CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
Lee Webb Math Field Day 2010
Individual Medley, Junior – Senior Level
For each of the following questions, blacken the appropriate circle on the answer
sheet. Each correct answer is worth four points. One point is deducted for each
incorrect answer. An unanswered question is given zero points. Note that
random guessing may adversely affect your score.
You have 50 minutes to complete the examination. If you finish early, review your
answers. When the exam is over, give your answer sheet to the proctor.
All calculators, cell phones, music players, and other electronic devices should be
put away in backpacks, purses, pockets, etc. Leaving early or otherwise disrupting
other contestants may be cause for disqualification.
Junior-Senior Individual Medley
Lee Webb Math Field Day 2010
1.
The sum of the reciprocals of the solutions to the equation ax 2  bx  c  0 is:
1 1

a b
b
d)
c
a)
2.
c) 2
b) 2.25
e) 2.4
c) 2.3
b) 22%
e) 25%
c) 23%
The angle between the hour hand and minute hand on a standard wall clock at 3:15 is:
a) 0
d) 10
6.
b) 1
e) 4
Jorge randomly draws a card from a standard deck of 52 cards. Then Summer also
randomly draws a card (Jorge did not replace his card). What is the best approximation to
the probability that Summer’s card is the same suit as Jorge’s?
a) 21%
d) 24%
5.
b
c
A line has x-intercept 4 and y-intercept 3. Which of the following best approximates the
distance from the line to the origin?
a) 2.2
d) 2.35
4.
c) 
How many points of intersection do the graphs of the following two equations have:
y  3x 2  13x  2010 and y  2010 x 2  3x  13
a) 0
d) 3
3.
c
b
a
e) 
b
b) 
b) 5
e) 12.5
c) 7.5
The polynomial 3 x 3  5 divides evenly into 6 x5  9 x 4  Bx3  10 x 2  15 x  35 . Find B.
a) 21
d) 38
b) 25
e) none of the above
c) 30
Junior-Senior Individual Medley
Lee Webb Math Field Day 2010
7.
An investor sold half his stock at a profit of 20% and 1/6 of it at a loss of 16%. In order to
make 15% over all, what is the profit rate he needs for the remainder of the stock?
a) 7%
d) 23%
8.
c) 21%
For points  x, y  on the curve y  1  x 2 , the maximum value of the sum of x and y is
a) 1
d) 
9.
b) 8%
e) 25%
b) 5
4
e) not enough information
c) 3
2
A rectangular swimming pool measures 20 feet by 50 feet. At the shallow end (the end
along one of the 20 feet sides), the water is 3 feet deep. At the deep end the water is 12 feet
deep. Assuming the bottom of the pool has a constant linear slope, what is the volume of
water in the pool (in cubic feet)?
a) 7500
d) 9000
b) 12000
e) 10000
c) 12500
10. The price of five Zesty Chili Dogs is the same as the price of four Super Sizzlin’
Sandwiches. The price of three Super Sizzlin’ Sandwiches is the same as the price of five
Bustin’ Burgers. What is the ratio of the price of Zesty Chili Dogs to Bustin’ Burgers?
a) 5:5
d) 3:4
b) 3:5
e) 4:3
1
11. The domain of the function f  x  
a)
d)
 ,1
 0,  
b)
c) 5:3
x  x3
2
is
 1,1
c)
 0,1
e) none of these
12. A bag of Scrabble tiles contains 2 O’s, 2 M’s, 2 H’s, 2 I’s, and 2 P’s. Four tiles are chosen
randomly. What is probability that the chosen tiles can be arranged to spell “OHIO?”
a) 2
105
1
d)
630
b) 1
315
c) 2
315
e) 1
1260
Junior-Senior Individual Medley
Lee Webb Math Field Day 2010
13. Let f  x   x2  1 , g  x   2  x , and h  x   1  3x . The function s  x   3x 2  2 can be
written as the composition
a) s  f g h
d) s  h f g
b) s  g f h
e) s  h g f
c) s  g h f
14. Let U  {1, 2,3} . Assuming that A and B are subsets of U, how many possible choices are
there for the pair of sets, A and B such that A  B ?
a) 12
d) 27
b) 19
e) 64
c) 20
15. From one corner of a cube, draw the diagonals across two of the faces containing this
corner. What is the angle formed by these two diagonals?

3
5
d)
6
a)
b)

4
c)

6
e) None of these
16. Each of the following lists has an average of 12. Which list has the largest standard
deviation?
a)
b)
c)
d)
e)
0
0
0
0
0
0
1
3
6
12
20
12
12
12
12
20
23
21
18
12
20
24
24
24
24
17. The day after the homecoming dance, Ms Renard gave an exam to all her students. Sixty
percent of them failed. Realizing her error, she later allowed the students to take a make-up
exam. This time fifty-five percent of the students who failed the first time, passed (those
who passed the first time did not retake the exam). At the end, the ratio of students who
passed to students who failed was:
a) 11:5
d) 73:27
b) 11:9
e) 77:23
c) 67:33
Junior-Senior Individual Medley
Lee Webb Math Field Day 2010
18. Which of the following are factors of x 4  7 x3  11x 2  7 x  12 :
I.
a) I and II only
d) All of them
x-1
II. x-2
III. x+1
b) I and III only
e) None of these
c) II and III only
19. Shown below are three views of the same arrangement of cubical blocks. How many blocks
are in the arrangement?
top
front
a) 6
d) 9
side
b) 7
e) 10
c) 8
20. As usual, let i  1 . One root of the polynomial z 2  (7  i) z  (14  5i) is (4  i ) . What is
the other root?
a) (4  i )
d)
b)
 2  3i 
e)
 3  2i 
 2  3i 
c)
 3  2i 
21. The domain of the function ln  6  x  2 x 2  is:
a) x  2 or
d) 2  x  3
2
x3
2
b) x  3
2
or
x2
c) 3  x  2
2
e) 0  x
Junior-Senior Individual Medley
Lee Webb Math Field Day 2010
x 1 1
  1
y y x
22. Simplify the complex fraction:
2x 2 1
  1
y y x
x y
x  2y
x
d)
2y  x
a)
23. The equation x 
x y
2x  y
x
e)
2y  x
b)
c)
yx
yx
y
 1 represents a region in the x-y plane. What is the area of the
2010
region?
a) 2010
d) 4020 2
b) 2010 2
e) 2010 
c) 4020
24. Square PQRS is inscribed in square ABCD. Side PQ makes forms an angle of 30 degrees
with side AB. Find the ratio of the area of the larger square to the smaller square.
a) 2 :1
b) (4  3) : 4
d) (2  3) : 2
e) (2  3) : 4
c) (4  3) : 2
25. Suppose  is in the third quadrant and for some positive numbers a and b, we have
a 2  b2
cos   2
. Then, tan  is:
a  b2
2ab
2
a  b2
b2  a 2
d)
2ab
a)
2ab
2
a  b2
2ab
e) 2
b  a2
b)
c)
a 2  b2
2ab
Junior-Senior Individual Medley
Lee Webb Math Field Day 2010