CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
Lee Webb Math Field Day 2010
Individual Medley, Freshman-Sophomore 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.
Freshman-Sophomore Individual Medley
Lee Webb Math Field Day 2010
1. How many passwords are there that fit the following conditions: a password is to be six
letters long, alternating consonants and vowels with no repetitions allowed among the vowels
(for this problem, consider “y” to be a vowel).
a) 820800
d) 920000
c) 960000
b) 900000
e) 1200000
2. An equation of the line passing through  1,  2  and parallel to the line through  5, 0  and
 0, 4 is:
a) 4 x  5 y  3  0
d) 4 x  5 y  6  0
b) 4 x  5 y  6  0
e) 4 x  5 y  6  0
c) 4 x  5 y  3  0
3. A rectangle has length x and width y. Another rectangle is 3 more than twice as long and 4
more than thrice as wide. Which of the following polynomials represents the area of the
second
a) 6xy+9x+8y+12
d) 6xy+9x+4y+6
b) 6xy+8x+9y+12
e) None of these
c) 6xy+6x+12y+12
4. The apothem of a regular hexagon is 10. What is the area of the hexagon?
a) 200 3
d) 200
b) 200 / 3
e) 600
c) 600 3
5. Xia and Alon each select one card from a standard deck of playing cards. Which of the
following is closest to the probability that their cards match (e.g. two kings, or two 7’s, etc)?
a) 1%
d) 6%
b) 2%
e) 8%
c) 4%
Freshman-Sophomore Individual Medley
Lee Webb Math Field Day 2010
6. A 30  60  90 triangle is given whose hypotenuse has length 2. A similar triangle has
hypotenuse length equal to the longer leg of the first triangle. What is the length of the
longer leg of the second triangle?
3
a)
d) 3/4
b) 3 / 2
e) 1/2
c) 3/2
7. The number halfway between 1/3 and 1/6 is
a) 1/18
d) 1/4
b) 1/9
e) 1/2
c) 1/5
8. The original price of a big screen TV at Ella’s Electronics was $1234. To prepare for the
President’s Day Sale, Ella marked it down 20%. But after having a rotten Valentine’s Day,
she raised the new price by 25%. The new price is approximately how much larger than the
original price?
a) $60
d) -$30
b) $30
e) -$60
c) $0
9. The two points  x, 0  and  0, x  are 18units apart. What is the area of the triangle that has
vertices at  2 x, 0  ,  0, 0  ,  0, x / 2 ?
a) 18
d) 60 2
b) 64
e) 100
c) 81
10. EBA’s Pizza place sells a 12” diameter pizza. Which of the following pizza sizes is closest
having double the area of the 12” pizza?
a) 15"
d) 18"
b) 16"
e) 20"
c) 17"
b) 1 2
e) 5
c) 0
5
 x3  x 2.5 
11. Solve for m :  1.5 4   x m
 x x 
a) -1
d) 1
Freshman-Sophomore Individual Medley
Lee Webb Math Field Day 2010
12. Which line is perpendicular to 3 x  4 y  5 ?
a) 8 x  6 y  5
b) 6 x  8 y  7
3
e) y   x  10
4
d) 6 x  8 y  9
c) 6 x  2 y  8
13. The values of x that are at most 8 units from 5 can be described using absolute value as:
a)
x 5  8
b)
x 5  8
d)
x 8  5
e) none of these
c)
x 8  5
14. Suppose that a dart player is as likely to hit a round dart board at any point as at any other
point. What is the probability of hitting a point closer to the outside edge than the bullseye
(the middle of the target)?
a) 10%
d) 50%
b) 25%
e) 75%
c) 40%
15. Among 35 children, 23 say they enjoy playing soccer; 13 say they enjoy football. Five
children were in both of these categories. How many do not enjoy either sport?
a) 0
d) 5
b) 2
e) 6
c) 4
16. Solve the system of equations:
2 3
 4
x y
4 3
 2
x y
a)
 4, 1
b)
 2, 1
d)
 1, 12 
e)
 2,1
c)
 12 , 38 
Freshman-Sophomore Individual Medley
Lee Webb Math Field Day 2010
17. Suppose functions f and g are given by the tables below
x
1 2 3 4 5
f ( x) 5 3 2 1 4
x
1 2 3 4 5
g ( x) 3 4 1 5 2
Find f ( g ( f ( g ( g ( f ( f (1))))))) .
a) 1
d) 4
b) 2
e) 5
c) 3
 One angle of a parallelogram has measure a . The measures of the two adjacent angles are
b and (a  10) . What is the measure, in degrees, of the smallest angle of the
parallelogram?
a) 70
d) 85
b) 75
e) 90
c) 80
19. Josy put $100 in the bank. Several years later, her balance has grown by 1000%. This
means there is how much money in the account?
a) $900
d) $10000
b) $1000
e) $11000
c) $1100
20. For two sets A and B , the symmetric difference, A B is the set of elements that are in A or
B but not both. Suppose that A  1, 2,3, 5, 7,8 , B  1, 2, 4, 5,6, 8,9 , and
C  1, 4,5,6,8,9 . What is the set  A B  C ?
a)
d)
1,3,5,7,8
1, 2, 5, 6
b)
3, 7
c)
1, 8
e) 
Freshman-Sophomore Individual Medley
Lee Webb Math Field Day 2010
21. Which of the following can NOT be the measure of the exterior angle of a regular polygon?
a) 30
d) 50
b) 40
e) 60
c) 45
22. Starting with two natural numbers r1 and r2 , perform a repeated division process as follows.
Divide r1 by r2 and take note of the remainder, r3 . Then divide r2 by r3 and obtain a new
remainder r4 . Continue until you find r6  1 . What is the smallest possible value for r1 ?
a) 13
d) 21
b) 15
e) not enough information
c) 18
23. The degree measures of a quadrilateral are x, 2 x,3 x, 4 x . What is the sum of the degree
measures of the two larger angles?
a) 180
d) 252
b) 235
e) 270
c) 240
24. The average of 3 numbers is 14. The 1st two numbers are consecutive even integers and the
3rd number is half the first. Then the largest of the numbers is
a) 16
d) 22
b) 18
e) not enough information
c) 20
25. A train and a car are 144km apart. If they travel toward each other, they will meet in 40
minutes. If they travel in the same direction, the train will overtake the car in 90 minutes.
What is the speed of the train, in km/h?
a) 120
d) 256
b) 132
e) 312
c) 156
Freshman-Sophomore Individual Medley
Lee Webb Math Field Day 2010