Download AB Exam - Math TAMU

AB EXAM
HIGH SCHOOL MATH CONTEST
FALL 2006
1. A digit is placed in each empty square in the grid below so that each row
contains each of the digits 1,2,3,4,5 and each column contains each of the
digits 1,2,3,4,5. What digit is placed in the square at the bottom right
corner of the grid?
5
1
2
4
3
5
3
3
1
2. A group containing boys and girls took a test. If exactly 2/3 of the boys
and exactly 3/4 of the girls passed the test and if an equal number of boys
and girls passed the test, then what fraction of the entire group passed
the test?
3. The sum of 49 consecutive integers is 74 . What is the first integer?
4. Exactly one of the statements A,B,C is true and the other two are false.
Also, suppose that exactly one of the following statements a,b,c,d,e below
is true. Which is it? (a) B is true, (b) A is false and B is true, (c) C is
false and A is true, (d) C is true, and (e) B is false and A is true.
5. What is the smallest positive integer n for which the decimal expansion
of n! ends in 4 zeros?
6. A stock loses 10% of its value on Monday. On Tuesday it loses 20% of the
value it had at the end of the day on Monday. What is the overall percent
loss in value from the beginning of Monday to the end of Tuesday?
7. Three friends share a full bag of jellybeans. Mike took 1/3 of the jellybeans
in the full bag, Zac took 1/2 of the jellybeans in the full bag and Kary
took what was left. Mike ate 1/2 of his jellybeans, Zac ate 1/3 of his
jellybeans and Kary ate all of hers. If Mike and Zac now have a total of
45 jellybeans together, how many jellybeans did Kary eat?
8. Ten unit cubes are glued together as shown. What is the surface area of
the resulting solid?
9. The graph shows the total distance Sam drove from 6 a.m. to 11 a.m.
How many miles per hour is the car’s average speed for the period from 6
a.m. to 11 a.m.?
160
Total Driving Distance
Since 6 a.m. (miles)
120
80
40
0
6
7
8
9
10
11
Time of Day (a.m.)
10. Five balls are numbered 1 through 5 and placed in a bowl. Josh will
randomly choose a ball from the bowl, look at its number and then put it
back into the bowl. Then Josh will again randomly choose a ball from the
bowl and look at its number. What is the probability that the product of
the two numbers will be even and greater than 10? Express your answer
as a common fraction.
11. A grocer makes a display of cans in which the top row has one can and
each subsequent row has two more cans than the row above it. If the
display is made up of 100 cans, how many rows does it contain?
12. A set of 3 points is chosen randomly from the grid. Each set has the same
probability of being chosen. What is the probability that the points lie in
a straight line?
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
13. A company sells peanut butter in cylindrical jars. Marketing research
suggests that using wider jars will increase sales. If the diameter of the
jars is increased by 25% without altering the volume, by what percent
must the height be decreased?
14. Alicia earns $20 per hour, of which 1.45% is deducted to pay local taxes.
How many cents per hour of Alicia’s wages are used to pay local taxes?
15. The two points A(2,0) and B(3,5) are given. Find all values of c such that
a third point C(0, c) makes ∆ABC a right triangle with the right angle at
C.
16. If f(x) = ax + b and f −1 (x) = bx + a with a and b real, what is the
value of a + b ?
17. The point A(−3,2) is rotated 90◦ counterclockwise around the origin to
point B. Point B is then reflected about the line y = x to point C. What
are the coordinates of C?