MTH Scored Activity 2

Transcription

1 Algebraic and Graphical Modelling MTH Scored Activity 2 Score for Part 1: Score for Part 2: Date corrected: Evaluator s signature: Student Identification Name: Address: Telephone: Date submitted:

2 MTH Algebraic and Graphical Modelling This scored activity was produced by the Société de formation à distance des commissions scolaires du Québec (SOFAD). Production Team (French Version) Project Coordinators Author: Content Revisors: Linguistic Revisors: Docimological Revisor: Illustrations: Graphic Design: Proofreading: Robert Longpré (SOFAD) Nancy Mayrand (SOFAD) Nicole Perreault Gilles Gascon Alain Bombardier Michelle Côté Marie-Pierre Gazaille Julie Gravel Serge Mercier Serge Mercier Johanne St-Martin Production Team (English Version) Project Coordinators: Jean-Simon Labrecque (SOFAD) Valerie Vucko (i-edit) Translator: Rhonda Sherwood Content Revisor: Alex Roslin Typesetting: Anik Dessureault Proofreading: Alex Roslin First Edition: September 2014 Sources: Shutterstock : p. 3 Barry Barnes, p. 7 Edyta Pawlowska p. 9 WilleeCole, p. 11 Irina Nartova p. 15 MeePoohyaPhoto p. 17 (cottage at left) ipics; (cottage at right) mradlgruber; (snowmobile at left) Fredrick Corey Chestnut; (snowmobile at right) iofoto This work is financed by the Ministère de l Éducation, du Loisir et du Sport du Québec. Part of this financing comes from the Canada-Québec bilateral agreement related to minority language education and second languages instruction. Despite the following statement, SOFAD authorizes all adult education centres that use the corresponding learning guide to reproduce this scored activity. SOFAD All rights for translation and adaptation, in whole or in part, reserved for all countries. Any reproduction by mechanical or electronic means, including microreproduction, is forbidden without the written permission of a duly authorized SOFAD representative. 2 SOFAD

3 Scored Activity 2 Scored Activity 2 covers Learning Situations 3 to 5 in the Algebraic and Graphical Modelling learning guide. It is divided into two parts. PART 1 - Explicit Evaluation of Subject-Specific Knowledge This section contains a series of unrelated questions. Each question targets one or more specific concepts. PART 2 - Evaluation of Competencies You will be presented with a situation similar to the ones you encountered in each of the learning situations. You will be asked to complete a series of tasks involving the concepts you have learned, but in a new context. The evaluation grid that follows the second part of this scored activity contains important information about the evaluation criteria. Be sure to refer to it when completing this section. This grid will be completed by the evaluator. Once you have completed this scored activity, promptly submit it to your tutor along with any accompanying documents. Most education centres require students to have an average of 60% or more in order to take the final examination. Instructions Complete the Student Identification section. Carefully read each question before answering. Write your answers in the space provided, showing the details of your work if applicable. Show all the steps of your calculations. The total points for each question are indicated in parentheses to the left of the question number. The use of a calculator is permitted. SOFAD 3

4 MTH Algebraic and Graphical Modelling Memory Aid General form of the equation of a line: y= ax+ b where a represents the rate of change and b is the y-intercept. Rate of change: y a = x y x ( x1, y1) and ( x2, y2) represent any two points on the line. Perimeter: Rectangle P = 2l+ 2w Triangle P = s1+ s2 + s3 4 SOFAD

5 Scored Activity 2 Scored Activity 2 Points (2) 1 PART 1: Explicit Evaluation of Subject-Specific Knowledge Joëlle buys a package of 200 loose-leaf sheets at the beginning of the school year. She uses an average of four sheets per day. Identify the variables, and give the rule representing the number of sheets remaining as a function of time. (5) 2 The graph below illustrates the relation between the time remaining and the distance left to travel for a high-speed train. Time remaining as a function of distance left to travel TIME (min) y (60, 25) (120, 5) x DISTANCE (km) a) Identify the variables, and find the rule of this function. SOFAD 5

6 MTH Algebraic and Graphical Modelling b) What does the function s rate of change represent? (13) 3 Two compact vehicles, one a hybrid, the other conventional, have gas tanks of the same capacity. The hybrid vehicle consumes 5 L/100 km, and the conventional vehicle consumes 8.5 L/100 km. Both gas tanks have a capacity of 55 litres. a) Determine the variables, and find the rule representing the volume of gas remaining as a function of the distance travelled for each car. Hybrid vehicle: Conventional vehicle: b) Graph this situation. c) Which vehicle will run out of gas first? Explain your answer. 6 SOFAD

7 Scored Activity 2 d) What is the difference between the distance traveled by both vehicles with a full tank of gas? (5) 4 You and a friend want to buy the latest tablet on the market. One store is selling the tablet for $620 including taxes and is offering interest-free instalment payments. You decide to make a down payment of $120 with monthly payments of $100. Your friend makes a down payment of $195 and makes the same monthly payments as you do. a) Identify the variables, and establish the rules representing your debt repayment and that of your friend. b) Who will pay off the debt first? Explain your answer. SOFAD 7

8 MTH Algebraic and Graphical Modelling (8) 5 Read the following text, and identify the inequalities. Then qualify them (implicit or explicit), and if possible, express them algebraically. According to the federal government, there were an estimated homeless people in Canada in 2005, of which approximately lived in Montréal. More than fines have been handed out to over 4000 homeless people in Montréal in the last 12 years. Despite the creation of no fewer than 700 social housing units directly for homeless people, the number of Canadians relying on shelters such as La maison du père and the Old Brewery Mission continues to rise. (12) 6 Complete the following table. Assume that the reference set is the set of real numbers. Algebraic representation Number line Interval Set-builder notation x ] 5, 2] { x x < 0} 8 SOFAD

9 Scored Activity 2 (5) 7 Audrey offers a dog-walking service in her neighbourhood. Almost all of her neighbours have a dog and are happy to have their pet go for a walk while they are at work. Mrs. Voisine wants her Jack Russell Terrier to take his walk any time from 9:00 a.m. but before 3:00 p.m. Mr. Bastien insists that his dog have his daily walk after 10:00 a.m. but before 4:00 p.m. Meanwhile, Mr. Rocheleau doesn t really care when his dog goes for a walk, as long as it s not before 8:00 a.m. or after 5:00 p.m. Audrey does not want to spend more than three consecutive hours walking the dogs. Is this possible? If yes, in what time interval should she walk them? (Represent each interval on a timeline.) (12) 8 Solve the following inequations, and express your answers in the form requested. Assume the reference set is the set of integers. Verify your answers. a) 4x 2> 2x+ 3. Express your answer on a number line. SOFAD 9

10 MTH Algebraic and Graphical Modelling b) 2( a 1 3) 2 (8 2 a). Express your answer using the roster method. c) 3c c. Express your answer using set-builder notation. 2 3 (5) 9 The perimeter of the rectangle below is greater than 36 units. Given that the rectangle s length and width cannot be negative, calculate the possible values of the variable x. 3x 12 x 10 SOFAD

11 Scored Activity 2 (4) 10 More than people in Canada used the services of a food bank in Of this number, there were twice as many adults as children. What is the minimum number of children who used a food bank in 2011? Express the solution set in set-builder notation. (8) 11 Serge supports an environmental cause and has decided to make a monetary donation. He s trying to decide between two options: giving a fixed amount that will be deducted directly from his pay every two weeks or making a monthly donation that will be automatically deducted from his savings account. If he chooses the second option, the deduction will be $17.50 more than if he makes payments every two weeks. If Serge makes the same donation in both cases, determine the annual amount of his donation. Find the solution algebraically. SOFAD 11

12 MTH Algebraic and Graphical Modelling (9) 12 Louison and Marcel are both sales reps working at the same company. Louison receives a base salary of $500 per week plus 2% of the value of the sales he makes. Marcel prefers to be paid solely based on a percentage of his sales. He receives 5% of the total value of the sales he makes. Use the table of values below to find, to the nearest hundred dollars, the total sales Marcel has to make in order to earn a higher weekly salary than Louison. You must base your problemsolving approach on this table of values. Louison s and Marcel s weekly salaries as a function of sales Sales ($) Louison s salaries ($) Marcel s salary ($) , , , , ,000 30,000 1,100 1, SOFAD

13 Scored Activity 2 (9) 13 The rectangle and isosceles triangle shown below have the same perimeter. Use the two figures below to determine the rule associated with each one s perimeter. Then solve the system of equations graphically to find the lengths of all of the sides for both figures as well as their perimeter. 10 x 2(x + 1) 2x 2x Side lengths of the rectangle: Side lengths of the triangle: Perimeter of both figures: SOFAD 13

14 MTH Algebraic and Graphical Modelling (14) 14 Monique buys a new car. Despite making a large down payment, she still has to borrow $18,000. She is paying off her loan by making monthly payments of $600. Her brother Robert buys a used car. He takes out a $12,000 loan that he is paying off with $300 monthly payments. The situation of their respective balances is represented by the following functions: B= m B= m B: balance at the end of each month m: number of months a) Find the ordered pair solution algebraically. b) Complete the two tables of values below using the appropriate values for this situation, and then represent the situation in a Cartesian plane. Comparison method Graphical method Table of values m B Table of values m B 14 SOFAD

15 Scored Activity 2 c) What does the ordered pair solution mean? d) How many months will it take Monique to pay off her loan? e) How much will Robert still owe when his sister has paid off her debt? f) How many months longer will it take Robert to pay off his debt than Monique? (9) 15 Émile plants a tree that is 120 cm high. It grows at a rate of 15 cm per year. Annabelle plants another species of tree that is 55 cm high; it grows 20 cm each year. If y (number of years) represents the independent variable and C (height of the tree) is the dependent variable, establish the rule that represents the height of each tree as a function of years. a) Émile s tree. b) Annabelle s tree. SOFAD 15

16 MTH Algebraic and Graphical Modelling c) In how many years will both trees be the same height, and what will the height be? 1) Use an algebraic method. 2) Verify your solution by representing both functions in a Cartesian plane. Total for part 1: out of 120 points 16 SOFAD

17 Scored Activity 2 PART 2: Evaluation of Competencies A well-deserved break! Four friends want to spend their Christmas vacation in the Laurentians and are planning to rent a chalet for three nights. They also want to rent two snowmobiles so they can go on a ride at least 200 km but not more than 350 km long. After doing some research on the Internet, they narrow their choices down to two chalets. They also find numerous snowmobile rental offers, but there are two in particular that interest them. Chalet rentals The Gentle Slope $50.00 per person per night Chalet rentals Guaranteed R&R $ rent plus $35.00 per person per night Snowmobile rentals Ultimate Ride $60.00 flat rate $0.60 per kilometre (gas at renter s expense) VEHICLE SPECIFICATIONS 40-L tank capacity Average fuel consumption: 0.14 L/km Snowmobile rentals Roarin Good Time No flat rate $0.80 par km (cost of gas not included) VEHICLE SPECIFICATIONS 40-L tank capacity Average fuel consumption: 0.15 L/km SOFAD 17

18 MTH Algebraic and Graphical Modelling Your task 1) Determine which chalet rental is more affordable. Solve this algebraically. 2) Determine which snowmobile rental is more affordable. Solve this using two different approaches. 3) Calculate the cost of gas for both snowmobile rental options. Assume gasoline costs $1.40 a litre. Re-evaluate whether the snowmobile rental chosen in 2) is still more affordable. 4) Calculate the total cost of the group s vacation in the Laurentians. 18 SOFAD

19 Scored Activity 2 SOFAD 19

20 MTH Algebraic and Graphical Modelling Evaluation Grid for Scored Activity 2 Evaluation situation: A well-deserved break! This grid, which will be completed by the evaluator, contains indicators for the two competencies being evaluated. Part of the task may be evaluated using more than one indicator from both competencies. For each indicator, the ratings have the following meanings. 5. The student exceeds expectations (excellent). 4. The student meets expectations (very good). 3. The student meets expectations but makes minor errors (good). 2. The student partially meets expectations but makes at least one major error (poor). 1. The student does not meet expectations (very poor). Competency 1: Uses strategies to solve situational problems Indicator Evaluation Reference The learner identifies the relevant information, and distinguishes the useful information from the superfluous. (Criterion 1.1) The learner chooses the best functional model for solving the situation. (Criterion 1.2) The learner chooses the best mode of representation. (Criterion 1.2) The learner interprets the algebraic or graphical model related to the situational problem. (Criterion 1.2) The learner uses the appropriate approach when solving a situational problem involving equations or inequations. (Criterion 1.3) The learner validates his or her statements using mathematical arguments. (Criterion 1.4) Activities 3.1 and Activity Activities 1.2, 4.2 and Activities 3.1, 3.3 and Activities 3.1 and Activities 3.3 and SOFAD

21 Scored Activity 2 Competency 2: Uses mathematical reasoning Indicator Evaluation Reference The learner identifies the mathematical characteristics of a relation or the parameters of the equation of a line. (Criterion 2.2) The learner solves the evaluation situation using a system of first-degree equations in two variables. (Criterion 2.2) The learner makes a conjecture from a given situation. (Criterion 2.1) The learner can validate his or her conjecture. (Criterion 2.3) The learner is able to draw an appropriate conclusion from his or her results. (Criterion 2.5) The learner follows mathematical rules and conventions when solving the situational problem. (Criterion 2.4) Activities 2.1, 3.1 and Activities 5.1 and Activities 3.3, 4.3, 5.1 and Activities 5.1 and Activities 5.1 and Activities 2.3, 3.3, 4.4 and 5.2 Total for part 2: out of 60 points SOFAD 21

22 MTH Algebraic and Graphical Modelling Student s questions 22 SOFAD

23 Scored Activity 2 Tutor s comments SOFAD 23

24 September 2014