Please Note: Remember that not all these questions were actually used during the
math bowl.
Math Bowl 2007
JV Round 1
SAMPLE
Rewrite the equation of the line in slope-intercept form.
3x + 4y = 12
1.
Ans.
y=-3x+3
4
or
Simplify. Write your answer as a fraction in simplest form.
3
1
4

 2.25 * 0.3
3
1
*
5 0.6(20)
2.
y = -.75x + 3
Ans.
6
Ans.
30
Find the area of the shaded regions, in square centimeters.
6 cm.
10 cm.
3.
Find the least common multiple of 12x5yz2 and 20x2y2z.
Ans.
60x5y2z2
4.
Simplify 10  13  12  4
Ans.
5
5.
Line 1 passes through the points (-12, -4) and (-8, 0). Line 2 passes through the
points (2, 4) and (8, 6). Line 3 passes through the points (-2, 4) and (8, 6).
Which line is steepest?
Ans.
Line 1
6.
Find x. Drawing is not to scale.
3
Ans.
x = 7/3
7
45º
4
x
45º
7.
Solve for x.
1
x2  x  4
0
Ans.
x=

1
2
8.
Two cars leave from the same point at the same time. One travels north at 70 mph, the
other travels south at 50 mph. How long will it be until the cars are 180 miles apart?
Ans. 1.5 or 3/2 hours
9.
In a box of candy bars, 8% of the candy bars have nuts. If 10 of the candy bars have
nuts, how many bars of candy are in the box?
Ans. 125
10.
If you roll two dice, what is the probability that the sum of the dice will be less than 5?
Ans.
1
6
or
6
36
11. A dress that originally sold for $60 had been previously marked down 20%. Last
Saturday the store had a one-day sale, "Take an additional 30% off any item, including
previously marked down items." What was the sale price of the dress?
Ans. $33.60
12. Stephanie planted a bulb garden. The ratio of daffodils to tulips was 5 to 2. If she
planted 210 bulbs, how many tulips did she plant?
Ans. 60
13.
What number should be subtracted from both the numerator and the denominator of
13
5
to make the result equal to ?
19
8
Ans.
3
Math Bowl 2007
JV2
SAMPLE
1.
If 2x = 1/16, then x = ?
Ans.
-4
Simplify as much as possible.
3 12 * 2 6
8
Ans.
18
2.
For the natural numbers from 3 to 37, which is the median number?
Ans. 20
3.
An isosceles triangle with a base 1 cm longer than the sides has a perimeter of
16 cm. What is the area of the triangle, in square centimeters?
Ans.
4.
12
Below is a scalene triangle adjoined to a regular hexagon. Find the measure of angle
x in degrees.
Ans.
x = 20º
5x
x
5.
If x3 – y3 = 12, and x6 – y6 = 24, then x3 + y3 = ?
6.
The supplement of an angle is 12 more degrees than twice the complement of the
angle. What is the measure of the angle in degrees?
Ans.
Ans.
2
12º
7.
Sue can bike 10 miles in 2 hours. How long will it take her to bike 12 miles? State
your answer in hours and minutes.
8.
Ans.
2hrs & 24 min.
A weight loss clinic advertised that their clients lost an average of 10 lbs over 2
months. Of the following statements, one or more must be true. Write down the
letter(s) of the correct statement(s).
A.
The number of clients who lost less than 10 lbs is the same as the number of
clients who lost more than 10 lbs.
9.
B.
At least one client lost exactly 10 lbs.
C.
Some of their clients lost more than 8 lbs.
D.
At least one client lost 10 lbs. or more.
E.
None of the above.
Ans.
C&D
Rachel’s gas tank is ¼ full. After adding 5 gallons, it is now 2/3 full. How many
gallons of gas does Rachel’s tank hold?
Ans.
10.
What is the range of the function f(x) = x2 + 4x + 4?
Ans.
11.
Ans.
48
Ans.
2 x
Simplify as much as possible.
3x
 x
x
13.
0,
Find the fourth term in the sequence.
3, 12, 27, ___, 75, …
12.
12 gal
What is the y intercept of the graph of the equation?
4y  2x  3x 2 
4 x
x 2
Ans.
y = ½ or 0.5
Math Bowl 2007
JV3
1.
Simplify as much as possible. Leave no negative exponents in your answer.
3
2.
4 x2 * x
3
4x
4
1
x
3
Ans.
If the length of each side of a square increases by 5 cm, the area increases by
95 cm2. What is the area of the original square, in square centimeters?
3.
5 + 12i
Ans. y = 9
Below are the first five terms of a sequence. How many triangles are there in the 134th
term?
6.
Ans.
Find the equation of the line with y intercept equal to 9, that is tangent to the circle (x
– 3)2 + ( y – 5)2 = 16
5.
49cm2
Simplify and write your answer in the form a + bi.
(3 + 2i)2
4.
Ans.
Ans.
89
A cylinder is 15 cm tall, with a radius r. For what values of r, in centimeters, will the
magnitude of the surface area exceed the magnitude of the volume?
Ans.
r<
30
cm
13
7.
Simplify as much as possible.
8.
Solve the inequality for x.
log 3 27
log 3 9
3 x  5  6
Ans.
Ans.
3/2 or 1.5
.  7 U 3,
Also OK: x ≥ -3 or x ≤ -7 (need both parts, with or not and)
9.
What points will trisect the line segment between points (-3, 2) and (9, 11)?
Ans.
10.
(1, 5) & (5, 8)
Line l1 is parallel to line l2. Find the measure of angle x, in degrees.
l1
x
l2
11.
75º
45º
Ans. x = 60º
A = {multiples of three}
B = {perfect squares}
C = {natural numbers ≤ 45}
Find A I B I C . Be sure to include set brackets in your answer.
12.
Ans.
{9, 36}
It takes Bob 10 hours on a Saturday to paint his kitchen. When his friend Mark helps,
they finish the job in 4 hours. How long would it take Mark to do the job by himself? State
your answer in hours and minutes.
13.
Ans.
6 hr 40 min.
How many points with integer coordinates are there in the first quadrant such that the
sum of the coordinates is 20?
Math Bowl 2007
JV4
Ans.
19
1.
Write the equation of the ellipse in standard form.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Ans.
x  32  y2
9
16
1
5
2.
 2n  3
Simplify
Ans.
15
n1
3.
A rectangular box is three times as long as it is wide, with a height equal to twice the
width. It has a volume of 162 cm3. Find the length of the box, in centimeters.
Ans.
4.
Find both real values of x which satisfy the equation.
2
 x 1   x 1 

 
 6
2x  4   2x  4 
5.
L = 9cm
Convert from base 4 to base 10.
Ans.
32BASE 4 = ______BASE 10
x = 3,
Ans.
11
7
14
6.
Suppose 240 square tiles, each 25 cm on a side, are needed to cover a rectangular floor.
The floor is 5 meters long. How wide is the floor, in meters?
Ans.
3m
7.
SKIP
8.
A six foot tall man standing under a streetlight casts a 10 foot shadow on the ground. If
the base of the streetlight is 35 feet from the man, what is the height of the streetlight,
in feet?
9.
Ans.
Simplify as much as possible.
3x 3  18x 2  20x  8
x2
10.
27 feet
Ans.
3x2 + 12x – 4
A businesswoman enters a bank at lunchtime and deposits half the money in her wallet.
She leaves, spends $10 on lunch and returns to the bank. Again she deposits half the money in
their wallet and leaves. She later spends $20 on dinner, and then has $180 left. How much
money did she have originally?
Ans.
eln x + ln x = 9
$820
11.
Solve for x.
Ans.
x=3
12.
Maribel and Suzanne bought tulip and daffodil bulbs at the nursery. Maribel bought 5
tulip and 8 daffodil bulbs, and spent $11.50. Suzanne bought 10 tulip and 4 daffodil bulbs, and
spent $14.00. What is the price of one daffodil bulb?
13.
Solve for x.
x
x2
4


x2 x3 x2
Ans.
$.75
Ans.
x = -8