube.com/watch?v=y99lNRqLjBA Quick Way of Graphing a Quadratic Function in Vertex Form (3:53 min)

7.7 https://www.youtube.com/watch?v=JSwjmTFMDwg

Solving Quadratic Equations using the Quadratic Formula (4:27 min)

7.8 https://www.youtube.com/watch?v=RE732MTV-dk

Solving Problems using Quadratic Models (8:15 min)

7.8 https://www.youtube.com/watch?v=IGGnn9oa4QY

More Word Problems Using Quadratic Equations - Example 1(4:57 min)

Quadratic Functions & Equations

Unit 4 Practice Guide - Chapter 7 (Check Mark as You Complete)

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

358 Read over “Explore the Math”. Watch video “Exploring

Quadratic Relations” (4:49 min).

359 Read over “In Summary”.

360 Under “Further Your Understanding” do # 1-6.

361-362 Read over “Learn About the math”. Go over Example 1.

363-364 Go over “Apply the Math”.

https://www.youtube.com/watch?v=C8YcqPLAz3Ahttps://www.youtube.com/watch?v=2K9Wf3FznVUhttps://www.youtube.com/watch?v=1RknGmFnJiUhttps://www.youtube.com/watch?v=SDe-1lGeS0Uhttps://www.youtube.com/watch?v=y99lNRqLjBAhttps://www.youtube.com/watch?v=JSwjmTFMDwghttps://www.youtube.com/watch?v=RE732MTV-dkhttps://www.youtube.com/watch?v=IGGnn9oa4QY


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365-367 Go over Examples 3 and watch video “Graphs of Quadratic Functions”

(5:26 min) and go over Example 4.

368-369 Read over "In Summary". Watch video “Properties of Graphs of

Quadratic Functions” (4:36 min). Under “Check Your Understanding”

try # 1-3.

369-372 Under “Practising” try # 4, 5ac, 6, 7i, 8, 9ac, 10, 11i and iv,

12, 14, and 16.

373-378 Read over “Investigate the Math” and watch video “Solving

Quadratic Equations by Graphing” (12:53 min). Go over Examples

1-3.

379-381 Read over “In Summary”. Under “Check Your Understanding” try # 1-4.

Under “Practising", try # 5ac, 6ac, 7, 8ac, 10, and 13.

383-389 Watch video “Quadratic Relations of the Form y = a(x r)(x s)” (7:41

min). Go over Examples 1-4.

390 Read over "In Summary". Watch video "Factored Form of Quadratic

Function.mp4" (9:20 min).

391 Under “Check Your Understanding” try # 1abc, 2ab and 3.

391-395 Under “Practising, try # 4acf, 5, 7, 8, 10ace, 11ad, 13, 15, 17 and 19.

398 Under “Practising, try # 1ad, 2, 3, 4, 6, 8, 9, 10 and 12.

399-404 Read over “Learn About the Math”. Watch video “Solving Quadratic

Equations Using the TI-83 Calculator" (7:10 min)

Go over Examples 1- 5. Watch video “Solving Quadratic Equations by

Factoring - Basic Examples” (7:18 min).

405-407 Read over “In Summary”. Under “Check Your Understanding” try # 1ad

and 2aceg. Under “Practising, try # 3ad, 4ad, 5, 6ad, 7, 8, 9, 10, 12, 13

14, and 18.

408 Read over “Investigate the Math”. Watch video “Quick Way of

Graphing a Quadratic Function in Vertex Form” (3:53 min)

410-415 Go over Examples 1-4.

416 Go over “In Summary”.

417 Under “Check Your Understanding” try #1ace and 2ace.

417-421 Under “Practising”, try # 4, 5, 6, 7, 8, 11, 12, 14, 17, 18, and 19.

422-426 Watch video “Solving the Quadratic Equation using the Quadratic

Formula" (4: 27 min). Go over Examples 1-4.

427-429 Read over “In Summary” and under “Check Your Understanding”

try # 1ad, 2ad, 4ad, 6ad, 7, 8, 10, and 11.

431-434 Watch video “Solving Problems using Quadratic Models” (8:15 min).

Go over Examples 1-3.


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435 Watch video “More Word Problems Using Quadratic Equations -

Example 1”(4:57 min). Go over Example 4.

436-438 Read over “In Summary” and Under “Practising” try # 2, 3, 5, 7, and

11.

440 Under “Chapter Self-Test” try # 1ad, 2a, 3, 5, 6ad, 7ad and 8.

443-444 Under “Practising” try # 1b, 2, 4ac, 5, 8ac, 9, 11, 13ac, 15, and 17.

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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Math 11 Foundations Unit 4 Test A: Systems of Linear

Inequalities

Name____________________ Date _________ ________

Marks 45

1. Match the descriptions on the bottom with the corresponding letter to the terms on the left.

5 _____ Linear inequality

_____ Solution set

_____ Continuous

_____Solution region

_____ Half plane

_____ Optimal solution

_____ Constraint

_____ Objective function

_____ Feasible region

_____ Discrete

A. A limiting condition of the optimization problem.

B. The part of a graph that represents the solution set.

C. A relationship between two expressions where one may have symbols such as ≥, ≤, >,

and


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2. Graph the solution set for this inequality. -8x + 4y ≤ 12

2

3 . Graph the solution set for the following inequality on the Cartesian Plane below.

{ (x,y) | -2y + 4 ≥ -8 + y , x Є I, y Є I }

2


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4. A sports store sells softball bats for $100 each and sells hardball bats for $ 150 each. The

owner wants to have revenue of at least $ 1500.00 per day for the combined sales in bats. (a)

Graph the combinations that will meet his sales target.

(b) What restrictions are there on the domain and range?

(c) Select one combination and state its characteristics.

4

5. For the following system of linear inequalities describe what you can infer from the graph

( 4x + 5y ≤ 20 and 7x - 2y ≥ 14) about the restrictions on the domain and range of the

solution.

3

Graph courtesy of www.emathzone.com

http://www.google.ca/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=XMxHL1ymS-wNqM&tbnid=bVicrLBcXjsekM:&ved=0CAQQjB0&url=http%3A%2F%2Fwww.emathzone.com%2Ftutorials%2Flinear-programming%2Fexamples-of-linear-inequalities-in-two-variables.html&ei=q0VpU-GgL5HboATz9oC4Dg&bvm=bv.66111022,d.cGU&psig=AFQjCNFV6WgMHM3CifCogJYLj0_zSHuhoA&ust=1399494127060478


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6. For the following linear inequality system

(a) Graph the solution set.

(b) Describe the solution region.

(c) Determine a solution and check its validity.

{ ( x,y) | 3x + 10y > 42, x Є W, y Є W }

{ ( x,y) | 6x - 18 ≤ 3y, x Є W, y Є W }

5

7. A catering company is making two types of appetizers: tapas and sushi. Up to a maximum

of 900 appetizers are needed but there are to be at least three times as many sushi appetizers

compared to tapas.

(a) Write a system of inequalities that models this situation and define the variables.

(b) Outline the restrictions on the variables.

(c) Sketch a graph to determine the solution set.

(d) State two combinations of numbers of appetizers that could be used to prepare the

appetizers.

6


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8. The following model represents an optimization problem. Determine the maximum solution.

3 Optimization Model

Restrictions: c Є R, d Є R

Constraints: c ≥ 0, d ≥ 0, 3c + 4d ≤ 36, c + d ≥ 6

Objective function: S = 2.5c + 5.5d

9. A hockey team needs help to coordinate their trip to the playoffs in Kelowna BC. The

team is made up of 22 players and 2 coaches. Due to the abundance of equipment, the team

needs to use minivans and SUVs. Each minivan can accommodate 4 members and each

SUV 6 members of the team but only 6 minivans and 4 SUVs are available. The coordinator

wants to determine the combination of minivans and SUVs that will require the minimum

and maximum number of vehicles. Create a model to represent this situation. State a

combination that will maximize and minimize vehicles.

8


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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

https://www.youtube.com/watch?v=OQ9Mv2jwQWo


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Investments and Loans Using the Financial Calculator

Graphing calculators like the Ti-83+ have the capability to do financial calculations such as

investments, loans, leases, mortgages, and annuities.

Your calculator has a financial application that is used to determine properties of investments

involving compound interest (it is not used for simple interest investments). Here is a summary

of the functions:

1. Press APPS

2. Press ENTER twice to access

the financial application called

the TMV Solver.

N = number of payments per year X

number of years (is the total number of

payments for the term of the

investment)

I% = interest rate as a percentage

PV = Present value or Principle typed

in as a negative number for

investments

PMT = regular payment amount in

$ typed in as a negative number

FV = Future value of investment

P/Y = number of payments per year

C/Y = Compounding frequency per

year (n from previous formula)


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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).

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)


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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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Watch video "Ti84 TVM Solver - Future Value with Compound Interest" (5:02)

https://www.youtube.com/watch?v=sJ396p6kLG4

Example 3:

If 8500 is invested at 5.5% compounded semi-annually, find the future value of the investment

which includes interest after 12 years.

Solution 3:

The future value is $16,299.82

Future Value Problems

Problem 22:

A $8000 investment is made in a 6 year closed GIC compounded quarterly at 6%. Calculate the

value of this investment at the end of the term. Fill in the spaces with the values that you used in

your calculation

N =

I =

PV =

FV =

P/Y = C/Y =

PMT: End Begin
https://www.youtube.com/watch?v=sJ396p6kLG4

foundations of mathematics 11 - matheducurriculum - foundations of... · 2019. 3. 31. · math 11...

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