Practice

pdf

School

A. Y. Jackson Secondary School *

*We aren’t endorsed by this school

Course

Subject

Mathematics

Date

May 24, 2024

Type

pdf

Pages

Uploaded by MajorArt13133

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 1/13 Exercises Lesson 1: Alternate Forms of an Equation of a Line 1. Given the following graph, what is the equation of the line in: a. point-slope form b. slope- -intercept form c. form 2. Determine the slope and intercept of the line . 3. A line has a slope of and passes through the point . a. Write the equation of the line in point-slope form. b. Using your equation from part a) determine three additional points that lie on the line. 4. A line is represented by the equation . Rewrite the equation in the form and . 5. Determine the value of such that the line represented by the equation has a -intercept of and then rewrite the equation of the line in the form .

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 2/13 6. At C, g of carbon dioxide has a volume of L. For each degree the temperature, , increases, the volume, , of the carbon dioxide increases by . a. Write an equation that represents the relationship between the volume of the g of the carbon dioxide gas and temperature in point-slope form. b. What is the volume of the g of the carbon dioxide at C? 7. Determine if the following lines represent a partial or direct variation. a. b. c. 8. A line is represented by the equation . a. Determine the equation of a line that is parallel to the given line. b. Determine the equation of a line that is perpendicular to the given line. c. Determine the values of slope that would result in a line that is steeper than the given line. Lesson 2: Comparing Linear and Non-Linear Relations 1. Determine if the following graphs represent a linear or non-linear relation.

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 3/13 a. b. c.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 4/13 d. 2. Determine if the following tables of values represent a linear or non-linear relation. a. b. c.

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 5/13 3. Determine if the following equations represent a linear or non-linear relation. a. b. c. d. 4. Determine which of the following equations does NOT represent a linear relation. a. b. c. d. 5. Hyacinth says that is linear because she believes the degree on the variables and is one. Kody disagrees and shows Hyacinth that the graph of the relation is not a straight line. Rewrite the equation so that Hyacinth can clearly see that the degree on all of the variables is not equal to one. 6. To calculate the volume of a cylinder we can use the formula , where represents the radius and represents the height. a. A cylinder has a ±xed height of units. Is the relationship between volume and radius linear or non-linear? b. A cylinder has a ±xed radius of units. Is the relationship between volume and height linear or non-linear?

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 6/13 7. When a piece of paper is folded in half, one crease line and two sections of paper are created. The paper is then folded in half again and again, each time increasing the number of crease lines by one. Identify the relation between the number of creases and the number of sections of paper as linear or non-linear. Justify your answer. Lesson 3: Applications of Linear Relations 1. Euclid High School has two clubs: the Chess Club and the Math Olympics Club. The Chess Club gets new members each week. After six weeks the club had members. The Math Olympics Club has been tracking the linear relationship between membership and number of weeks in the table shown here: Time (weeks) Number of Members a. Which club accepts the greater number of members each week? b. Which club has the greater number of founding members? 2. Jada is considering two di²erent payment plans for a gym membership. The ±rst plan charges a ³at rate of plus per hour she uses the gym. The second plan has no ³at rate but charges per hour. a. Graph both membership plans on the same grid. b. At a certain point, the cost and number of hours for the two plans are identical. After how many hours would the cost of both memberships be the same?

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 7/13 3. Jenna borrowed money from her parents to spend on a trip to Whistler. She repays the loan by making weekly payments. The graph shows how the money, , is paid over time, . a. How much money did Jenna originally borrow? b. When will Jenna have fully repaid her parents? c. What would the graph of Jenna's repayments look like if she only borrowed and pays back each week? d. Considering the two di²erent repayment plans, when would Jenna owe the same amount on both plans? 4. The line intersects the line at the point . Find the values of and . 5. Leyda's family lives near the beach. They have decided to renovate the basement suite in their home so they can rent it out. The cost of the renovations is and they expect that it will cost them each night the suite is rented to cover the costs of cleaning, utilities and upkeep. The family plans to rent the suite out for per night. Use a graph to determine how many nights will be needed to rent the basement before the cost of the renovations and nightly costs equal their rental proceeds. 6. Betty is building a fence. She went to two carpenters that each charge an initial fee plus an additional fee for each metre of fencing.

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 8/13 The relationship between the total price, (in dollars), with respect to the length of fence, (in metres) is linear. The ±rst carpenter uses the equation to determine his pricing for his clients. The second carpenter uses the following graph to determine the pricing for his clients: Which of the two carpenters would charge Betty the least amount of money for metres of fencing? 7. Three hockey teams are ordering practice jerseys from Hockey Designs. The total cost includes an initial design fee of and a cost of per jersey. Hockey Designs requires a minimum order of jerseys. The teams have allocated a combined total of to spend on the jerseys. a. Determine the possible values for the number of jerseys ordered and the possible values for the total cost. b. If each of the three teams have players, do the teams have enough money allocated for everyone to get a jersey? Lesson 4: Interpreting Stories and Graphs

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 9/13 1. Match each description to one of the given graphs. a. A child runs at a constant speed for seconds before stopping. b. A sloth moves slowly at a constant speed for seconds before stopping. c. A panther stalks its prey, moving slowing at a constant speed, stopping occasionally to make sure it remains unseen. d. A chipmunk runs away from a dog, not stopping for anything! 2. Nick and Mary are siblings who are riding their bikes from school to home. They both leave school at the same time; however, Mary peddles faster and reaches their house before Nick. Determine which distance time graph best represents the situation described.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 10/13 i. ii. iii. iv. 3. Sunny and Ravi are out for a walk. They walk at a moderate pace for minutes, then walk at a slow pace for minutes, and then walk at their fastest pace for the last minutes. Sketch a distance time graph to represent their movement.

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 11/13 4. A hiker starts at a trailhead and hikes to the end of the trail and back. The graph shows the hiker's distance from the trailhead during their trip. a. How long did the hiker's entire trip take to complete? b. What is the length of the trail? c. What does the ³at portion on the graph represent? d. Was the hiker traveling faster on the way to the end of trail or on their way back to the trailhead? Justify your answer. 5. Xiulan is going on a hike. Her trip is represented by the distance time graph shown. Use the table to describe the various portions of Xiulan's hike.

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 12/13 Segment Direction Distance (km) Time (h) Speed (km/h) 6. Tiago is getting some exercise by walking from his house to the park and then back home again. The distance time graph represents his trip with the vertical axis labelled as distance from his home , in metres. Draw an equivalent distance time graph where the vertical axis is labelled as distance from the park , in metres.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

9/5/2019 CEMC's Open Courseware - All Exercises, Answers, and Solutions https://courseware.cemc.uwaterloo.ca/42/141/assignments/1125/0 13/13 7. If you walk in a perfect circle in front of a motion detector, what would the distance time graph look like? © 2018 University of Waterloo. Except where noted, all rights reserved.

Practice

Related Documents