AMC 12 Math Test 2013 Time Limit 75 minutes 25 Questions Mock Test. You can try American Mathematics Competitions (AMC) 12 Math Practice Test 2013 Questions and Answers Online Mock test or you can download both Set A and Set B 2013 exam questions with answer keys and explanations in PDF for better MAA AMC Prep.
This American Mathematics Competitions 64th Annual AMC 12 Exam for American Mathematics Contest was held on Tuesday, February 5, 2013.
AMC 12 Math Test 2013 [Time Limit ]
Test Prep For  AMC 12 Practice Test 2024 
Test Content  AMC 12 Math Test 
SET  A 
Test Year  2013 
Test Type  Online Mock Test 
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AMC 12 Math Practice Test 2013
Total Items: 25
Time Limit: 75 minutes
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AMC 12 Math Practice Test 2013
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Question 1 of 25
1. Question
1 pointsSquare ABCD has side length 10. Point E is on \overline{\rm BC} , and the area of ΔABE is 40. What is BE ?

Question 2 of 25
2. Question
1 pointsA softball team played ten games, scoring 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 runs. They lost by one run in exactly five games. In each of their other games, they scored twice as many runs as their opponent. How many total runs did their opponents score?

Question 3 of 25
3. Question
1 pointsA flower bouquet contains pink roses, red roses, pink carnations, and red carna tions. One third of the pink flowers are roses, three fourths of the red flowers are carnations, and six tenths of the flowers are pink. What percent of the flowers are carnations?

Question 4 of 25
4. Question
1 pointsWhat is the value of

Question 5 of 25
5. Question
1 pointsTom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $105, Dorothy paid $125, and Sammy paid $175. In order to share the costs equally, Tom gave Sammy t dollars, and Dorothy gave Sammy d dollars. What is t − d ?

Question 6 of 25
6. Question
1 pointsIn a recent basketball game, Shenille attempted only threepoint shots and two point shots. She was successful on 20% of her threepoint shots and 30% of her twopoint shots. Shenille attempted 30 shots. How many points did she score?

Question 7 of 25
7. Question
1 pointsThe sequence S1, S2, S3, . . . , S10 has the property that every term beginning with the third is the sum of the previous two. That is,
S_{n} = S_{n}−2 + S_{n1} for n ≥ 3
Suppose that S_{9} = 110 and S_{7} = 42. What is S_{4} ?

Question 8 of 25
8. Question
1 pointsGiven that x and y are distinct nonzero real numbers such that x + \sqrt{2x} , what is xy ?

Question 9 of 25
9. Question
1 points 
Question 10 of 25
10. Question
1 pointsLet S be the set of positive integers n for which \frac1n has the repeating decimal representation 0.\overline{\rm ab} = 0.ababab . . ., with a and b different digits. What is the sum of the elements of S ?

Question 11 of 25
11. Question
1 pointsriangle ABC is equilateral with AB = 1. Points E and G are on \overline{\rm AC} and points D and F are on \overline{\rm AB} such that both \overline{\rm DE} and \overline{\rm FG} are parallel to \overline{\rm BC} . Furthermore, triangle ADE and trapezoids DF GE and F BCG all have the same perimeter. What is DE + FG ?

Question 12 of 25
12. Question
1 pointsThe angles in a particular triangle are in arithmetic progression, and the side lengths are 4, 5, and x. The sum of the possible values of x equals a + √b + √c, where a, b, and c are positive integers. What is a + b + c ?

Question 13 of 25
13. Question
1 pointsLet points A = (0, 0), B = (1, 2), C = (3, 3), and D = (4, 0). Quadrilateral ABCD is cut into equal area pieces by a line passing through A. This line intersects \overline{\rm CD} at point (\frac{p}{q}, \frac{r}{s}) , where these fractions are in lowest terms. What is p + q + r + s ?

Question 14 of 25
14. Question
1 pointsThe sequence
log_{12} 162, log_{12} x, log_{12} y, log_{12} z, log_{12} 1250
is an arithmetic progression. What is x ?

Question 15 of 25
15. Question
1 pointsRabbits Peter and Pauline have three offspring—Flopsie, Mopsie, and Cottontail. These five rabbits are to be distributed to four different pet stores so that no store gets both a parent and a child. It is not required that every store gets a rabbit. In how many different ways can this be done?

Question 16 of 25
16. Question
1 pointsA, B, and C are three piles of rocks. The mean weight of the rocks in A is 40 pounds, the mean weight of the rocks in B is 50 pounds, the mean weight of the rocks in the combined piles A and B is 43 pounds, and the mean weight of the rocks in the combined piles A and C is 44 pounds. What is the greatest possible integer value for the mean in pounds of the rocks in the combined piles B and C ?

Question 17 of 25
17. Question
1 pointsA group of 12 pirates agree to divide a treasure chest of gold coins among themselves as follows. The k^{th} pirate to take a share takes \frac{k}{12} of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for which this arrangement will allow each pirate to receive a positive whole number of coins. How many coins does the 12^{th} pirate receive?

Question 18 of 25
18. Question
1 pointsSix spheres of radius 1 are positioned so that their centers are at the vertices of a regular hexagon of side length 2. The six spheres are internally tangent to a larger sphere whose center is the center of the hexagon. An eighth sphere is externally tangent to the six smaller spheres and internally tangent to the larger sphere. What is the radius of this eighth sphere?

Question 19 of 25
19. Question
1 pointsIn ΔABC, AB = 86, and AC = 97. A circle with center A and radius AB intersects \overline{\rm BC} at points B and X. Moreover \overline{\rm BX} and \overline{\rm CX} have integer lengths. What is BC ?

Question 20 of 25
20. Question
1 points 
Question 21 of 25
21. Question
1 pointsConsider
A = log (2013 + log (2012 + log (2011 + log(· · · + log (3 + log 2) · · ·)))).
Which of the following intervals contains A ?

Question 22 of 25
22. Question
1 pointsA palindrome is a nonnegative integer number that reads the same forwards and backwards when written in base 10 with no leading zeros. A 6digit palindrome n is chosen uniformly at random. What is the probability that \frac{n}{11} is also a palindrome?

Question 23 of 25
23. Question
1 pointsABCD is a square of side length √3 + 1. Point P is on \overline{\rm AC} such that AP = √2. The square region bounded by ABCD is rotated 90^{◦} counterclockwise with center P , sweeping out a region whose area is \frac{1}{c} (aπ + b), where a, b, and c are positive integers and gcd(a, b, c) = 1. What is a + b + c ?

Question 24 of 25
24. Question
1 pointsThree distinct segments are chosen at random among the segments whose end points are the vertices of a regular 12gon. What is the probability that the lengths of these three segments are the three side lengths of a triangle with positive area

Question 25 of 25
25. Question
1 points
Download AMC 12 Math Test 2013 [PDF]
Test Questions  Answers/Solution 
2013 Set A  12A 2013 Solutions 
2013 Set B  12B 2013 Solutions 