AMC 12 Math Practice Test 2012 Online Quiz with PDF. You can try American Mathematics Competitions (AMC) 12 Math Practice Test 2012 Questions and Answers Online Mock test or you can download both Set A and Set B 2012 exam questions with answer keys and explanations in PDF for better MAA AMC Prep.
The American Mathematics Competitions 63rd Annual AMC 12 American Mathematics Contest was held on Wednesday, February 22, 2012. This is a twentyfivequestion multiple choice test. Each question is followed by answers marked A, B, C, D, and E. Only one of these is correct.
AMC 12 Math Practice Test 2012
Test Prep For  AMC 12 Practice Test 2024 
Test Content  AMC 12 Math Test 
SET  B 
Test Year  2012 
Test Type  Online Mock Test 
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AMC 12 Math Practice Test 2012
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AMC 12 Math Practice Test 2012
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Question 1 of 25
1. Question
1 pointsEach thirdgrade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the thirdgrade classrooms?

Question 2 of 25
2. Question
1 pointsA circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2 : 1. What is the area of the rectangle?

Question 3 of 25
3. Question
1 pointsFor a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide?

Question 4 of 25
4. Question
1 pointsSuppose that the euro is worth 1.30 dollars. If Diana has 500 dollars and ́Etienne has 400 euros, by what percent is the value of ́Etienne’s money greater than the value of Diana’s money?

Question 5 of 25
5. Question
1 pointsTwo integers have a sum of 26. When two more integers are added to the first two integers the sum is 41. Finally when two more integers are added to the sum of the previous four integers the sum is 57. What is the minimum number of even integers among the 6 integers?

Question 6 of 25
6. Question
1 pointsn order to estimate the value of x − y where x and y are real numbers with x > y > 0, Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct?

Question 7 of 25
7. Question
1 pointsSmall lights are hung on a string 6 inches apart in the order red, red, green, green, green, red, red, green, green, green, and so on continuing this pattern of 2 red lights followed by 3 green lights. How many feet separate the 3rd red light and the 21st red light?
Note: 1 foot is equal to 12 inches.

Question 8 of 25
8. Question
1 pointsA dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?

Question 9 of 25
9. Question
1 pointsIt takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to walk down the escalator when it is operating. How many seconds does it take Clea to ride down the operating escalator when she just stands on it?

Question 10 of 25
10. Question
1 pointsWhat is the area of the polygon whose vertices are the points of intersection of the curves x^{2} + y^{2} = 25 and (x − 4)^{2} + 9y^{2} = 81 ?

Question 11 of 25
11. Question
1 pointsIn the equation below, A and B are consecutive positive integers, and A, B, and A + B represent number bases:
32_{A} + 43_{B} = 69_{A+B} .
What is A + B ?

Question 12 of 25
12. Question
1 pointsHow many sequences of zeros and/or ones of length 20 have all the zeros con secutive, or all the ones consecutive, or both?

Question 13 of 25
13. Question
1 pointsTwo parabolas have equations y = x^{2} + ax + b and y = x^{2} + cx + d, where a, b, c, and d are integers (not necessarily different), each chosen independently by rolling a fair sixsided die. What is the probability that the parabolas have at least one point in common?

Question 14 of 25
14. Question
1 pointsBernardo and Silvia play the following game. An integer between 0 and 999, inclusive, is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds 50 to it and passes the result to Bernardo. The winner is the last person who produces a number less than 1000. Let N be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of N ?

Question 15 of 25
15. Question
1 pointsJesse cuts a circular paper disk of radius 12 along two radii to form two sectors, the smaller having a central angle of 120 degrees. He makes two circular cones, using each sector to form the lateral surface of a cone. What is the ratio of the volume of the smaller cone to that of the larger?
A. \frac18
B. \frac14
C. \frac{\sqrt{10}}{10}
D. \frac{\sqrt{5}}{6}
E. \frac{\sqrt{10}}{5}

Question 16 of 25
16. Question
1 pointsAmy, Beth, and Jo listen to four different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. In how many different ways is this possible?

Question 17 of 25
17. Question
1 pointsSquare P QRS lies in the first quadrant. Points (3, 0), (5, 0), (7, 0), and (13, 0) lie on lines SP , RQ, P Q, and SR, respectively. What is the sum of the coordinates of the center of the square P QRS ?

Question 18 of 25
18. Question
1 pointsLet (a1, a2, . . . , a10) be a list of the first 10 positive integers such that for each 2 ≤ i ≤ 10 either ai + 1 or ai − 1 or both appear somewhere before ai in the list. How many such lists are there?

Question 19 of 25
19. Question
1 points 
Question 20 of 25
20. Question
1 pointsA trapezoid has side lengths 3, 5, 7, and 11. The sum of all the possible areas of the trapezoid can be written in the form of r1 √n1 + r2 √n2 + r3, where r1, r2, and r3 are rational numbers and n1 and n2 are positive integers not divisible by the square of a prime. What is the greatest integer less than or equal to
r1 + r2 + r3 + n1 + n2 ?

Question 21 of 25
21. Question
1 pointsSquare AXY Z is inscribed in equiangular hexagon ABCDEF with X on \overline{\rm BC} , Y on \overline{\rm DE} , and Z on \overline{\rm EF} . Suppose that AB = 40 and EF = 41(√3 − 1). What is the sidelength of the square?

Question 22 of 25
22. Question
1 pointsA bug travels from A to B along the segments in the hexagonal lattice pictured below. The segments marked with an arrow can be traveled only in the direction of the arrow, and the bug never travels the same segment more than once. How many different paths are there?

Question 23 of 25
23. Question
1 pointsConsider all polynomials of a complex variable, P (z) = 4z^{4} + az^{3} + bz^{2} + cz + d, where a, b, c, and d are integers, 0 ≤ d ≤ c ≤ b ≤ a ≤ 4, and the polynomial has a zero z_{0} with z_{0} = 1. What is the sum of all values P (1) over all the polynomials with these properties?

Question 24 of 25
24. Question
1 pointsNote: a sequence of positive numbers is unbounded if for every integer B, there is a member of the sequence greater than B.

Question 25 of 25
25. Question
1 points
Download AMC 12 Math Test 2012 [PDF]
Test Questions 
Answers/Solution 
2012 Set A  12A 2012 Solutions 
2012 Set B  12B 2012 Solutions 