CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
MATHEMATICS FIELD DAY 2004
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. When the exam is over, give
your answer sheet to the proctor.
Freshman-Sophomore Individual Exam – March 2004
1. If a code name is to consist of three letters (taken from A to Z) followed by 4 digits and if no
digits are allowed to be the same, then the total number of possible code names is:
a)
d)
 26 10 
 26 10 
3
1
4
3
4
2
b)
 26  10 9 8 7 
e)
 26 25 241098 7 
3
c)
 26  25 24  104 
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. Which of the following is a polynomial
i) 0
a) (i) only
d) (i), (ii), and (iv)
4. Solve for x:
a) –4
d) –4, 4
 x
ii) 

 3 
iii)
b) (iii) only
e) all
 x  1
2
iv)
 x  1
3
c) (i) and (iv)
2x  3  4x  5
b)  1 3
e) no solution
c) 4,  1 3
5. Select one card at random from a standard deck of 52 playing cards; what is the probability
the chosen card is an Ace or a face card (Jack, Queen, or King)?
a) 3
169
d) 2
13
b) 8
e) 4
169
c)
1
16
13
Freshman-Sophomore Individual Exam – March 2004
6. Four shapes are drawn in a plane in such a way that they intersect. For example, four circles,
four rectangles, or four squares are drawn. Which shape can produce the maximum number
of points at intersections?
a) all equal
d) square
b) circle
e) rectangle and square
c) rectangle
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 marked price of a bracelet is 20% less than the suggested retail price. Niki purchased the
bracelet, for 25% off the marked price at a Fiftieth anniversary sale. What percent of the
suggested retail price did Niki pay?
a) 50
d) 75
b) 55
e) 80
c) 60
9. Find x so that the distance between the two points  x, 0  and  0, x  is 18?
a) 3
d) 9 2
b) 2 3
e) 13
c) 12
10. What is the prime factorization of 630?
a) 2  5  63
d) 32  5 14
b) 2  32  5  7
e) 7  9 10
c) 2  5  7  9
11. If you halve the length of the hypotenuse in a right isosceles triangle, then the sides of the
new triangle are what multiple of their original length?
a) 1 4
b) 1 2
d)
e) 2
2
c) 1
2
Freshman-Sophomore Individual Exam – March 2004
12. Which line is parallel to 3 x  4 y  5 ?
a) 3x  4 y  5
d) 6 x  8 y  9
b) 6 x  8 y  7
e) y  3x  10
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 the board at any point as at any other point. What
is the chance of hitting the shaded region on the dartboard?
a) 10%
d) 50%
b) 25%
e) 75%
c) 40%
15. A class of 28 students has 16 boys. Eighteen of the students are right-handed. There are 10
right-handed boys. How many of the girls are left-handed?
a) 4
d) 8
b) 5
e) 12
c) 6
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 Exam – March 2004
17. Simplify 4 x  3 y  7  y  9 x  8 y  10  2 x
a) 5 x  4 y  1
d) 15 x  12 y  3
b) 5 x  4 y  1
e) 15 x  12 y  7
c) 15 x  11y  3
 Given that line L1 is parallel to L2 and T is the given transversal. What is the angle    
a) 146o
d) 216 o
b) 160o
e) not enough information
c) 180o
19. Kristin’s account balance on January 1st was $50. On December 31st her account balance had
grown to $150. What was the percent increase in her account?
a) 50%
d) 200%
b) 66%
e) 300%
c) 100%
20. Suppose that A  1, 3, 5, 7 , B  2, 4, 6, 8 , and C  1, 8 . What is the set
 A  B    A  C  , that is A intersect B union with A intersect C
a)
d)
1
1, 3, 5, 7
b)
8
c)
1, 8
e) empty set
Freshman-Sophomore Individual Exam – March 2004
1
 x1/ 2 
x

21. If
 1/ 3  , then n equals:
x x
n
a)
1
d) 5
b) 5
6
6
c) 6
5
e) 6
4
22. A girl jogs up a hill at 4 mph and rides her bike down again at 12 mph. It takes 20 minutes to
complete the round trip. The distance up the hill is:
a) 0.8 miles
d) 2.33 miles
b) 1 mile
e) not enough information
c) 1.33 miles
23. Let f  x   x2  2 and g  x   x  2 . Compute f g 1 :
a) –5
d) 3
b) –3
e) none of these
c) –1
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. Given the data values –3, 5, x, 9, 13 have the properties that
(i)
(ii)
5<x<9
the median equals the mean.
Then x equals
a) 5
d) 6.5
b) 5.5
e) not enough information
c) 6
Freshman-Sophomore Individual Exam – March 2004
CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
MATHEMATICS FIELD DAY 2004
Team Medley, Freshman-Sophomore Level
Each correct answer is worth ten points. Partial credit may be given. An
unanswered question is given zero points.
No calculators are allowed. You have 50 minutes to complete the Exam. When
the exam is over, give only one set of answers per team to the proctor.
Elegance of solutions may affect score and may be used to break ties.
Freshman-Sophomore Team Exam – March 2004
1. What is the sum 2  4  6  8 10  ...  2002  2004 ?
2. If the roots of the equation x 2  bx  c  0 are –2 and 3, what are the values of b and c?
ax  1
 a  0 . Define f n  x  as the composition of the function f with
a
itself n times, in other words:
3. Suppose that f  x  
f 2 ( x)  f
f  x
f 3  x  f
f
f  x
f 4  x  f
f
f
f  x  , etcetera.
Evaluate f 100 1 .
Freshman-Sophomore Team Exam – March 2004
4.
1
of the bag of M&Ms to Elizabeth; then he
2
1
1
gives of the remaining M&Ms to Greg; then he gives
of the remaining M&Ms to Kim;
3
4
1
then he gives of the remaining M&Ms to Phil. If Jonathon was left with 48 M&Ms how
5
many did he have in the beginning?
Jonathon has a large bag of M&Ms. He gives
5. The line segment AF is divided into ten equal parts and the semicircles are drawn as
indicated in the figure below. What is the percentage of the area of the circle that is shaded?
Freshman-Sophomore Team Exam – March 2004
6. The right triangle ABC is shown in the figure below. The points D and E bisect the
respective sides of the triangle. If the area of ABC is 24 then what is the area of DFB ?
7. What is the largest value of N so that the sum of the first N natural numbers is less than 500?
Freshman-Sophomore Team Exam – March 2004
8. Solve for x in terms of a and b. Simplify your answer if possible.
a a b b
1    1    0
b x a x
9. Southside Bakery charges $1.10 for a cream filled donut and 85¢ for a glazed donut. David
bought a total of 90 glazed and cream-filled donuts for $88.00. How many of each type were
sold?
10. During the summer heat, a 2-mile bridge expands 2 feet in length. If we assume that the
bulge occurs straight up the middle (see figure below), how high is the bulge? Most bridges
have expansion spaces to avoid such a buckling. (1 mile = 5280 feet).
Freshman-Sophomore Team Exam – March 2004