Ninth Grade Test - Excellence in Mathematics Contest - 2007
1.
The title of this competition is the “The 10th Prime Contest”.
What is the sum of the first 10 prime numbers?
A. 101
2.
3.
A. 38%
B. 40%
D. 45%
E. 46%
If x = –12, evaluate:
B. 15
D. 37
E. 87
B. Always an odd number
D. Never a multiple of 3
B. 31
C. 171
D. 243
E. 1321
C. –4
D. 6
E. 12
x2
.
24  x
B. –6
B. 120o
C. 220o
B

A
C
D. 260o
E. 280o
The point (–5, 3) lies on the lines y = Ax – 3 and y = Bx. What is A+B?
A. –9/5
9.
C. 26
Angle θ measures the amount of counter-clockwise rotation
in degrees from Ray AB to Ray AC.
Select the best estimate of θ.
A. 100o
8.
C. 43%
In 2006, poor Pluto was declassified as a “planet”. Assume that Pluto and the Earth are both
spheres and that the diameter of Pluto is 2296 km while the diameter of the Earth is 12756 km.
Approximately what is the ratio of the volume of Earth to the volume of Pluto?
A. –12
7.
E. 160
The sum of three consecutive prime numbers is:
A. 5.6
6.
D. 129
Sharon’s age is 11 years more than a perfect cube and 11 years less than a perfect square. What
is the least number of years until her age is a perfect cube?
A. Always an even number
C. Always a multiple of 3
E. None of the above
5.
C. 125
A target consists of six concentric squares of side
lengths: 1, 3, 5, 7, 9, and 11. What per cent of the target
is shaded? Round to the nearest percent.
A. 11
4.
B. 117
B. –3/5
C. –1
D. 3/5
E. 6/5
The area of triangle ABC is 130 square centimeters. Angle B is a right angle and BC = 20 cm.
To the nearest tenth of a centimeter, what is the perimeter of triangle ABC?
A. 48.2
B. 56.9
C. 57.4
D. 61.3
E. 66
Ninth Grade Test - Excellence in Mathematics Contest - 2007
10.
 and
are two distinct operations from the set:
, , ,  .
If 9  6  45 , what is the value of 6  3 ?
2
A. 3/16
11.
12.
12
6
B. 6
8
C. 12
D. 15
E. 20
From a solid wooden cube of side length 2, a tetrahedron with slant
lengths 1 (as shown) is cut from EACH of the eight vertices of
the cube. One such tetrahedron is shown in the diagram.
How many faces does the remaining solid have?
A. 6
B. 10
D. 14
E. 16
1
C. 112
1
y
The equation of this line can be written in
the form: y = Mx + B .
4
3
2
1
0
What is the product MB?
13.
A. 3
B. –3
D. –4/3
E. –2
4
5
C. 4/3
B. 14
C. 16
D. 18
E. 20
B. 64
C. 89
D. 96
E. 144
B. 112%
C. 120%
D. 125%
E. 130%
In square units, what is the area of the triangle formed by the x-axis, the y-axis, and
the line 2x – 9y = 180 ?
A. 180
17.
3
With 84 m of fence, Matt enclosed a square corral for his horse. With his 84 m of fence, Nick
built a corral which was an equilateral triangle. What is the ratio of the area of Matt’s corral to
the area of Nick’s corral? Express your answer to the nearest per cent.
A. 100%
16.
2
The first four terms of a sequence are: 2, 3, 6, 18, … where each term is the product of the
previous two terms. If the 10th term is written 2 p 3q , what is the sum p+q?
A. 55
15.
1
How many different numbers can be expressed as the sum of exactly three different numbers
from the set {1, 2, 3, 10, 11, 12}?
A. 12
14.
1
1
B. 360
C. 450
D. 720
E. 900
If the measures of two angles of an isosceles triangle are 80o and xo, there are three possibilities
for x. What is the sum of those three possible values?
A. 160o
B. 90o
C. 100o
D. 180o
E. 150o
x
Ninth Grade Test - Excellence in Mathematics Contest - 2007
18.
0
A
2
B
3
On this number line, what is the sum of the numbers A+B?
A. 5/12
19.
B. –4
B. 78
B. 480
C. 100
D. 120
E. 125
C. 504
D. 520
E. 630
C. 10 cm
D. 12 cm
E. 15 cm
C. 8
D. 9
E. 10
If 1  x  0 , what is the median of these five expressions?
A. –2x
2x
B. 2x
x2
C. x2
x3
x4
D. x3
E. x4
A rectangle is three times as long as it is wide. If the length of its diagonal is x, what is the area
of the rectangle?
A. x2/10
26.
B. 6 cm
B. 7
–2x
25.
E. –11
How many positive integers less than or equal to one million are both perfect squares and perfect
cubes?
A. 6
24.
D. –7
C. 7
On rectangle ABCD, AD = 12 cm and AB = 30 cm. E is a point on AB such that the area of
triangle EBC is one-half the area of trapezoid AECD. What is the length of AE ?
A. 5 cm
23.
E. 7/12
The sum of four distinct positive integers is 20.
What is the maximum possible product of these four integers?
A. 420
22.
D. 1/3
In the time that the minute hand of a clock rotates 1500 degrees, how many degrees has the hour
hand rotated?
A. 25
21.
C. 2/3
The first four elements of a sequence are: 7, 11, 4, –7,… Each new element is obtained by
subtracting the 2nd to last element from the last element. For example, the 4th element is –7
because: 4 – 11 = –7. What is the 2007th element of this sequence?
A. 4
20.
B. 1/2
B. 3x2/10
C. x2/2
D. x2/4
E. 3x2
A dodecahedron is a 3-dimensional polyhedron which consists solely of 12 pentagonal faces.
How many edges does a dodecahedron have?
A. 24
B. 26
C. 30
D. 36
E. 60
Ninth Grade Test - Excellence in Mathematics Contest - 2007
27.
The circumference of a smaller circle equals the radius of a larger circle. What is the ratio of the
area of the larger circle to the area of the smaller circle?
A. 2π
28.
C. π2
D. 2π2
E. 4π2
In 1990, the average age of Tad and his older sister was 6. In 2002, the average age of Tad, his
older sister, and their twin brothers was 13. In what year were the twin brothers born?
A. 1993
29.
B. 4π
B. 1994
C. 1998
D. 1999
E. 2000
For an adult weight W in pounds and height H in inches, the Body Mass Index or BMI is given
by the formula: BMI  703*
W
. If Brian is 5 foot 10 inches tall, to reduce his BMI from 28.2
H2
to 24.0, how many pounds must Brian lose? Round to the nearest pound.
A. 21
30.
B. 1471
E. 29
C. 2446
D. 2926
E. 2942
C. 800 feet
D. 1200 feet
x and y are positive integers such that 150x is a perfect square and 150y is a perfect cube.
What is the least possible value of the sum x+y?
A. 36
33.
D. 27
The Sonderman’s and the Bozek’s own cottages 2400 feet apart at opposite ends of a lake. At
9:00 AM, Amy and Dan Sonderman begin canoeing to Bozek’s cottage. A while later, Brian
Bozek begins swimming to Sonderman’s cottage. When they meet in the lake, Amy and Dan
have paddled twice as fast as Brian swam and have paddled twice as many minutes.
How far has Brian swum?
A. 480 feet
B. 600 feet
E. Insufficient information is given
32.
C. 25
The latitude of St. Louis is 38o35 North, while Suzanne is studying in Uppsala, Sweden, at
latitude 59o52 North. Assume that the Earth is a sphere with radius 3960 miles.
How many miles further north of the equator is Uppsala than St. Louis?
A. 1463
31.
B. 23
B. 66
C. 156
D. 186
E. 216
The centers A and B of the two congruent circles lie on a diameter of the largest circle.
The four circles are tangent as shown. What is the ratio of the area of the
largest circle to the area of the smallest circle?
A. 12
B. 9
D. 6 3
E. 9 3 / 2
C. 6 2
A
34.
B
2, 8, 14,… and 11, 26, 41,… are two arithmetic sequences.
What is the 15th number that appears in both sequences?
A. 441
B. 446
C. 476
D. 866
E. 926
Ninth Grade Test - Excellence in Mathematics Contest - 2007
35.
For the given cube, compute
C
ABE  ABD  ABC .
A. 135o
B. 150o
D. 180o
E. 195o
B
C. 165o
D
36.
37.
38.
A. 5
B. 6
D. 8
E. More than 8
1 cm
1 cm
C. 7
In this Magic Square, the sum of the three numbers
in each row and in each column is the same.
What is the value of B–C?
A. 5
B. –5
D. –9
E. Cannot be determined
C. 9
A
B
8
B
13
–3
E
8
C
D
F
Point C is the center of arc ABD . Point D is the center of arc CE .
Angle ACB is congruent to angle BCD.
C
A
Determine α –β. Round to the nearest degree.
α
α
o
o
o
A. 38
B. 43
C. 45
E. 54o
E
β
D
B
In a college, for each professor there are 10 male students and 12 female students. If there are M
male students, what is the total number of students and professors?
A. 23M
40.
E
In this 2x4 grid of dots, the dots are 1 cm apart both
horizontally and vertically. Using three dots of the grid
as the vertices of a triangle, how many distinct
non-congruent triangles can be drawn?
D. 51o
39.
A
B. 61M/5
C. 71M/6
D. 23M/10
Place the numbers: 4, 6, 7, 8, and 9, (without repetition) in the
five regions marked A, B, C, D, and E so that each sum of the
numbers in the three regions between each pair of short and
long arrows (namely: A+1+D; A+B+2; 3+E+C; and 5+E+D)
equals the same number. What is the value of C+D?
A. 13
D. 16
B. 14
E. 17
E. 29M/15
A
1
2
D
C. 15
B
C
5
E
3