1.
Ninth Grade Test - Excellence in Mathematics Contest - 2003
(1980, #23) Pete has received grades of 76%, 83%, and 93% on three algebra tests. What would he have to
average on the next two tests so that his overall average on the five tests would be 90%?
A.
2.
3.
4.
B.
Less than one day
D.
Between 277 and 278 days
8.
97%
D.
99%
E.
108%
B.
Between 11 and 12 days
E.
C.
Between 115 and 116 days
Between 694 and 695 days
(1982, #23) During a storm, a flagpole broke 18 feet above the ground.
The top hit the ground 24 feet from the base of the pole.
What was the height of the flagpole before the storm?
A.
30 feet
B.
42 feet
D.
54 feet
E.
60 feet
C.
48 feet
(1983, #40) A dealer bought an article for $7, sold it for $8, bought it back for $9, and sold it for $10. How
much profit did he make?
$0
B.
$1
C.
$2
D.
$3
E.
$6
(1984,#84) In a school with S students and T teachers, there are 20 students for each teacher. Which of the
following equations must be true?
B. T = 20S
C. S + T = 20
D. S - T = 20
E. ST = 20
(1985, #46) If the radius of a circle is increased by 3 units, what is the ratio of the new circumference to the
new diameter?
A.
7.
C.
A.
A. S = 20T
6.
96%
(1981, #14) If you count “one, two, three, …” naming one number per second, how many days would it take
you to count to one million?
A.
5.
94%
2
(1986, #5)
B.
3  1
2
C.
3
D.

E.
6
If M and N represent two distinct prime numbers, then M+N is
A.
Always prime
B.
Never prime
C.
D.
Always odd
E.
None of these
Always even
(1987, #13) Multiply your age by 5 and add 3; double that result and subtract 6; divide that result by half of
your age. What is your answer?
A.
5
B.
10
C.
20
D.
-1-
40
E.
Your age
Ninth Grade Test - Excellence in Mathematics Contest - 2003
9.
(1988, #13) The numerator and the denominator of a fraction are positive numbers and their product is 588.
If the fraction is equivalent to 3/4, what is the sum of the numerator and the denominator?
A.
10.
B.
49
C.
56
D.
70
E.
84
1996
C.
2000
D.
2004
E.
2008
E.
15 km
Which of these five measurements is closest to your height?
150 mm
(1991, #2)
A.
13.
1992
(1990 #3)
A.
12.
B.
(1989, #6) Based on past records, the winning distance D in the discus throw in the Olympics can be
approximated by: D = 176 + 1.75t ; where D is measured in feet and t is the number of years since 1948.
Using this formula, in what year would the winning distance in the discus throw be 260 feet?
A.
11.
48
B.
15 cm
C.
150 cm
D.
15 m
If a rectangle has an area of 120 cm2 and a width of 8 cm, what is its perimeter?
15 cm
B.
23 cm
C.
46 cm
D.
64 cm
E.
245 cm
(1992, #5) Replace each of A, B, C, and D with a number to form pairs of numbers whose product is 20; for
example, (5,4).
(10, A)
(80, B)
(8, C)
(0.4, D)
The sum: A+B+C+D equals
A.
14.
12.5
B.
12.75
C.
10.65
D.
54.75
E.
58.5
(1993, #28) After four tests, Suzanne’s average (mean score) is M. After Suzanne receives an 83 on her
fifth test, what is her new average (mean score)?
A.
M  83
2
B.
4M  83
5
C.
M  83
5
(This was my daughter’s 9th grade debut!)
-2-
D.
M
83
5
E.
M
M  83
5
Ninth Grade Test - Excellence in Mathematics Contest - 2003
15.
16.
(1994,#40) Using the four digits 1, 2, 3, and 4, number the regions on this map so that if two regions share a
border, they are numbered differently. Four regions are numbered already.
Region R must be labeled:
A.
1
B.
2
C.
3
D.
No solution exists
E.
More than one solution exists
2
4
R
3
1
(1995,#32) Patty, Jane, Kristen, and Margaret are four talented artists. One is a dancer, one is a painter, one
is a singer, and one is a writer, but not necessarily in that order.
1. Patty and Kristen were in the audience the night the singer made her debut.
2. Both Jane and the writer have sat for portraits by the painter.
3. The writer wants to write a biography of Patty and has a biography of Margaret on the bestseller list.
4. Patty has never heard of Kristen.
Who is the writer?
A.
17.
(1996, #3)
A.
18.
Patty
6
B.
Jane
C.
Kristen
D.
Margaret
If 3x + 2y = 14 and 3x = 2y, what is the value of x + y ?
B.
5
5
6
C.
5
1
6
D.
4
5
6
(1997, #9) In rectangle ABCD, BC = 4, CD = 10, and BE = x .
What is the area of the shaded region?
A
19.
E. Dr. Carol Edwards
A. 20 + 2x
B. 20 + 4x
D. 20 + x
E. 40 + 2x
C. 40 
E.
3
1
2
E
B
x
2
C
D
(1998, #4) In 1910, a bricklayer earned $5.50 one week by working six 10-hour days. If he worked 42
hours during the next week at the same hourly rate, how much did he earn the second week?
(Data from Ogilivie’s Ready Reckoner, 1916)
A.
$3.78
B.
$3.85
C.
$4.28
-3-
D.
$5.78
E.
$231
Ninth Grade Test - Excellence in Mathematics Contest - 2003
20.
(1999, #15) A Leap Year has 366 days and the year 2000 was a Leap year. Rick’s 49th birthday on April 1,
1999, was on a Thursday. Rick’s 50th birthday was on a
A.
21.
C.
Friday
D.
Saturday
E.
Sunday
A painter has finished painting
3:00 pm
B.
4:00 pm
C.
4:30 pm
D.
(2001, #4) The Scholar’s Arithmetic, written in 1815 by
Daniel Adams, included this conversion table.
How many more gallons are in one Puncheon of
Beer than in one Puncheon of Ale?
A. 0
23.
B. Wednesday
2
3
of a room by 2:00 pm and of the same room by 2:30 pm.
3
4
At this rate, when does she finish painting the room?
(2000, #7)
A.
22.
Tuesday
B. 2
C. 4
D. 6
5:00 pm
E.
5:30 pm
8 gallons make one Firkin of Ale
9 gallons make one Firkin of Beer
2 Firkins make one Kilderkiln
2 Kilderkilns make one Barrel
2 Barrels make one Puncheon
E. 8
(2002, #18) Place the nine integers: -4, -3, -2, -1, 0, 1, 2, 3, and 4 into these nine boxes (without repetition)
so that the sum of the integers in any two consecutive boxes is a perfect square number.
There are two different numbers that could be in the middle square. What is the sum of these two numbers?
A.
-3
B.
-1
C.
0
D.
1
E.
2
(Note: Last year, I thought that there was only one solution - a teacher found the other!)
24.
What is the ratio of the measure of the interior angle of an equilateral triangle to the measure of the interior
angle of a square?
A.
25.
B.
1
2
C.
3
4
D.
5
6
E.
4
3
What is the smallest whole number value of N such that 30N is larger than 10 billion?
A.
26.
2
3
5
B.
6
C.
7
D.
8
E.
9
E.
92
For any three consecutive months, what is the least possible number of days?
A.
88
B.
89
C.
90
D.
-4-
91
27.
Ninth Grade Test - Excellence in Mathematics Contest - 2003
For a training ride, a bicyclist first warms up by biking at 12 mph for 10 minutes and at the end cools down
by biking at 8 mph for 15 minutes. In between the warm-up and cool down, he bikes at an average of 24
mph. In a two-hour training ride, how many total miles does he bike?
A.
28.
70
4
344
-10
45
E.
46
B.
75
C.
90
D.
96
E.
120
B.
6
C.
8
D.
10
E.
12
B.
368
C.
442
D.
536
E.
1608
B.
-4
C.
0
D.
2
E.
8
B. 911,234
C. 1,055,729
D. 1,246,412
E. 1,680,527
The inequality: 2x  x5 is true for all x > N , where is N is some natural number.
What is the smallest value of N for which this is true?
A.
34.
D.
Exactly three 6-digit whole numbers are both perfect square numbers and perfect cube numbers.
What is the sum of these three numbers?
A. 332,064
33.
44
The lines ax + by = -32 and bx + ay = 12 intersect at the point (x, y) = (2, 3). What is the sum a+b ?
A.
32.
C.
An 8 foot long cylindrical log is 16 inches in diameter. If the wood weighs 48 pounds per cubic foot, how
much does the log weigh? Round to the nearest pound.
A.
31.
43
Given a square. How many distinct equilateral triangles share exactly two vertices with two vertices of the
square?
A.
30.
B.
In baseball, “Batting Average” is defined as “the number of hits divided by the number of official at-bats”.
On July 5, Suzuki’s batting average was 0.300. By getting 12 hits in his next 20 official at-bats, Suzuki
raised his average to 0.320 by July 11. What was his total number of hits by July 11?
A.
29.
42
0
B.
2
C.
16
D.
23
E.
None of these
To win the big game, Daarina must make at least two of her next three free throws. Her probability of
making each free throw is 2/3. What is the probability of Daarina’s team winning the big game?
A.
2/3
B.
4/9
C.
7/9
D.
-5-
8/27
E.
20/27
Ninth Grade Test - Excellence in Mathematics Contest - 2003
35.
For how many integers is the following expression a real number:
A.
36.
37.
7
39.
40.
8
C.
9
D.
x2  9
10
?
E.
In rectangle ABCD, AB = 10 cm and AD = 20 cm.
AED is an equilateral triangle. What is the area of the quadrilateral AFGD?
Round your answer to the nearest tenth of a square centimeter.
A.
142.3
B.
144.7
D.
150.0
E.
151.6
C.
11
E
B
F
G
C
146.2
A
D
While hiking the Peralta Trail to Wheeler’s Needle and back, Rick spent 60% of his time walking uphill to
Wheeler’s Needle and 40% of his time returning by the same trail. If he averaged 2 miles per hour uphill,
what was his average speed for the round-trip?
A. 2 1/3 mph
38.
B.
25  x 2
B. 2.25 mph
C. 2.4 mph
D. 2.5 mph
E. 2.6 mph
In this 5 by 7 grid of unit squares, what is the total number
of both 2 by 3 rectangles and 3 by 2 rectangles?
A.
32
B.
36
D.
40
E.
48
C.
38
(1983, #49) A square with area 40 square units is inscribed in a semicircle.
In square units, what is the area of a square inscribed in the circle?
A.
80
B.
100
D.
160
E.
200
C.
120
To win this game, you must start at one of the 15 buttons, follow the instruction on that button and all
subsequent buttons, and end at the Exit. For example, “2D” means to move two buttons “Down”; while
“3R” means to move three buttons to the “Right”.
In which column is the only button at which you could start, press all 15 buttons, and then land on the Exit
button on your last move?
C
A
B
D
E
A.
A
B.
B
D.
D
E.
E
C.
C
1D
2D
2L
1R
3L
1R
3R
1R
1U
2D
4R
2R
2U
3L
2L
Exit
-6-