Grade 11 University Prep Math Exam

8/10/2019 Grade 11 University Prep Math Exam

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JR. GENIUS EDUCATIONAL SERVICES INC.


Mock Exam

MCR3U: Functions and Relations

Grade 11, University Preparation

Duration – 3 hours

Non-Programmable calculator allowed

Answer all questions on the question paperUse blank side of the sheets for rough work, if needed.

Name: Date :

Section Your score Total Marks

Knowledge 25

Communication 25

Problem solving 25

Application 25

Total

100

Good Luck!

Jr. Genius -Grade 11 University Math Final Exam 1-866-9-Way To A JRGenius.com





3


(e) x = 22

6±

5. Simplify:63

43

24

18−−

y x

y x

(a)2

6

4

3

y

x

(b)4

3 10 y

(c)10

6

4

3

y

x

(d)4

3 106 y x *

(e)6

10

4

3

x

y

6. What is the value of x in the equation 04.01=

x?

(a) 5(b) 12(c) 16

(d) 25(e) 50

7. Which of the following functions represents an exponential growth function?

(a) y 3= x

(b) y = 3 x−

(c) x3 y =

(d)3

x y =

(e) 3

1

x y =

8. What is the amplitude of the graph of y= 8sin2x ?

(a) 2(b) 4(c) 8(d) 16(e) 180




4


9. Megan works at a local animal shelter. She needs to find out whether there are more dogs than cats inher country. Which of these methods would give Megan the best information?

(a) compare the number of dogs and cats at the animal shelter on a randomly selected day(b) compared the number of dogs and cats in one randomly selected acre of her town(c) compare the number of dogs and cats treated at the veterinary clinic on a randomly selected

day

(d) compare the number of dogs and cats in one randomly selected acre of every town and

township in her county(e) compare the number of dogs and cats at the animal shelter and clinic on a randomly selected

day

10. A random sample of 10,000 people was taken to determine the number of hours of TV watched perweek. The results of the survey showed a normal distribution with a mean of 4.5 hours and a standarddeviation of 0.5 hours. What is the median number of hours of TV watched?

(a) 0.5 hours(b) 4.0 hours

(c) 4.5 hours(d) 5.0 hours(e) 9.0 hours

11. To estimate the population of the deer herd in Potter County, an environmental researcher uses thecapture-tag-recapture method. He captures and tags 135 deer. He then releases them and waits two mouths before trying to recapture any deer. This time he captures 146 deer of which 2 were previously tagged.From this information, what is the best estimate of the number of deer in Potter County?

(a) 279(b) 281

(c) 1,849(d) 9,855(e) 19,710

12.Give the following salaries:$54,000; $75,000; $55,000; $62,000; $226,000;$65,000; $59,000; $61,000; $162,000; $59,000

The mean, median and mode, respectively are:

(a) $87,000; $62,000; $59,000(b) $61,000; $61,000; $61,000(c) $824,900; $61,500; $59,000(d) $87,800; $63,500; $54,000(e) $87,800; $61,500; $59,000

13. What is the solution ofn213

27

1 −= ?

(a) n=-3(b) n=0(c) n=1(d) n=2




5


(e) n=3

14. When a cannonball is shot into the air, its height, in feet, during the flight is given by the function h(t) =

160 + 480t-16t2 where h(t) is the height in seconds. What is the maximum height of the cannonball?

(a) 15 feet(b) 160 feet(c) 3,744 feet(d) 3,760 feet(e) none of the above

15. A circle with center (-3.4) is tangent to the x-axis in the standard (x,y) coordinate plane. What is theradius of this circle?

(a) 3(b) 4

(c) 5(d) 9(e) 16

16. In ABC, if <A and <B are acute angles, and sin A =13

10, what is the value of cos A

(a)13

69*

(b)13

3

(c)13

3

(d)13

133

(e)13

3

17. In the right triangle ABC below, what is the sine of <A?

(a)247

(b)25

7

(c)7

24




6


(d)25

24 *

(e)

24

25

18. What is the slope of the line 5y= -3x + 10

(a) –3

(b) -5

3 *

(c)3

5

(d) 2(e) 10

19. What is the largest possible product for 2 even integers whose sum is 34?

(a) 64(b) 68(c) 120(d) 240(e) 288

20. The measures of the angles of a triangle are in the ratio of 2x:3x:5x as illustrated below. What is themeasure of the smallest angle in the triangle?

(a) 18(b) 20(c) 30(d) 36˚

(e) 40

21. In the graphs below, all axes have the same scale. One of the graphs shows y=3x+1. Which is thatgraph?

(a) (d)




7


(b) (e)

(c) *

22. What positive value of k would make the lines below parallel in the standard (x,y) coordinate plane?kx + 2y = 818x + ky = 12

(a) 0(b) 2(c) 6 *(d) 8(e) 12

23. Lengths for the triangle below are given in feet. What is the value of x?

(a) 2

(b) 3

(c) 4(d) 5

(e) 15

24. What equation is graphed below?




8


(a) x + y = 4(b) 2x + y = 8

(c) x + 2y=8(d) x – 2y = 8(e) ½ x + y = -8

25. Which system of inequalities is represented in the graph?

(a) x > 4 (d) x < 44y < -3x + 2 4y > 3x + 12

(b) x < 4 (e) x < 4

4y > -4x + 16 4y < 3x + 16

(c) x > 4

3y > -4x +12

Communication Answer the following questions in the space provided.




9


26. (a) At what interest rate, to the nearest hundredth of a percent, compounded monthly, would you doublean investment of $50,000 in 10 years? [3 marks]

(b) Explain your strategy for part a. [2 marks]

(c) use an example to illustrate your percent for part a. [1 mark]

27. If the ellipses 19

)2(

4

)3( 22

=−

++ y x

and 14

)2(

9

)3( 22

=−

++ y x

were graphed, what features

would be the same? What features would be different. Explain. [5 marks]

28. In a city park, a sprinkler waters an area with a circumference that can be modeled by the equation x2 +y2 = 20. The sprinkler is located at the origin. A path through the park can be modeled by the equation 2x – y = 12. Will the sprinkler spray people walking along the path? Explain. [5 marks]




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29. Classify each of the following numbers into one or more of these sets: real, rational, irrational,complex, imaginary, pure imaginary. Explain your reasoning. [Show work below. 1 mark each]

(a) 5 (b) 4− (c) 1+ 3 (d) 3 + i 6

30. The graph of y= x is expanded vertically by a factor of 4, reflected in the y-axis, translated 5 units to

the left, and translated 4 units upward. Write the equation of the transformed function. [3 marks]

31. Describe how the graph of each of the following functions can be obtained from the graph of y=f(x).[1 mark each]

(a) y= 3f (4-x) – 7 (b) y= -f (0.5(x-3)) + 1

Problem solvingSolve the following problems. Please show work.

32. Let G be the graph if x

y1

= . H is the reflection of G in the line y=2x. The equation of H can be

written as 12x2 + bxy+ cy2 + d = 0. Find the values of b, c and d. [4 marks]






12


Application 36. Instead of paying $4000 at the end of 5 years and $3000 at the end of 10 years, Nicole agrees to makeequal monthly payments for 10 years. Find the monthly payment if the interest charged is 8% per annum,compounded monthly. Explain your method. [6 marks]

37. A cargo ship is tied up at a dock. At low tide, a 12-m long unloading ramp slopes down from the shipto the dock and makes an angle of 30 to the horizontal. At high tide, the ship is closer to the dock, andthe unloading ramp makes an angle of 45 to the horizontal. [6 marks]

(a) Determine the change in the horizontal distance from the ship to the dock from lowtide to high tide.

(b) Determine the change in the height of the upper end of the unloading ramp above thedock from low tide to high tide.






14


where x seconds is the time since the flare was fired. [5 marks]

(a) Describe how the graph of y= -5(x-4)2 + 80 can be obtained by transforming the graphof y= x2 (b) interpret the equation of the transformed function to find the maximum height reached

by the flare and the time it takes to reach this height.

-THE END-


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Grade 11 University Prep Math Exam