MHS Practice Examination

Transcription

1 MHS Practice Examination Exam # MATHEMATICS CULTURAL, SOCIAL AND TECHNICAL OPTION SEC V CST Student Question Booklet Parts A, B and C This resource can be used for FREE by any teacher or student with an active Math Help Services account Detailed video solutions to each question are available within your MHS account Copyright 2016 Supporting Teachers Developing Students

2 Practice Exam Sec V CST Exam #2 SUCCESS ON SUMMATIVE EXAMINATIONS The best way to prepare for a summative exam is to write multiple versions of that exam so that you become familiar with the format, the language and the time constraints. A memory aid is a much more valuable resource if you make it before you begin writing practice exams. We strongly suggest that you place yourself under the same time constraints while writing this exam as you will face when you write the ministry exam at the end of your course. Note that detailed video solutions to this exam are available in your Math Help Services account. Once your teacher makes the video solutions available you should watch the video solution to each question you had difficulty with to ensure that you know how to face this type of problem in the future. INSTRUCTIONS You may use a calculator (with or without a graphic display), a ruler, a set square, a compass, a protractor or additional graph paper. You may refer to the memory aid you prepared on your own before the examination. This memory aid consists of one handwritten letter-sized sheet of paper (8 ½ x 11). Both sides of the sheet may be used. Any reproduction of this memory aid is forbidden. Only the above mentioned materials may be used. You have 3 hours to complete this examination. Note: Figures are not necessarily drawn to scale. 464

3 Sec V CST Exam #2 Practice Exam PART A This part of the examination consists of Questions 1 to 6. Each question in this part of the examination is worth 4 marks Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The two figures below are equivalent. The perimeter of the rectangle is 24cm and its length is twice as long as its width. Perimeter = 24cm What is the height of the triangle? a) 2cm b) 4cm c) 8cm d) 12cm 2. Doug has 100cm 2 of sheet metal in his shop class. He wants to shape it into a closed solid that would have the largest volume possible. Which of the following shapes would give him the largest volume if he has 100cm 2 of sheet metal to work with? a) Sphere b) Cube c) Cylinder d) Cone 3. Determine the chromatic number of the graph shown below. a) 2 b) 3 c) 4 d) 5 465

4 Practice Exam Sec V CST Exam #2 4. The following system of inequalities represents the constraints related to an optimization situation. x 0 y 0 2x + y 14 x 2y + 2 x + y 14 Which of the following polygons of constraints represents this situation? a) c) b) d) 466

5 Sec V CST Exam #2 Practice Exam 5. A day camp wants to hire counselors for the summer. The owner can afford to hire at most 80 people. She wants to hire at least four times as many Junior counselors as Senior counselors. Let x: number of Junior counselors y : number of Senior counselors Which of the following systems of constraints could describe this situation? a) x 0 y + 0 x y 80 x 4y b) x 0 y + 0 x y 80 x 4y c) x 0 y + 0 x y 80 y 4x d) x 0 y 0 x + y 80 y 4x 6. Congruent triangles ABC and A B C are drawn in the Cartesian Plane below. Which of the following Geometric Transformations transform ABC to A B C? a) A rotation of 90 about the origin, followed by a translation of t : ( xy, 8,2 ) ( x + 8, y + 2 ) t : 4, 6 xy, x+ 4, y 6, followed by a reflection in the line x = 2. b) A translation of ( ) ( ) c) A reflection in the y-axis, followed by a translation of t ( xy) ( xy+ ) d) A reflection in the x-axis, followed by a reflection in the y-axis. 0,6 :,, 6 467

6 Practice Exam Sec V CST Exam #2 PART B This part of the examination consists of Questions 7 to 10. Each question in this part of the examination is worth 4 marks Short Answer 7. The following table provides information on the 200 students in the graduating class at Howard S. Billings High School. On the Honour Roll 45 Boys Girls Total Not on the Honour Roll 52 Total One of the 200 students was chosen at random. Given that the student chosen was a girl, what is the probability that she was on the honour roll? 8. Dawson s Garage does oil changes and tire changes. There are different constraints on the number of oil changes and tire changes this garage can do in one day. The following polygon of constraints is associated with this situation. Points A, B, C, and D are the vertices of the polygon of constraints. The profit per oil change is $70 and the profit per tire change is $75. What is the maximum profit the garage can make in one day? 468

7 Sec V CST Exam #2 Practice Exam 9. The Wilson sisters each have a cottage on a large piece of land in Wakefield. The graph below shows the location of the six cottages and the distances of the roads that connect them. All of the lengths are scaled in meters. In the winter, it is expensive to pay for the snow removal on these roads. The sisters want to have each cottage connected (so that no cottage is left isolated) but have the minimum length of road remain open in order to reduce the snow plow costs. If it costs $0.50 per meter to have the snow removed, what is the minimum cost to plow the network of roads that would need to remain open through the winter? 10. Given the system of inequalities and the corresponding polygon of constraints below, determine the coordinates of vertex B. ➁ ➀ 7x+ 3y 41 ➁ 3x + 7y 69 ➂ y x 3 ➀ ➂ 469

8 Practice Exam Sec V CST Exam #2 PART C This part of the examination consists of Questions 11 to 16. For each question, you must show all your work to justify your answer. Your work must be organized and clearly presented and cannot simply involve listing the calculator applications or programs used to obtain results or information. Each question in this part of the examination is worth 10 marks. Show all work for each question. 11. Norris Ltd. makes two types of watches. One is gold plated, the other is silver plated. These watches are very popular, so Norris Ltd. must make at least 200 gold watches and at least 100 silver watches each day. The company produces at least twice as many gold watches as silver watches. Norris Ltd. produces a maximum of 600 watches each day. The profit on a gold watch is $40.00 and the profit on a silver watch is $ Graph the polygon of constraints and determine the number of each type of watch the company should make to maximize its profit. Use x : number of gold watches y : number of silver watches 12. Explain the difference between Majority Ballot voting procedure and a Plurality Ballot Voting Procedure. Use examples and tables in your explanation. 13. A U.S. Airline operates seven flights through five cities. The following table indicates which cities are connected by this airline s flight paths. Atlanta Boston Chicago Detroit El Segundo Atlanta Connected Not Connected Connected Not Connected Boston Connected Connected Connected Not Connected Chicago Not Connected Connected Connected Connected Detroit Connected Connected Connected Connected El Segundo Not Connected Not Connected Connected Connected Eddie is an airline service inspector who wants to fly along each path once and only once to evaluate the service on the planes flying this route. Construct a graph for this situation. Name the type of path Eddie is using to fly along each edge of the graph once and only once. Finally, name the path (the order of the cities) that he will travel. 470

9 Sec V CST Exam #2 Practice Exam 14. David and Sheila each have a bag of marbles. David has 24 marbles in his bag and Sheila has 14 marbles in her bag. Both bags contain either red or blue marbles. David has 20 red marbles. If a marble is drawn at random from each bag, the probability that both marbles will be blue is What is the probability of drawing two red marbles if one marble is drawn at random from each bag? 15. Dan is in charge of the food for this year s Athletic Banquet. The table below shows the different steps involved in preparing the food. Dan is experienced at preparing large meals and therefore can complete several of the steps at the same time. Step Tasks Time Prerequisite Task(s) A Washing the Vegetables 25 min None B Cooking the Meat 60 min None C Slicing the Bread 15 min None D Slicing the Meat 40 min B E Slicing the Vegetables 35 min A F Making the Sandwiches 20 min C and D G Making the Dip 20 min E H Packaging the Food 10 min F and G I Delivering the Food 30 min H J Setting the Food out at the Banquet 15 min I What is the minimum time required for Dan to prepare the food and have it ready to eat at the Banquet? 16. Consider the Geometric Transformation ( ) ( ) h0, n : x, y nx, ny where n > 1 on a polygon in the Cartesian Plane. Formulate a conjecture describing the relationship between the area of the original polygon and the area of the transformed polygon. 471