Download MOCK AMC 8 A - Art of Problem Solving

MOCK AMC 8 A
AoPS Classroom Math Forum
Written by Carl Lian aka Jonas Clarke aka
Mthomba Mb’dbonouoe aka
JclarkemathL314159
Rules and Regulations
1. You have 40 minutes to complete the test, you are on your honor to take
only 40 minutes.
2. You are allowed no other aids other than: Pencil, Scratch Paper, Graph
Paper, Calculator Acceptable for the SAT, Compass, Ruler, Eraser. None of
the problems require a calculator.
3. There are a total of 25 questions, your score is the number of questions
you answer correctly
4. Each question has 5 answer choices, only one is the correct answer
5. There is no penalty for guessing.
6. Once you finish, you may use the remaining time to check your answers.
7. Immediately after the 40 minutes elapses, pm your final answer sheet,
with your answer choices ONLY, to jclarkemathL314159.
8. Do not continue to the next page until you begin timing.
Mock AMC 8 A 2006
Page 1 of
1, A circle, an equilateral triangle, and a line are drawn on the same plane.
What is the maximum number of points of intersections that these three
figures can have?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
2. The sum of five consecutive numbers is 20. What is the largest of these
numbers?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
3. My birthday, August 11, fell on a Friday in the year 2006. I turned 13 on
this day. On what day of the week will my 40th birthday fall on?
(A) Thursday
(B) Friday
(C) Saturday
(D) Sunday
(E) Monday
4. A square and a regular hexagon have the same perimeter. What is the ratio
of the sidelength of the square to the sidelength of the hexagon?
(A) 2:3
(B) 3:2
(C) 1:1
(D) 5:4
(E) 2:1
5. How many positive integer factors does the number 256 have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
6. Find the value of ½+1/6+1/12+1/20+1/30+1/42+1/56.
(A) 8/9
(B) 1
(C) 7/8
(D) 51/56
(E) 481/560
7. At Jamal’s Ice Cream, everyone is given 1 or 2 scoops of the same flavor
of ice cream, a type of cone, and a topping. If there are 8 flavors of ice
cream, 4 types of cones and 6 toppings, how many different combinations of
number of scoops, flavors, cones, and toppings can be made?
(A) 21
(B) 192
(C) 194
(D) 384
(E) 576
8. Two concentric circles are drawn in the plane, such that the region outside
the inner circle and inside the outer circle has the same area as the inner
circle. Given that the radius of the outer circle is 6 cm, find the radius of the
inner circle rounded to the nearest whole centimeter.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
9. Old McDonald has cows and chickens only on his farm. When I went to
his farm, I counted 19 heads and 62 legs. How many cows does Old
McDonald have on his farm?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 15
10. Find the sum of the first 40 terms in the sequence 1, 3, 5, 7, 9, …
(A) 79
(B) 840
(C) 1600
(D) 1640
(E) 1680
11. Find the sum of the real values of x that makes the following proportion
true:
x/64 = 81/x.
(A) 17
(B) 145
(C) 5184
(D) 72
(E) 0
12. If the base 3 representation of x is 1122201020020010, what will be the
sum of the digits of the base 9 representation of x?
(A) 14
(B) 18 (C) 22
(D) 32
(E) 37
13. If 2x = 30, find the value of 2x+3.
(A) 8
(B) 5
(C) 240
(E) 200
(D) 250
14. How many integer values of x will satisfy the inequality |15/x| > 4 ?
(A) 6
(B) 7
(C) 8
(D) 3
(E) 4
15. In quadrilateral AOPS, angle OAS is a right angle. Given that diagonal
OS = 17, SA : AO = 1.875, and triangles OAS and OPS are congruent, find
the perimeter of the quadrilateral.
(A) 23
(B) 40
(C) 46
(D) 100
(E) 120
16. How many ways can we rearrange the letters of the word FACIAL if
each rearrangement of the letters cannot start with a vowel? The A’s are
indistinguishable.
(A) 4320
(B) 720
(C) 540
(D) 360
(E) 180
17. A dust particle walks on the number line. Every minute, it walks either to
the integer directly to its left or the integer directly to its right, with an equal
probability of walking to either. After 6 minutes, what is the probablility that
the dust particle returns to its starting point?
(A) 5/32
(B) 10/32
(C) 1/36
(D) 1/6
(E) 1/3
18. Jim builds a 3 x 3 x 3 cube out of 1 x 1 x 1 blocks. If he places it in space,
and does not have x-ray vision, what is the maximum number of 1 x 1 x 1
blocks that he can see at a time that are part of the larger cube?
(A) 27
(B) 25
(C) 19
(D) 15
(E) 8
19. If the ratio of the surface area of a cube in square inches to the volume of
the same cube in cubic inches is 1:1, which is closest to the length of the
longest possible line segment connecting two vertices, in inches?
(A) 8
(B) 9
(C) 9.5
(D) 10.5
(E) 12.5
20. In a research study conducted by a wildlife reserve agency, 1001
monkeys were randomly captured in a large forest, tagged, then released into
the same forest. A week later, the agency went back into the forest, and
captured 1001 monkeys at random. 77 had tags. What is the best estimate for
the number of monkeys in the forest?
(A) 11500
(B) 12000
(C) 12500
(D) 13000
(E) 13500
21. How many ordered triples of positive integers (x,y,z) satisfy (xy)z = 64?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
22. Let (an)n>0 define a sequence such that a1 = 1 and 3an+1 – 3an = 1 for all
n>0. Find a2005.
(A) 667
(B) 668
(C) 669
(D) 670
(E) 671
23. Rod has 5 rods with lengths 1, 2, 3, 4, and 5. If Rod randomly selects 3
rods, what is the probability that Rod can build a triangle with those three
rods as the sides?
(A) 0
(B) 1/10
(C) 3/20
(D) 3/10
(E) 1
24. For how many real values of n is the expression n2 – 7n + 2 a prime
number?
(A) 0
(B) 1
(C) 2
(D) 3
(E) More than 3
25. Participation in the lopcal soccer league this year is 10% higher than last
year. The number of males increased by 5% and the number of femailes
increased by 20%. What fraction of the soccer league is now female?
(A) 1/3
(B) 4/11
(C) 2/5
(D) 4/9
(E) 1/2