Math Field Day 2009
Individual Medley
Varsity Level
CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
MATHEMATICS FIELD DAY 2009
Individual Medley, Varsity Level
There are 25 problems. You will have 50 minutes. You will only turn in the answer sheet – you
may keep the test. Each correct answer is worth one point. Each incorrect answer will receive a
one-fourth point penalty. If you believe there is an error of some sort in a particular problem,
please quietly discuss it with one of the proctors.
For each of the questions, blacken the appropriate circle on the answer sheet. When the exam is
over, give your answer sheet to the proctor.
Calculators of any kind are not allowed.
GOOD LUCK
Math Field Day 2009
Individual Medley
Varsity Level
1. The area inside the curve 4 x 2  9 y 2  36 is
(a) 4 
(b) 6 
(c) 8 
(d) 9 
(e) none of these
2. sin 3000 = ?
(a)
3/2
(b)  3 / 2
(c) 1/ 2
(d) 1/ 2
(e) none of these
3. a1  2, an  an1  n for all n. What is a10 ?
(a) 46
(b) 52
(c) 55
(d) 56
(e) none of these
4. A geometric sequence is one in which successive terms have the same ratio. A geometric
sequence has 3rd term 1 and 6th term 8. What is the 9th term?
(a) 16
(b) 32
(c) 48
(d) 64
(e) none of these
5. If I toss a balanced coin 4 times, what is the probability I get an odd number of heads?
(a) 1/4
(b) 3/8
(c) 5/8
(d) 3/4
(e) none of these
6. If I expand ( x  2 y)5 , what is the numeric coefficient of x3 y 2 ?
(a) 10
(b) 20
(c) 28
(d) 40
(e) none of these
7. I have 3 math books and 4 physics books that I want to arrange on a shelf so that all the math
books are together and all the physics books are together. How many ways can I do this?
(a) 72
8. tan( A rcsin(
(b) 124
(c) 144
(d) 288
(e) none of these
5
))  ?
13
(a) -5/12
(b) 12/13
(c) -12/13
(d) -13/12
(e) none of these
9. If I expand ( x 2  1/ x)6 then what is the numeric value of the constant term?
(a) 10
(b) 15 (c) 20
(d) 36
(e) none of these
Math Field Day 2009
Individual Medley
Varsity Level
10. How large (in degrees) is each interior angle of a regular pentagon?
(a) 96
(b) 100
(c) 104
(d) 108
(e) none of these
11. A bicyclist and I walk around the edge of a park, beginning at the same spot and going in
opposite directions. I pass the bicyclist for the 5th time just as I complete the first circuit around
the park. What is the ratio of the bicyclist’s speed to my speed?
(a) 3
(b) 4
(c) 5
(d) 6
(e) none of these
12. The product of the least common multiple and greatest common divisor of 40 and 64 is:
(a) 480
(b) 580
(c) 1280
13. If f ( x)  x 2  x and g ( x) 
(a) 2
(b) 6
(c) 16
(d) 2440
x2
then ( g
x2
(d) 20
(e) none of these
f )(3) is
(e) none of these
14. Define x * y  2 x  y for all numbers x, y . What is (2 * 3) * 4  2 * (3* 4) ?
(a) -4
(b) -2
(c) 0
(d) 2
(e) none of these
15. In a class of 30 students there are 20 math majors and 8 physics majors; of these 3 major in
both subjects. How many students major in neither math nor physics?
(a) 2
(b) 3
(c) 4
(d) 5
(e) none of these
16. An urn contains 4 red and 6 blue marbles. If I draw out 2 marbles, what is the probability
they are of differing colors?
(a) 6/15
(b) 7/15
17. If we solve the system:
(a) 2/3
(b) 1
(c) 1/2
1 2
  8,
x y
(c) 4/3
(d) 2
(d) 8/15
(e) none of these
2 1
  1 then 2x + 3y = ?
x y
(e) none of these
Math Field Day 2009
Individual Medley
Varsity Level
18. One faucet can fill a tub in 3 minutes; another in 2 minutes; if the drain is open, the tub can
be emptied in 4 minutes. How many minutes will it take to fill the tub if both faucets are turned
on and the drain is opened?
(a) 12/7
(b) 2
(c) 12/5
(d) 24/7
(e) none of these
19. If I roll a die 3 times, what is the probability I get exactly 2 sixes?
(a) 5/72
(b) 1/12
(c) 1/18
(d) 1/24
(e) none of these
20. AB is the diameter of a circle and C is a point on the circle. If AB = 6 and AC = 4 then what
is BC?
(a) 5 2
(b) 3 2
(c) 5 3 (d) 3 3
(e) none of these
21. A solution to sin 2x  sin x is:
(a)  / 6
(c)  / 2
(b)  / 3
(d) 2 / 3
(e) none of these
22. The cosine of the angle beween the line from the origin to (1,2) and the line from the origin
to (2 ,1 ) is:
(a) 0
(b) 1/5
(c) 2/5
(d) 4/5
(e) none of these
23. x 40  x 20  x10  3 is divided by x+1. What is the remainder?
(a) -2
(b) -1
(c) 0
(d) 1
(e) none of these
24. How many solutions are there to the equation 32 x  2  3x  8  0 ?
(a) 0
(b) 1
(c) 2
(d) 3
(e) none of these
25. A triangle has sides 3 and 4 with an included angle of 600 . The length of the third side is:
(a) 12
(b) 13
(c) 14
(d) 15
(e) none of these