Algebraic and Graphical MODELLING IN A FUNDAMENTAL CONTEXT 1

Transcription

1 Algebraic and Graphical MODELLING IN A FUNDAMENTAL CONTEXT 1 MTH Scored Activity 1 Student Identification Name: Address: Telephone: Date submitted: Part 1 Eplicit Evaluation of Subject-Specific Knowledge: /20 Total Part 2 Evaluation of Competencies: /80 /100 Date corrected: Evaluator s signature:

2 MTH ALGEBRAIC AND GRAPHICAL MODELLING IN A FUNDAMENTAL CONTEXT 1 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: Design: Content Revisor: Docimological Revisor: Linguistic Revisor: Illustrations/page layout: Proofreading: Ronald Côté (SOFAD) Isabelle Tanguay (SOFAD) Suzie Asselin Jean-Claude Hamel Alain Bombardier Julie Gravel Michelle Côté Serge Mercier Johanne St-Martin Production Team (English Version) Project Coordinators: Translator: Content Revisor: Typesetting: Proofreading: Jean-Simon Labrecque (SOFAD) Valerie Vucko (i-edit) Rhonda Sherwood Ale Roslin Graeme McDonald Ale Roslin Sources Page 10 Nadia-Lia/Shutterstock This work is financed by the Ministère de l Éducation, Enseignement supérieur et Recherce du Québec. Part of this financing comes from the Canada-Québec bilateral agreement related to minority language education and second languages instruction. SOFAD Any reproduction by mechanical or electronic means, including microreproduction, is forbidden without the written permission of a duly authorized SOFAD representative. Despite the preceding statement, SOFAD authorizes all adult education centres that use the corresponding learning guide to reproduce this scored activity. 2 SOFAD

3 SCORED ACTIVITY 1 Introduction Scored Activity 1 covers Learning Situations 1 and 2 in the Algebraic and Graphical Modelling in a Fundamental Contet 1 guide. It is divided into two parts. Part 1 Eplicit 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 situations 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 contet. Most education centres require you to have an average of 60% or more on the scored activities in order to take the final eamination. Instructions Complete the Student Identification section. Carefully read each question before answering. X=0 Y=0 Write your answers in the space provided. STAT PLO Y= Show all the steps of your work and calculations. MATH MATR X 10 e S LN STO OFF ON X EE N LOG RCL I 2, u E T 4 1 CATAL OG 0 COS 1 { O 7 L4 L1 DRAW PRGM J Y i P 8 U Z 2. GRAP F5 H : DISTR VARS TAN 1 K ( 5 L2 C F COS v L5 TABLE E STAT E B SIN F4 TRAC LIST X,T,0,n APPS SIN 1 CALC DEL ANGL D 1 F3 INS LINK A FORMAT ZOOM MODE ALPHA TEST F2 WINDOW K Once you have completed this scored activity, promptly submit S O FAD TBLSET QUIT A-LOC The use of the calculator is permitted. that you retain a copy for your own records. F1 2nd Locate the weighting of each question. it to your instructor or tutor. As a precaution, we recommend T } L3 ANS L ) w V 6 O 3 ( )? e Q 9 L6 π G TAN [ ] MEM CLEAR ALPHA H M R W + ENTRY SOLVE ENTER 3

4 MTH ALGEBRAIC AND GRAPHICAL MODELLING IN A FUNDAMENTAL CONTEXT 1 Part 1 Eplicit Evaluation of Subject-Specific Knowledge 1 The graph below shows the change in the number of students enrolled in a parachuting course as a function of time (in weeks). CHANGE IN NUMBER OF STUDENTS ENROLLED n(t) t Find the rule that corresponds to this graph. 2 points Rule of the function: 2 1 point The verte of a second-degree polynomial function is at the point (3, 1). Given that the parameter a is positive, determine the number of zeros of this function. Answer: 4 SOFAD

5 SCORED ACTIVITY 1 3 The following graph represents the quota overrun (in tonnes) of a trawler.* (* A trawler is a fishing boat that uses nets called trawls.) FISHING QUOTA OVERRUN (in tonnes) o (t) 14 t a) Determine the rule that corresponds to this graph. 2 points b) Describe in set-builder notation the range of this second-degree polynomial function. Answer: c) Over what interval is this function negative? 1 point Answer: 2 points SOFAD 5

6 MTH ALGEBRAIC AND GRAPHICAL MODELLING IN A FUNDAMENTAL CONTEXT 1 4 On the right is a table of values representing the number of students (in thousands of individuals) as a function of the financial support received (in thousands of dollars) in relation to data collected five years ago. For eample, by looking at this table we can state that 1000 fewer students received funding this year of $1,500 to $2,000 than five years ago. ]0, 0.5] ]0.5, 1] ]1, 1.5] ]1.5, 2] ]2, 2.5] f() a) Find the rule of the function represented by this table of values. 2 points Rule of the function: b) Give the set of zeros of this function. 1 point 5 Answer: Let the step function be f ( )= 1 ( ) a) Find the value of this function s parameters, and draw its graph. f() 2 points 1 1 b) What is the domain of this function? 1 point Answer: 6 SOFAD

7 SCORED ACTIVITY 1 6 Let a second-degree polynomial function have its maimum at the point ( 1, 6) and for which f(2) = 7.5. y a) Use a table of values to graph this function. Then draw the line of the ais of symmetry on the graph. f() points b) What is the function s interval of increase? Answer: 1 point 7 For what value(s) of is the function f() = 3( 2) 2 8 equal to 19? Answer: 2 points SOFAD 7

8 MTH ALGEBRAIC AND GRAPHICAL MODELLING IN A FUNDAMENTAL CONTEXT 1 8 On the right is the graph of the function f() = ( 2) 2. f() 14 Choose from among the graphs below the one that corresponds to the function: f() = 2( 2) 2 1 a) f() b) f() c) f() d) f() point Total for Part 1: /20 8 SOFAD

9 SCORED ACTIVITY 1 Part 2 Evaluation of Competencies This second part evaluates the development of your competencies in mathematics. It contains two evaluation situations. Each one is divided into two tasks. The following criteria (cr.) will be used to evaluate the competencies targeted in this section: Competency 1: Uses strategies to solve situation problems Cr. 1.1 Indication of an appropriate understanding of the situation problem Cr. 1.2 Mobilization of the appropriate mathematical knowledge and strategies Cr. 1.3 Development of an appropriate solution Cr. 1.4 Appropriate validation of the steps in the solution Competency 2: Uses mathematical reasoning Cr. 2.1 Formulation of a conjecture appropriate to the situation Cr. 2.2 Correct application of concepts and processes suited to the situation Cr. 2.3 Proper implementation of mathematical reasoning suited to the situation Cr. 2.4 Proper organization of the steps in an approach suited to the situation Cr. 2.5 Correct justification of the steps in an approach suited to the situation Competency 3: Communicates using mathematical language Cr. 3.1 Correct interpretation of a mathematical message Cr. 3.2 Production of a message appropriate to the contet and in keeping with the terminology, rules and conventions of mathematics SOFAD 9

10 MTH ALGEBRAIC AND GRAPHICAL MODELLING IN A FUNDAMENTAL CONTEXT 1 Scenario 1 Made-to-Order Calculations You work for a Québec company that wants to create a website which lets people buy poster-sized versions of their photos. The width and length of the posters are set at a fied ratio of 3:4. Users must upload their own photo and then enter the desired width of the poster. The area of the poster will be automatically calculated from this width, and the final price, including taes and handling and delivery fees, will be displayed. Your job is to help program this site to correctly display the price of a poster ordered online. The boss tells you that the price of a poster has two components: A fied amount of $13.50 for handling and delivery fees. An amount that depends on the area of the poster, which is $49.50/m 2 (this amount includes taes). 10 SOFAD

11 SCORED ACTIVITY 1 Task 1 Your boss wants to know how much posters will cost. To do this, you must determine the cost of a poster that is 0.72 m wide with an algebraic model that calculates the cost of a poster based on its width. Answer: Score for each criterion Cr Cr Cr /20 points SOFAD 11

12 MTH ALGEBRAIC AND GRAPHICAL MODELLING IN A FUNDAMENTAL CONTEXT 1 Task 2 Your boss is wondering if he should eliminate the handling and delivery charges and increase the price per square metre instead. He asks you to do the following: Determine the new price per square metre assuming that the cost of a 90-cm-wide poster remains the same. Make a conjecture about how the cost of the posters would be changed by this new calculation method, and then validate this conjecture. Eplain how this new method of calculating the cost would change the cost of the posters. Score for each criterion Cr Cr /20 points SOFAD

13 SCORED ACTIVITY 1 Scenario 2 Manual Percussion Drilling A group of interns has travelled to a small village in Niger to teach people a low-cost technique for digging wells to provide access to safe drinking water. The assembly is very simple: A heavy cylinder is rigged to a rope and pulley mounted on a tripod, as shown in the figure on the right. To dig the well, the cylinder is raised by pulling on the rope and then released. The heavy cylinder then falls into the borehole, breaking up the rock. Cylinder Pulley Tripod Before leaving on this mission, the team ran several tests with this assembly to determine the number of impacts needed to reach a certain depth. Since the soil s composition is not the same over its entire surface, the depth of the hole may vary for the same number of impacts. NUMBER OF IMPACTS AS A FUNCTION OF DEPTH OF THE HOLE NUMBER OF IMPACTS DEPTH OF HOLE (mm) SOFAD 13

14 MTH ALGEBRAIC AND GRAPHICAL MODELLING IN A FUNDAMENTAL CONTEXT 1 Task 3 The team has to dig a hole that is deep enough to install the well. Determine algebraically the depth of this hole after 0 impacts. Justify the steps in your approach with mathematical arguments. Depth of the hole after 0 impacts: Score for each criterion Cr Cr Cr /20 points 14 SOFAD

15 SCORED ACTIVITY 1 Task 4 The team has determined that the cylinder strikes the ground on average every 30 seconds. Given that the hole has to be 25 metres deep, determine the number of days it will take the villagers to finish digging the well. Number of days needed to reach a depth of 25 metres: Score for each criterion Cr Cr /20 points Total for Part 2: /80 SOFAD 15

16 MTH ALGEBRAIC AND GRAPHICAL MODELLING IN A FUNDAMENTAL CONTEXT 1 Student s questions Tutor s comments November SOFAD