Mock AMC 8
by evt917
Created in November 2024
1 Introduction
1. This is a 25-question, multiple-choice test.
2. Each question is followed by answers marked A, B, C, D, and E. Only one
of these is correct.
3. You will receive 1 point for each correct answer. There is no penalty for
wrong answers.
4. No aids are permitted other than plain scratch paper, writing utensils,
ruler,and erasers. In particular, graph paper, compass, protractor, calculators,
computers, smartwatches, and smartphones are not permitted.
5. Figures are not necessarily drawn to scale.
6. You will have 40 minutes working time to complete the test
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2 PROBLEMS
Problem 1: Clive has six apples. If Alice has two times the apples Clive has,
and Bob has three times fewer apples than Alice and Clive combined, how many
apples does Bob have?
(A) 3 (B) 4 (C) 6 (D) 12 (E) 18
Problem 2: The set 1,5,2,3,4,6,1 has a range, median, and mode. Find the sum
of those three numbers.
(A) 7 (B) 9 (C) 11 (D) 12 (E) 15
Problem 3: A certain triangle has angles in a 3:4:5 ratio. What is the smallest
angle?
(A) 45 (B) 50 (C) 60 (D) 90 (E) 120
Problem 4: An unfair coin has a 2/3 chance of landing tails. If you flip the coin
three times, the probability that all of them comes up tails can be expressed as
m/n, where m and n are relatively prime positive integers. What is m+n?
(A) 12 (B) 27 (C) 32 (D) 35 (E) 40
Problem 5: Let A = 581029 + 472998 - 58203. Which of the following is A
rounded to the nearest thousand?
(A) 995000 (B) 1000000 (C) 984000 (D) 927000 (E) 996000
Problem 6: A telephone company charges a certain fixed fee, along with a 60
cents charge for every minute on the phone. If the total cost for a 45 minute
call is 32 dollars, what is the fixed fee, in dollars?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
Problem 7: Company B advertises that their products contain 20 percent more
stuff and is for 10 percent less price, when compared to an identical product of
Company A. What is the percent discount for buying Company B’s products,
instead of Company A’s products?
(A) 50 (B) 35 (C) 25 (D) 20 (E) Less than 20
Problem 8: Five concentric circles have radii of 1,2,3,4, and 5. Find the posi-
tive difference between the total area covered by the purple, green, and orange
sections and the total area covered by the blue and yellow sections.
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(A) 15π (B) 10π (C) 7π (D) 5π (E) 3π
Problem 9: Tay collects lots of baseball cards. He notices that if he sorts the
cards into groups of 9, he would have 1 left over. He also notices that if he sorts
the cards into groups of 7, he would have 6 left over. What is the minimum
number of cards Tay could have?
(A) 51 (B) 52 (C) 53 (D) 54 (E) 55
Problem 10: A number is called “crazy” if all of its digits are different. How
many four-digit crazy numbers are there?
(A) 3000 (B) 4536 (C) 4600 (D) 4739 (E) 5012
Problem 11: The current score in a basketball game is 20-40. Mike notices the
trailing team is now scoring 5 points per 2 minutes, compared to the winning
team, who is scoring only 3 points per 2 minutes. Assuming this rate remains
constant, and it’s currently the 23rd minute, at what minute would the trailing
team be winning?
(A) 41 (B) 42 (C) 43 (D) 44 (E) 45
Problem 12: Let the nth Fibonacci number be denoted as Fn . The Fibonacci
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sequence is defined as Fn+2 = Fn+1 + Fn , with F1 = 1, and F2 = 1. Compute
F1 + F2 + F3 + · · · + F10 .
(A) 142 (B) 143 (C) 144 (D) 145 (E) 146
Problem 13: I’m starting from the origin in the coordinate plane. Assuming I
can only go to the right or up, how many ways can I go to the point (2,7)?
(A) 36 (B) 40 (C) 45 (D) 50 (E) 66
Problem 14: Let N = 24 · 35 · 46 · 67 . How many positive integer divisors does
N have?
(A) 300 (B) 304 (C) 308 (D) 310 (E) 312
Problem 15: If you randomly arrange the letters in the word VILLAGE, what
is the probability that the two ”L”’s are together?
2 1 2 1 5
(A) 7 (B) 3 (C) 5 (D) 2 (E) 7
Problem 16: A triangle is bounded by the graph of y = |x| and y = 2. What is
the area of that triangle?
(A) 2 (B) 2.5 (C) 3 (D) 3.5 (E) 4
Problem 17: Define the operation a ⋆ b = a2 − ab − b2 for all a and b. Also de-
fine the operation a@b = (a2 −b)(a−ab+b−b2 ) for all a and b. Find (1⋆2)@(3⋆4).
(A) -20000 (B) -20110 (C) 21025 (D) -21120 (E) -39270
Problem 18: In the diagram below, A is the center of the circle. AB, the radius,
equals 4. D is the intersection point of line BD and CD, and BD is a tangent to
the circle. Line CD is perpendicular to line BD, and AD = AC. We are given
that ̸ DAB = 30◦ . Find the length of CD.
4
√ √ √
(A) 2 2 (B) 3 3 (C) 8 (D) 8.25 (E) 4 5
Problem 19: A teacher writes six words on a board: “cat dog has max dim tag.”
She gives three students, Albert, Bernard and Cheryl each a piece of paper with
one letter from one of the words. Then she asks, “Albert, do you know the
word?” Albert immediately replies yes. She asks, “Bernard, do you know the
word?” He thinks for a moment and replies yes. Then she asks Cheryl the same
question. She thinks and then replies yes. What is the word?
(A) cat (B) dog (C) dim (D) max (E) None of the four listed.
Problem 20: On a weird planet far away from earth, math uses base b, instead
of base 10. Steve notices that if you square 17b , you get 341b as the result.
What is b?
(A) 8 (B) 9 (C) 11 (D) 12 (E) 13
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Problem 21: My school offers three sports: Flag football, Baseball, and Basket-
ball. The school board requires each kid to participate in at least one sport. I
did a poll to record the sports each kid participated in. 29 kids do Flag football,
34 kids do Baseball, and 33 kids do Basketball. 15 kids do both Flag football
and Baseball, 16 kids do both Baseball and Basketball, and 12 kids do Flag
football and Basketball. The poll included 57 kids. However, I spilled some
juice on the part that said how many kids did all three sports. How many kids
did all three sports?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
Problem 22: Point O is inside quadrilateral ABCD. A rotation of 180◦ about O
maps the quadrilateral ABCD back to itself, meaning each vertex of the image
is also a vertex of the original quadrilateral. Consider the following statements.
Which are true?
1. ABCD must be a parellelogram.
2. ABCD must be a rectangle.
3. ABCD must be a square.
4. ABCD is always cyclic.
(A) 1 and 4 (B) 1 and 2 (C) 1,2, and 3 (D) None of them (E) All of them
Problem 23: We are given a line with equation x + y = 5. We are also given a
circle with equation x2 + y 2 − 4y + 12x = 25. The two intersection points of the
circle and line can be expressed as (x1 , y1 ) and (x2 , y2 ), where x1 , y1 , x2 , y2 are
all real numbers. Find x1 + y1 + x2 + y2 .
(A) -8 (B) 0 (C) 10 (D) 12 (E) 16
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Problem 24: When the fraction 26 is expressed as a decimal, the result is
0.1ABCDEF , where A, B, C, D, E, F are digits. What is A−B+C −D+E −F ?
(A) 5 (B) 0 (C) -3 (D) -7 (E) -11
Problem 25: In the figure below, there is a square ABCB ′ with side length 6.
(note: I do not know why the square has vertices named that). Arc B ′ B is the
arc of a circle centered at C. and arc AC is the arc of a circle centered at B.
Those two arcs intersect at E, and D is the intersection point of line AC and
arc B ′ B. Lines CD, DE, and EC form a shape (specifically, part of arc B√ ′
B,
aπ
AC, and part of line AC). The area of the shape can be expressed as b − c d.
What is a + b + c + d?
(A) 26 (B) 27 (C) 28 (D) 29 (E) 30
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