Eighth Grade Test - Excellence in Mathematics Contest – 2011
1. In the movie 127 Hours, the rock climber was trapped for 127 hours. If his ordeal began at 10
AM on Saturday, when did his ordeal end?
A. Wednesday, 5 PM
B. Thursday, 5 PM
D. Thursday, 7 PM
E. None of These
C. Wednesday, 7 PM
2. According to the movie Facebook, Eduardo’s share of the company was reduced from 34% to
0.03%. What is 0.03% of $25 billion dollars?
A. $7.5 million
B. $7500
C. $750,000
D. $75 million
E. $750 million
3. What is the sum of the digits of the smallest two-digit prime number whose digits are also each
prime? (Note: Since a prime number must have exactly two divisors, 1 is not a prime number.)
A. 4
B. 5
C. 8
D. 10
E. 14
4. This is part of a Mother Goose rhyme:
As I was going to St. Ives, I met a man with seven wives;
Every wife had seven sacks; Every sack had seven cats;
Every cat had seven kits.
What is the total number of men, wives, sacks, cats, and kits that this person met?
A. 155
B. 2401
C. 2409
D. 2800
E. 2801
B
5. ACEG is a square and each of the four triangles is equilateral.
What is the ratio of the measure of the angle ABC to the
measure of the marked angle BCD?
C
A
H
A.
2/5
B. 1/2
D
C. 3/4
G
D.
3/5
E
E. 2/3
F
6. Which one of these five expressions is not equal to the other four expressions?
A. −2 +
2
3
B.
12−16
9−12
C.
−1 ÷ (−3 ÷ −4)
D.
−24
18
E.
1−5
4−1
7. On a multi-day bike ride across Missouri, a cyclist leaves Wentzville at 8:00 AM and averages 18
mph. At 11:00 AM, his support crew leaves Wentzville in a van along the same route and they
average 52 mph. At 12:30 PM, how many miles is the cyclist still ahead of the support crew?
A. 3 miles
B. 5 miles
C. 8 miles
D. 10 miles
E. 12 miles
8. B, C, and D are three different numbers from this set: { –5, –4, –3, –2, –1, 0, 1, 2, 3 }.
What is the least possible value of 𝐁 ∗ 𝐂 − 𝐃 ?
A.
–23
B. –19
C. –18
D. –17
E. None of These
Eighth Grade Test - Excellence in Mathematics Contest – 2011
9.
For a $15.20 bill at Omi’s Pizza, you give the waitress $19.00 and say, “Keep the change”.
What percent tip did you just leave?
A. 15%
B. 18%
C. 20%
D. 25%
E. 80%
10. In November, 2011, there will be the date 11/11/11.
How many hours are there from noon on 10/10/10 to noon on 11/11/11?
A. 8754
B. 8880
C. 9264
D. 9528
E. 9600
𝟐𝒙 − 𝟏 ≥ 𝟓𝒙 + 𝟕
11.
Of these five numbers:
A. 0
–5, –3, –2, 0, 2; how many make the above inequality true?
B. 1
C. 2
D. 3
E. 4
12. The surface area of a cube is 96 cm2. What is the volume of the cube?
A. 64 cm3
B. 96 cm3
C. 128 cm3
D. 216 cm3
E. 256 cm3
13. My daughter Zan was born on the Nth day of March.
From your age in years, you can calculate N and therefore know Zan’s birthday.
1. Make a 6-digit number by writing your age three times. (For example, if your teacher is 28
years old, your teacher would write 282828.)
2. Divide your 6-digit number by 1443.
3. Add 133 to that answer.
4. Divide that answer by 7.
5. From that answer, subtract your age in years. Your final answer is N.
When is Zan’s birthday?
A. March 7
B. March 12
C. March 14
D. March 19
E. March 28
14. What is the square of the sum of the square roots of 3 and 4? Round to the nearest tenth.
A. 5.0
B. 7.0
C. 9.9
D. 13.9
15. If x = –4, what is the largest number in the set {−𝟑𝐱 , 𝟓𝐱, 𝐱 𝟐 , 𝐱 𝟑 ,
A. –3x
B. 5x
C. x2
16. 6x3 – 6x2 + 2x – 28 = (2x + A)(3x2 + Bx + 7)
A. –3
B. –1
C. 2
−𝐱
}
𝟎.𝟐
D. x3
E.
25.0
?
E.
−𝐱
𝟎.𝟐
What is A+B ?
D. 3
E. 4
17. The measure of one angle of a quadrilateral is 12o. The measure of each of the other angles is No.
What is N?
A. 56o
B. 87o
C. 86o
D. 94o
E. 116o
Eighth Grade Test - Excellence in Mathematics Contest – 2011
18. What is the x-intercept of the straight line through the points (–30, –60) and (0, –75)?
A. (–150, 0)
B. (–90, 0)
C. (0, 0)
D. (90, 0)
E. (150, 0)
Use the following Rule for questions #19 and #20.
An Ulam-Collatz Sequence of integers is generated by these rules:
1. The first term is a positive integer.
2. If a number N in the sequence is odd , the next number is 3N + 1 .
3. If a number N in the sequence is even, the next number is N/2 .
For example: 6; 3; 10; 5; 16; 8; … is the start of one possible Ulam-Collatz Sequence.
19. If the first three terms of an Ulam-Collatz Sequence are: 30; 15; 46; what is the 8th term?
A. 52
B. 53
C. 54
D. 55
E. 56
20. The Ulam-Collatz Conjecture is that EVERY Ulam-Collatz Sequence eventually will include the
repeating sequence:
… 4; 2; 1; 4; 2; 1;…
If the first three terms of an Ulam-Collatz sequence are 9; 28; 14;, which term is the FIRST
occurrence of “4”?
A. 16th
21. If x = –10,
A. 1
B. 18th
𝐱 𝟐 − 𝟐𝐱+𝟏
𝐱𝟐 − 𝟏
C. 20th
D. 22nd
E. 24th
equals
B. –1
C.
11
9
D. −
11
E.
9
79
101
22. The product of the three numbers in each row and in each column
is given. Without repetition, place the numbers 1 through 9 in
these nine cells to produce these six products.
120
N
What is the number in the cell marked N?
A. 1
B. 2
D. 4
E. 6
C. 3
36
56
23. ABC is an equilateral triangle divided into four stripes of equal width.
What fraction of triangle ABC is shaded?
A. 1/2
B. 3/4
D. 7/12
E. 9/16
84
120
54
B
C. 5/8
A
C
Eighth Grade Test - Excellence in Mathematics Contest – 2011
24. For how many ordered pairs (x, y) of positive integers does 2x + 5y = 100?
A. 9
B. 10
C. 18
D. 19
E. 20
25. A teacher noticed this sign in a movie cinema in Singapore.
Children under 2.5 feet or under
78 cm are admitted free.
Using 1 inch = 2.54 cm, what is the positive difference between 2.5 feet and 78 cm?
A. 0.6 cm
B. 0.7 cm
C. 1.2 cm
D. 1.6 cm
E. 1.8 cm
A
26. In equilateral triangle ABC, AD and AE divide angle BAC into
three equal parts while BF divides angle ABC into two equal parts.
What is the measure in degrees of angle BPA?
o
o
A.
95
B. 105
D.
115o
E. 120o
C. 110
F
P
o
B
D
E
C
27. On a number line, there are exactly two numbers that are “twice as far from 20 as from 35”.
What is the sum of those two numbers?
A.
10
B. 75
C. 80
D. 90
E. 100
28. Two congruent, over-lapping circles of radius 12 cm are
inscribed in a rectangle. If the centers of the circles are 4 cm apart,
what is the area of the rectangle?
A. 288 cm2
B. 480 cm2
C. 576 cm2
D. 672 cm2
29. Each vertical row of numbers and each horizontal row
of numbers is either an increasing arithmetic sequence
or a decreasing arithmetic sequence?
(Note: 42; 37; 32; 27 is an example of a
decreasing arithmetic sequence.)
E. 768 cm2
71
B
What is A + B?
A.
58
B. 62
C.
66
D. 68
E.
71
56
23
A
13
Eighth Grade Test - Excellence in Mathematics Contest – 2011
𝟐𝟐𝟓, 𝟎𝟎𝟎, 𝟎𝟎𝟎 = 𝟐𝐱 ∗ 𝟑𝐲 ∗ 𝟓𝐳
30.
What is the sum x + y + z?
A. 14
B. 15
C. 16
D. 17
E. 18
31. In the 120 mile drive from St. Louis to Columbia, a driver averaged 64 miles per hour from St.
Louis to Wentzville and then 74 miles per hour from Wentzville to Columbia. Wentzville is onethird of the way from St. Louis to Columbia. On the drive from St. Louis to Columbia, what was
the driver’s average speed? Round to the nearest tenth of a mile per hour.
A.
69.0 mph
B. 69.8 mph
C. 70.0 mph
D. 70.3 mph
E. 70.7 mph
32. In the sequence 𝟐𝟏𝟓𝟕𝟒𝟏𝟑𝟑𝟑𝟒 shown below, note that exactly two sets of consecutive digits
sum to 11. 7+4 = 11 and 4+1+3+3 = 11 (Note that two such sets are allowed to overlap.)
𝟐𝟏𝟓𝟕𝟒𝟏𝟑𝟑𝟑𝟒 𝑎𝑛𝑑 𝟐𝟏𝟓𝟕𝟒𝟏𝟑𝟑𝟑𝟒
In the following sequence, how many sets of consecutive digits sum to 11?
𝟏𝟒𝟓𝟑𝟏𝟑𝟐𝟐𝟕𝟑𝟖𝟏𝟐𝟗𝟔𝟐𝟓
A.
Fewer than 3
B. 3
C. 4
D. 5
E. More than 5
33. If x + y = 10, then what does the expression 3x – 3(7 – y) equal?
A.
–11
B.
9
C. 21
D. 23
E. Cannot be determined
34. On a Cartesian plane, points A(–2, 8), B(10, 8), and C(x, y) form a triangle of area 66 square units.
How many of the following four points could represent point C?
(𝟒, −𝟑)
A.
0
B. 1
(−𝟏𝟐, −𝟑)
(𝟗, 𝟏𝟗)
C. 2
(𝟒, 𝟏𝟏)
D. 3
E. 4
35. If 𝐀 = 𝟎. 𝟓𝐛(𝐡 + 𝐝) , which one of these five expressions represent h?
A.
D.
𝟐𝐀
𝐛
−𝐝
B.
𝐀−𝟎.𝟓𝐝
E.
𝟎.𝟓
𝟐𝐀−𝐝
𝐛
C.
𝐀
𝟐𝐛
−𝐝
𝐀−𝐛𝐝
𝐛
36. How many positive 9-digit numbers that are multiples of 4 can be written using only the digits
“0”, “1”, and “2”?
A. 2916
B. 4374
C. 6561
D. 8748
E. 13,122
Eighth Grade Test - Excellence in Mathematics Contest – 2011
37. Six girls: Alana, Bella, Cora, Dasia, Ericka, and Fiona; and two boys: Gerald and Harold; are to
sit in a row of eight chairs. In how many ways can this be done if the two boys do not sit next to
each other?
A. 20,160
B. 28,800
C. 30,240
D. 35,280
E. 38,880
38. The sum of four consecutive odd numbers equals the sum of five consecutive even numbers.
Which one of the following five numbers could NEVER be one of the nine numbers referred to in
this problem?
A. 745
B. 746
C. 747
D. 748
E. 749
39. N is a whole number greater than 2. The six faces of a 5x5xN block of wood are painted red and
then the block cut into 25N 1x1x1 unit cubes. If exactly 100 unit cubes have 2 or more faces
painted red, how many unit cubes have no red paint?
A. 144
B. 153
C. 162
D. 171
E. 180
40. Three-Pile Nim is a two-person game. Pattie and Malik take turns. There are three piles of chips.
On each turn, a player takes one or more chips from any ONE pile. The player to take the last
chip wins.
At one point of the game, there are 1 chip; 2 chips; and 6 chips remaining in the three piles.
It is Malik’s turn. If both players make their best plays, there is only one winning play for Malik.
What is it?
A. Take 1 chip from the 6-chip pile
C. Take 3 chips from the 6-chip pile
E. Take 1 chip from the 1-chip pile
B. Take 2 chips from the 6-chip pile
D. Take 1 chip from the 2-chip pile