MTH-2101 Algebraic Modeling

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Gertrude Harrington
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1 MTH-2101 Algebraic Modeling Formative evaluation The pool November 2015 Student name Record number Teacher name Birthday Center Date Schoolboard Mark

2 INSTRUCTIONS Page 2 of 15 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» This is the knowledge section. This part contains five rather short questions. This section goes for 20% of your score. Question 1 If you pay $2,45 per 100 grams of minced meat, how many will youp ay for 0,350 kilogram of minced meat? Show your work Answer : Question 2 Here are the fees of a taxi company in Quebec : o Base price : $ 3,50 o Rate per kilometer : $ 1,65 Do not forget to identify the variables! Produce an algebraic model to calculate the price a user will have to pay according to the distance it has traveled.

4 Page 5 of 15 Question 3 The gray arrow below is composed of a rectangle and an isosceles triangle. Find its total area. Show your work. 33 cm 8 cm 15 cm 28 cm Answer Area of the gray arrow : Question 4 Solve the following equation : X =

5 Page 6 of 15 Question 5 Determines the height (h) of this solid if its total area is 534 cm2 Leave comprehensive traces of your reasoning r = 5 Show your work Height h :

Page 7 of 15 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.

6 Page 7 of 15 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 Installing a pool Another hot summer day! So you start to dream about buying a pool. You have just received this week an advertisement from the Aqua Club Company. It offers various pools models. The pool model you will pick must respect municipal regulations. That's not all; you must also keep in mind the cost of landscaping around it. To address this situation scenario you need: Task 1. Determine the types of pool that comply with municipal regulations. Task 2. Determine the type of landscaping that meet your budget. 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 Page 8 of 15 Task 1 Determine which pool models comply with regulations In the Aqua Club circular, you pick three models that are in the price range you are willing to invest. Here are the sketches of the 3 pools and of your lot. (Sketches. Not to scale) Model 2 Model 1 5 m 4,5 m 7 m 4 m 9 m 2 m Semi circle r = 2 m Model 3 Semi circle r = 2 m 5 m Sketch of your lot: Backyard 5,2 m House 9,3 m Front yard 13,5 m

8 Page 9 of 15 The pool installation must comply with the following municipal regulations: The pool area must not be larger than one-third of the area of the full court (front and back yard regardless of the house). The pool should be placed in the backyard and must not exceed 50% of the area of that court. Tell whether each of three models meets or not municipal regulations and justify your answer in each case. Tip: a good justification must include mathematical arguments (numbers). You must also indicate the quantities and ideally compare sizes. Show your work!

9 Page 10 of 15 Does each type of pool respects municipal regulation? Does Model 1 respects regulations? Justification : Does Model 2 respects regulations? Justification : Does Model 3 respects regulations? Justification :

10 Page 11 of 15 Task 2 Determine the landscaping that meets your budget The pool price includes installation. But a minimum of paving around it would be required. Aqua Club offers 3 types of pavements that can fit many budgets. The price will depend on the materials and time required to perform the work. 1st Landscaping (basic) 2 nd Landscaping (quality) 3 rd Landscaping (superior quality) Material $500 Material $680 Material $720 Work duration: 6h à 7h Work duration: 8h Work duration: 5h à 6h The team at Aqua Club bill $ 55 per hour of work for all types of landscaping. If you have a budget of $ 1,000 for the installation and you do not want to exceed it, which of the three facilities would respect your limit. You have to produce a mathematical model to solve this task.

11 Page 12 of 15 Do not forget to identify the variables To get a perfect marrk, you must absolutelly use an algebraic model, even if you think you can find tje answer without using one.

12 Page 13 of 15 Answer : Does each type of landscaping respects your budget og $ 1000?? Landscaping 1 (basic) : Justification : Landscaping 2 (quality ): Justification : Landscaping 3 (superior quality) : Justification :

13 Page 14 of 15 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

14 Page 15 of 15 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

1 algebraic. expression. at least one operation. Any letter can be used as a variable. 2 + n. combination of numbers and variables

1 algebraic. expression. at least one operation. Any letter can be used as a variable. 2 + n. combination of numbers and variables 1 algebraic expression at least one operation 2 + n r w q Any letter can be used as a variable. combination of numbers and variables DEFINE: A group of numbers, symbols, and variables that represent an