Mathematics 504 Competency 2. Secondary 5 MATHEMATICS 504 USES MATHEMATICAL REASONING PRACTICE MIDYEAR EXAM

Transcription

1 Mathematics 504 Competency 2 Secondary 5 MATHEMATICS 504 USES MATHEMATICAL REASONING PRACTICE MIDYEAR EXAM

2 PART A: MULTIPLE CHOICE EACH QUESTION IS WORTH 4 MARKS 1. The following system of inequalities is associated to the graph below: 2x + y 5 and x y 4 What is the solution region associated to the given system of inequalities? A) E B) F C) G D) H

3 2. The following polygon of constraints is given: Which of the following corresponds to the coordinates of one of the vertices of the polygon of constraints? A) (4, 2) B) (2,-1) C) (1, -2) D) (8, -4)

4 3. Rectangle ABCD and its image are represented in the Cartesian below: Which of the following rules represents the transformation of rectangle ABCD? A) (x, y) (x + 8, y + 4) B) (x, y) (x 8, y 4) C) (x, y) (x + 4, y + 8) D) (x, y) (x 4, y 8)

5 4. Sandy works two different jobs to pay for a summer trip to Portugal. She works as a waitress on the weekends and babysits during the week. Let x represent the number of hours that she works as a waitress and y represent the number of hours that she babysits in one week. The constraints associated to this situation are: x + y 32 x y 2 Which of the following describes the system of inequalities for this situation? A) Sandy works at least 32 hours per week. The number of hours spent waitressing are at most half the number of hours spent babysitting. B) Sandy works at least 32 hours per week. The number of hours spent babysitting are at most half the number of hours spent waitressing. C) Sandy works at most 32 hours per week. The number of hours spent waitressing are at most half the number of hours spent babysitting. D) Sandy works at most 32 hours per week. The number of hours spent babysitting are at most half the number of hours spent waitressing.

6 5. The following figures are equivalent. 60 m 30 m What will be the circumference of the circle to the nearest meter? A) 75m C) 150m B) 90m D) 180m 6. The two cylinders shown below are similar. The area of the base of the smaller cylinder is 50.24cm 2 and its height measures 6cm. The area of the base of the larger cylinder is cm 2. What is the volume of the larger cylinder? A) cm 3 C) cm 3 B) cm 3 D) cm 3

7 PART B: SHORT ANSWER EACH QUESTION IS WORTH 4 MARKS 7. Jack is organizing a weekend basketball tournament at LBPHS. The tournament will host the juvenile boys and juvenile girls of the AAA division. The maximum number of teams that can register for the tournament is sixteen. The number of girl teams is at most half the number of boy teams. Let and x be the number of juvenile boy teams y be the number of juvenile girl teams What are the inequalities that represent these two constraints? 8. The graph below displays two triangles associated by a transformation. What is the rule of the transformation that associates the two triangles?

8 9. The following polygon of constraints is given: What are the inequalities associated to the given polygon of constraints?

9 10. The following two figures are equivalent: The area of the rectangle is 1200cm 2. The measure of the small base of the trapezoid is represented by x. The measure of the large base of the trapezoid is two units more than the small base. The measure of the height of the trapezoid is 15cm. What is the value of x?

10 PART C: APPLICATION EACH QUESTION IS WORTH 10 MARKS 11. ANOTHER FUNDRAISER LBPHS is organizing a fundraiser to raise money for one of their many charities. The fundraiser will consist in selling t-shirts and sweatshirts. The price of a t-shirt is $8 and the price of a sweatshirt is $20. Let x represent the number of t-shirts and y represent the number of sweatshirts. The organizers bought the items in bulk and, therefore, only paid $1 per t-shirts and $5 per sweatshirt. The organizers have a maximum of 2000 items to sell. The number of t-shirts available for sales is at least 800 and at most The number of sweatshirts available is at most the same as the number of t-shirts. What is the maximum net profit the school can expect to make?

11 12. THE BASKETBALL TOURNAMENT Every year LBPHS organizes a basketball tournament. The tournament is always open to boy and girl teams. Each team has to pay a registration fee of $150. The following polygon of constraints is associated to the profits made by the school in 2014: Where x represents the number of girl teams and y represents the number of boy teams Last year a maximum number of teams registered for the tournament. This year, because of water infiltration in the gym, the number of boy teams is at most half the number of girl teams. What is the difference between the amount collected last year and this year s maximum profit?

12 13. TRANSFORMATION SOFTWARE You have been asked by your math teacher to explore a new software design program. The software allows you to change an initial figure into a different version through a series of transformations. The initial figure is shown in the graph below: The initial figure must undergo the following transformations: 1) (x, y) (x + 3, y 1) 2) (x, y) ( x 2, y 2 ) Using the graph above, draw the three figures associated to each transformations.

13 14. A FENCING SITUATION The following two diagrams represent two parks that are equivalent: 80m 98m 4 x+5 80m 90m 120m The city is planning on fencing the two parks The cost of fencing is $75/m. What is the total cost of fencing required?

14 15. MOTEL MONTREAL A small motel outside of Montreal rents out single and double occupancy rooms. The owner charges $80/night for single occupancy rooms and $120/night for double occupancy rooms. Let x represent the number of single occupancy rooms and y the number of double occupancy rooms. The following constraints were used in 2013 by the owner because of renovations that were taking place: y x x 3 x 6 x + y 10 x 3y The following polygon of constraints is associated to the expected daily profits that the owner made last year: Last year, the owner made a maximum daily profit. This year, the owner no longer needs to have at most the same number of double occupancy as single occupancy rooms to rent. By how much will his maximum profit increase?

15 16. SIMILAR SOLIDS The following two solids are similar: The volume of the smaller prism is 2800cm 3. The volume of the larger prism is cm 3. If the area of the base of the smaller prism is 200cm 2, what is the height of the larger prism?