Math Field Day 2009
Individual Medley
Junior Varsity Level
CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
MATHEMATICS FIELD DAY 2009
Individual Medley, Junior 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
Junior Varsity Level
1. A line y  mx  b passes through the points (1, 1) and (3, 5). What is m  b ?
(a) 1
(b) 2
(c) 3
(d) 4
(e) none of these
2. a1  2, an  an1  n for all n. What is a10 ?
(a) 46
(b) 52
(c) 55
(d) 56
(e) none of these
3. 1 + 3 + 5 + 7 + … + 15 = ?
(a) 49
(b) 58
(c) 64
(d) 70
(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. For what value of k does 2 x 2  4 x  k  0 have exactly one solution?
(a) 0
(b) 1
(c) 2
(d) 4
(e) none of these
6. How many distinct real roots does x 4  x 2  8 have?
(a) 0
(b) 1
(c) 2
(d) 4
(e) none of these
7. Using a large mower, a lawn can be mowed in an hour. Using a small mower, it takes 3
hours. How many hours will it take if both mowers are used?
(a) 1/2
(b) 2/3
(c) 3/4
(d) 4/5
(e) none of these
8. How large (in degrees) is each interior angle of a regular pentagon?
(a) 96
(b) 100
(c) 104
(d) 108
(e) none of these
9. The three interior angles of a triangle are in linear progression. The smallest is 240 . What is
the largest?
(a) 96 (b) 100 (c)104 (d) 108
(e) none of these
Math Field Day 2009
Individual Medley
Junior Varsity Level
10. A bicyclist and I walk around the edge of a park, beginning at the same spot and going in
opposite directions. I pass the bicylist 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
11. If 1  x  0 then || 2 x  1 | 3 | can be simplified to
(a) 4 – 2x
(c) 2 – 2x
(b) 2 + 2x
(d) 4 + 2x
(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
15. Which point on the line x + y = 1
(a) (-1,2)
(b) (0,1)
(e) none of these
is closest to the point (2,5)?
(c) (1/2, 1/2)
(d) (-1/2, 3/2)
(e) none of these
16. 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
17. The last digit of 4343 is
(a) 1
(b) 3
(c) 7
(d) 9
(e) none of these
Math Field Day 2009
Individual Medley
1 2
  8,
x y
18. If we solve the system:
(a) 2/3
(b) 1
(c) 4/3
(d) 2
Junior Varsity Level
2 1
  1 then 2x + 3y = ?
x y
(e) none of these
19. 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
20. AB is a 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. One angle of a quadrilateral is half the sum of the others. Its measure in degrees is:
(a) 90
(b) 120
(c) 140
(d) 150
(e) none of these
22. 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
23. 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
24. The line y  mx  b passes through the point (2,3) and is perpendicular to the line
x  y  4 . What is m  b ?
(a) 0
(b) 1
(c) 2
(d) 4
(e) none of these
25. 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
(b) 124
(c) 144
(d) 312
(e) none of these