시험 완료
|
AMC 10A 2015
0.0%
0/25
문제별 결과
1
Competition Math
오답률 100%
오답
What is the value of \(( 2^0 - 1 + 5^2 + 0 )^{- 1} \times 5 ?\)
A
\(- 125\)
B
\(- 120\)
C
\(\dfrac{1}{5}\)
D
\(\dfrac{5}{24}\)
E
\(25\)
해설 없음
2
Competition Math
오답률 100%
오답
A box contains a collection of triangular and square tiles. There are
\(25\) tiles in the box, containing \(84\) edges total. How many square
tiles are there in the box?
A
\(3\)
B
\(5\)
C
\(7\)
D
\(9\)
E
\(11\)
해설 없음
3
Competition Math
오답률 100%
오답
Ann made a 3-step staircase using 18 toothpicks as shown in the figure.
How many toothpicks does she need to add to complete a 5-step staircase?
A
\(9\)
B
\(18\)
C
\(20\)
D
\(22\)
E
\(24\)
해설 없음
4
Competition Math
오답률 100%
오답
Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three
times as many eggs as Sofia, and Sofia had twice as many eggs as Mia.
Pablo decides to give some of his eggs to Sofia and Mia so that all
three will have the same number of eggs. What fraction of his eggs
should Pablo give to Sofia?
A
\(\dfrac{1}{12}\)
B
\(\dfrac{1}{6}\)
C
\(\dfrac{1}{4}\)
D
\(\dfrac{1}{3}\)
E
\(\dfrac{1}{2}\)
해설 없음
5
Competition Math
오답률 100%
오답
Mr.~Patrick teaches math to \(15\) students. He was grading tests and
found that when he graded everyone's test except Payton's, the average
grade for the class was \(80\). After he graded Payton's test, the test
average became \(81\). What was Payton's score on the test?
A
\(81\)
B
\(85\)
C
\(91\)
D
\(94\)
E
\(95\)
해설 없음
6
Competition Math
오답률 100%
오답
The sum of two positive numbers is \(5\) times their difference. What is
the ratio of the larger number to the smaller number?
A
\(\dfrac{5}{4}\)
B
\(\dfrac{3}{2}\)
C
\(\dfrac{9}{5}\)
D
\(2\)
E
\(\dfrac{5}{2}\)
해설 없음
7
Competition Math
오답률 100%
오답
How many terms are there in the arithmetic sequence \(13\), \(16\), \(19\), .
. ., \(70\), \(73\)?
A
\(20\)
B
\(21\)
C
\(24\)
D
\(60\)
E
\(61\)
해설 없음
8
Competition Math
오답률 100%
오답
Two years ago Pete was three times as old as his cousin Claire. 2 years
before that, Pete was four times as old as Claire. In how many years
will the ratio of their ages be \(2\)~: \(1\)?
A
\(2\)
B
\(4\)
C
\(5\)
D
\(6\)
E
\(8\)
해설 없음
9
Competition Math
오답률 100%
오답
Two right circular cylinders have the same volume. The radius of the
second cylinder is \(10 %\) more than the radius of the first. What is the
relationship between the heights of the two cylinders?
\(\mathbf{\text{(B)}} \text{The first height is } 10 % \text{ more than the second.} \) bold("(C)") "The second height is " 21 % " less than the first." \( \mathbf{\text{(D)}} \text{The first height is } 21 % \text{ more than the second.}\)\(\mathbf{\text{(E)}} \text{The second height is } 80 % \text{ of the first.}\)
A
\(\text{The second height is } 10 % \text{ less than the first.}\)
해설 없음
10
Competition Math
오답률 100%
오답
How many rearrangements of \(a b c d\) are there in which no two adjacent
letters are also adjacent letters in the alphabet? For example, no such
rearrangements could include either \(a b\) or \(b a\).
A
\(0\)
B
\(1\)
C
\(2\)
D
\(3\)
E
\(4\)
해설 없음
11
Competition Math
오답률 100%
오답
The ratio of the length to the width of a rectangle is \(4\)~: \(3\). If the
rectangle has diagonal of length \(d\), then the area may be expressed as
\(k d^2\) for some constant \(k\). What is \(k\)?
A
\(\dfrac{2}{7}\)
B
\(\dfrac{3}{7}\)
C
\(\dfrac{12}{25}\)
D
\(\dfrac{16}{25}\)
E
\(\dfrac{3}{4}\)
해설 없음
12
Competition Math
오답률 100%
오답
Points \(( \sqrt{\pi} , a )\) and \(( \sqrt{\pi} , b )\) are distinct points
on the graph of \(y^2 + x^4 = 2 x^2 y + 1\). What is \(\| a - b \|\)?
A
\(1\)
B
\(\dfrac{\pi}{2}\)
C
\(2\)
D
\(\sqrt{1 + \pi}\)
E
\(1 + \sqrt{\pi}\)
해설 없음
13
Competition Math
오답률 100%
오답
Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin.
There are exactly 17 different values that can be obtained as
combinations of one or more of her coins. How many 10-cent coins does
Claudia have?
A
\(3\)
B
\(4\)
C
\(5\)
D
\(6\)
E
\(7\)
해설 없음
14
Competition Math
오답률 100%
오답
The diagram below shows the circular face of a clock with radius \(20\) cm
and a circular disk with radius \(10\) cm externally tangent to the clock
face at \(12\) o'clock. The disk has an arrow painted on it, initially
pointing in the upward vertical direction. Let the disk roll clockwise
around the clock face. At what point on the clock face will the disk be
tangent when the arrow is next pointing in the upward vertical
direction?
A
\(2 o' c l o c k\)
B
\(3 o' c l o c k\)
C
\(4 o' c l o c k\)
D
\(6 o' c l o c k\)
E
\(8 o' c l o c k\)
해설 없음
15
Competition Math
오답률 100%
오답
Consider the set of all fractions \(\dfrac{x}{y} ,\) where \(x\) and \(y\) are
relatively prime positive integers. How many of these fractions have the
property that if both numerator and denominator are increased by \(1\),
the value of the fraction is increased by \(10 %\)?
A
\(0\)
B
\(1\)
C
\(2\)
D
\(3\)
E
\(\text{infinitely many}\)
해설 없음
16
Competition Math
오답률 100%
오답
If \(y + 4 = ( x - 2 )^2 , x + 4 = ( y - 2 )^2\), and \(x \neq y\),
what is the value of \(x^2 + y^2\)?
A
\(10\)
B
\(15\)
C
\(20\)
D
\(25\)
E
\(\text{30}\)
해설 없음
17
Competition Math
오답률 100%
오답
A line that passes through the origin intersects both the line \(x = 1\)
and the line \(y = 1 + \dfrac{\sqrt{3}}{3} x\). The three lines create an
equilateral triangle. What is the perimeter of the triangle?
A
\(2 \sqrt{6}\)
B
\(2 + 2 \sqrt{3}\)
C
\(6\)
D
\(3 + 2 \sqrt{3}\)
E
\(6 + \dfrac{\sqrt{3}}{3}\)
해설 없음
18
Competition Math
오답률 100%
오답
Hexadecimal (base-16) numbers are written using numeric digits \(0\)
through \(9\) as well as the letters \(A\) through \(F\) to represent \(10\)
through \(15\). Among the first \(1000\) positive integers, there are \(n\)
whose hexadecimal representation contains only numeric digits. What is
the sum of the digits of \(n\)?
A
\(17\)
B
\(18\)
C
\(19\)
D
\(20\)
E
\(21\)
해설 없음
19
Competition Math
오답률 100%
오답
The isosceles right triangle \(A B C\) has right angle at \(C\) and area
\(12.5\). The rays trisecting \(\angle A C B\) intersect \(A B\) at \(D\) and
\(E\). What is the area of \(\triangle C D E\)?
A
\(\dfrac{5 \sqrt{2}}{3}\)
B
\(\dfrac{50 \sqrt{3} - 75}{4}\)
C
\(\dfrac{15 \sqrt{3}}{8}\)
D
\(\dfrac{50 - 25 \sqrt{3}}{2}\)
E
\(\dfrac{25}{6}\)
해설 없음
20
Competition Math
오답률 100%
오답
A rectangle with positive integer side lengths in \(\text{cm}\) has
area \(A \) "cm"^2\( and perimeter \)P \( \text{cm}\). Which of the
following numbers cannot equal \(A + P\)?
A
\(100\)
B
\(102\)
C
\(104\)
D
\(106\)
E
\(108\)
해설 없음
21
Competition Math
오답률 100%
오답
Tetrahedron \(A B C D\) has \(A B = 5\), \(A C = 3\), \(B C = 4\), \(B D = 4\),
\(A D = 3\), and \(C D = \dfrac{12}{5} \sqrt{2}\). What is the volume of the
tetrahedron?
A
\(3 \sqrt{2}\)
B
\(2 \sqrt{5}\)
C
\(\dfrac{24}{5}\)
D
\(3 \sqrt{3}\)
E
\(\dfrac{24}{5} \sqrt{2}\)
해설 없음
22
Competition Math
오답률 100%
오답
Eight people are sitting around a circular table, each holding a fair
coin. All eight people flip their coins and those who flip heads stand
while those who flip tails remain seated. What is the probability that
no two adjacent people will stand?
A
\(\dfrac{47}{256}\)
B
\(\dfrac{3}{16}\)
C
\(\dfrac{49}{256}\)
D
\(\dfrac{25}{128}\)
E
\(\dfrac{51}{256}\)
해설 없음
23
Competition Math
오답률 100%
오답
The zeroes of the function \(f ( x ) = x^2 - a x + 2 a\) are integers.
What is the sum of the possible values of \(a\)?
A
\(7\)
B
\(8\)
C
\(16\)
D
\(17\)
E
\(18\)
해설 없음
24
Competition Math
오답률 100%
오답
For some positive integers \(p\), there is a quadrilateral \(A B C D\) with
positive integer side lengths, perimeter \(p\), right angles at \(B\) and
\(C\), \(A B = 2\), and \(C D = A D\). How many different values of \(p < 2015\)
are possible?
A
\(30\)
B
\(31\)
C
\(61\)
D
\(62\)
E
\(63\)
해설 없음
25
Competition Math
오답률 100%
오답
Let \(S\) be a square of side length \(1\). Two points are chosen at random
on the sides of \(S\). The probability that the straight-line distance
between the points is at least \(\dfrac{1}{2}\) is \(\dfrac{a - b \pi}{c}\), where
\(a\), \(b\), and \(c\) are positive integers with \(\gcd ( a , b , c ) = 1\).
What is \(a + b + c\)?
A
\(59\)
B
\(60\)
C
\(61\)
D
\(62\)
E
\(63\)
해설 없음