MTH-2101 Algebraic Modeling

Transcription

1 MTH-2101 Algebraic Modeling Formative evaluation The trip Student name Record number Teacher name Birthday Center Date Schoolboard Mark July 2015

2 INSTRUCTIONS Page 2 of 14 Time 2 h 30 Answers If needed, use additional sheets. Shows all of your steps for each task.. Expected Write all your calculations. process Meet mathematical language conventions. Allowed material Calculator Dictionary Prohibited material Course notes Other reference materials

3 Section A «Assessment of knowledge» Here is the knowledge section. This part contains five rather short questions. Page 4 sur This 14 section goes for 20% of your score. Question 1 If three pairs of socks cost 4.55$. How much will pay you for 15 pairs of socks? Show your work Answer : Question 2 Show all operations you do with your calculator ( ) = 6 Answer: _

4 Page 5 of 14 Question 3 You must fill water bottles for 20 people. Each person will receive a bottle of water of the following dimensions: 15 cm How many liters of water will you need? 8 cm Show your work Answer I need liters of water. Question 4 Solve the following equation : 2( 5x 3) + 4 = 12x - 14 X =

5 Page 6 of 14 Question 5 Find the width (W) of this solid if the lateral area is 572 cm 2. Show all your work. 13 cm 14 cm? cm Width W :

6 Page 7 of 14 Section B «Skills assessment» The scenario presents you the topic of the two tasks that will follow. This section accounts for 80% of your final mark. Scenario A trip in South Carolina Three friends and yourself have decided to go to South Carolina to celebrate the end of your studies. You have decided to rent a recreational vehicle. You have to: Task 1. Select the type of recreational vehicle. Task 2. Determine the amount you have to save before then. Each task will be assessed according to these criteria. Interpreting (20%): are you decoding the symbols correctly? Are you taking into account all the important elements? Did you identify the relationships between quantities? Producing (20%): Do you build an algebraic model? Do you define your variables? Observable manifestations Evaluation criteria EX VG G W VW Producing Interpreting Determining Results /80 Determining (40%): Are you are doing algebraic manipulations? Do you simplify? Are you doing the right operations?

7 Rental amount Page 8 of 14 Task 1 Choice of the means of transportation You hesitate between renting a vehicle that can accommodate 4 people and another that can accommodate 6 people. Indeed, you will invite two other people if it is cheaper to be 6 to go. The distance between your city and South Carolina is 1750 kilometers. Using algebraic models, determine whether it is more economical to travel in groups of 4 or 6 people. Be sure to indicate the total amount each person will have to pay. VR Company - Rental flat rate Rental flate rate include: Basic fees per person: $ 75 To which must be added an amount that varies according to kilometers traveled (round trip). See graph below : Rental amount according to the number of kilometers traveled Véhicules 4 Persons 4 6 Véhicules Persons 6 personnes Vehicle Vehicle personnes Kilometers travelled (round trip)

8 Do not forget to identify all the variables! Tips: to get a good score, you must absolutely use the algebraic model, even if you think you can find the answer without using a model. Answer : For our trip, it is cheaper to be: 4 persons 6 persons Indicate the total amount per person:

9 Page 10 of 14 Task 2 A question of savings (A FUNDamental question) For your trip of one month in South Carolina, you have to save $ 4,000. Your friends would like to leave in eight weeks. Using algebraic models, determine whether it is possible to leave in 8 weeks. Useful information Job Computer repairman weekly wage 700 $ On call Bonus Number of nights on call (per week) 35 $ by night Between 1 and 3, it is you who choose. Weekly expenses 250 $ Do not forget to identify the variables!

10 Page 11 of 14 it is possible to leave in 8 weeks: Yes No Answer Tip: a good justification must include mathematical arguments (numbers). You must indicate the amounts and, ideally, calculate the missing or excess amount. Justify

11 Page 12 of 14 Conversions and Formulas DETACHABLE SHEET Conversions of measures 1 cm 3 = 1 ml 1 m 3 = 1000 liters 1000 cm 3 = 1000 ml = 1 liter Kilometer Hectometer Decameter Meter Decimeter Centimeter Millimeter 0,001 0,01 0, Kiloliter Hectoliter Decaliter Liter Deciliter Centiliter Milliliter 0,001 0,01 0, The plane figures Area and perimeter formulas Square : Figure Perimeter Area s P = 4s A = s 2 Rectangle and Parallelogram h b P rectangle = 2 (b + h) P parallel = 2(b + s) A = bh Rhombus : d c D P = 4c Triangle : a c h b P = a + b + c Circle : r d C = 2 r or C = d A = r 2 = 3,14 Trapezoid: a h b B c P = a + b + c + B

12 Page 13 of 14 Solids: area and volume formulas Form Areas Volume Cube : c A lateral = 4s 2 A total = 6s 2 V = s 3 Rectangular prism h l w A lateral = 2lh + 2wh A total = 2lw + 2lh + 2wh V = l h w : Cylinder : h r A lateral = 2 rh A total = 2 rh + 2 r² V = r²h = 3,14 Cone : h r s A lateral = rs A total = rs + r² V r 2 h 3 Conversion between imperial and metric units 2,5 centimeters = 1 inch 12 inches = 1 foot 30 centimeters = 1 foot 2,2 pounds = 1 kilogram Volume : 1 in 3 = 15,625 cm 3 1 ft 3 = 1728 in 3 1 ft 3 = 0,027 m 3 Area : 1 ft 2 = 144 in 2 1 ft 2 = 0,09 m 2