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| | {{AMC10 Problems|year=2024|ab=A}} | | {{AMC10 Problems|year=2024|ab=A}} |
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| − | ==Problem 1==
| + | The AMC 10A Contest will occur on November 6, 2024. |
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| − | A bug crawls along a number line, starting at <math>-2</math>. It crawls to <math>-6</math>, then turns around and crawls to <math>5</math>. How many units does the bug crawl altogether?
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| − | <math> \textbf{(A)}\ 9\qquad\textbf{(B)}\ 11\qquad\textbf{(C)}\ 13\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 15 </math>
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| − | ==Problem 2==
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| − | What is the value of <math>\dfrac{11!-10!}{9!}</math>?
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| − | <math>\textbf{(A)}\ 99\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 110\qquad\textbf{(D)}\ 121\qquad\textbf{(E)}\ 132</math>
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| − | ==Problem 3==
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| − | When counting from <math>3</math> to <math>201</math>, <math>53</math> is the <math>51^{st}</math> number counted. When counting backwards from <math>201</math> to <math>3</math>, <math>53</math> is the <math>n^{th}</math> number counted. What is <math>n</math>?
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| − | <math>\textbf{(A)}\ 146 \qquad \textbf{(B)}\ 147 \qquad \textbf{(C)}\ 148 \qquad \textbf{(D)}\ 149 \qquad \textbf{(E)}\ 150</math>
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| − | ==Problem 4==
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| − | What is <math>\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}?</math>
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| − | <math>\textbf{(A)}\ -1 \qquad
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| − | \textbf{(B)}\ \frac{5}{36} \qquad
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| − | \textbf{(C)}\ \frac{7}{12} \qquad
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| − | \textbf{(D)}\ \frac{147}{60} \qquad
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| − | \textbf{(E)}\ \frac{43}{3} </math>
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| − | ==Problem 5==
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| − | At the theater children get in for half price. The price for <math>5</math> adult tickets and <math>4</math> child tickets is <math>\$24.50</math>. How much would <math>8</math> adult tickets and <math>6</math> child tickets cost?
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| − | <math>\textbf{(A) }\$35\qquad
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| − | \textbf{(B) }\$38.50\qquad
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| − | \textbf{(C) }\$40\qquad
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| − | \textbf{(D) }\$42\qquad
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| − | \textbf{(E) }\$42.50</math>
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| − | ==Problem 6==
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| − | The area of a pizza with radius <math>4</math> is <math>N</math> percent larger than the area of a pizza with radius <math>3</math> inches. What is the integer closest to <math>N</math>?
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| − | <math>\textbf{(A) } 25 \qquad\textbf{(B) } 33 \qquad\textbf{(C) } 44\qquad\textbf{(D) } 66 \qquad\textbf{(E) } 78</math>
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| − | ==Problem 7==
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| − | A circle has a chord of length <math>10</math>, and the distance from the center of the circle to the chord is <math>5</math>. What is the area of the circle?
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| − | <math>
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| − | \textbf{(A) }25\pi \qquad
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| − | \textbf{(B) }50\pi \qquad
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| − | \textbf{(C) }75\pi \qquad
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| − | \textbf{(D) }100\pi \qquad
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| − | \textbf{(E) }125\pi \qquad
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| − | </math>
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| − | ==Problem 8==
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| − | On an algebra quiz, <math>10\%</math> of the students scored <math>70</math> points, <math>35\%</math> scored <math>80</math> points, <math>30\%</math> scored <math>90</math> points, and the rest scored <math>100</math> points. What is the difference between the mean and median score of the students' scores on this quiz?
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| − | <math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5</math>
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| − | ==Problem 9==
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| − | In the plane figure shown below, <math>3</math> of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetry?
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| − | <asy>
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| − | import olympiad;
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| − | unitsize(25);
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| − | filldraw((1,3)--(1,4)--(2,4)--(2,3)--cycle, gray(0.7));
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| − | filldraw((2,1)--(2,2)--(3,2)--(3,1)--cycle, gray(0.7));
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| − | filldraw((4,0)--(5,0)--(5,1)--(4,1)--cycle, gray(0.7));
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| − | for (int i = 0; i < 5; ++i) {
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| − | for (int j = 0; j < 6; ++j) {
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| − | pair A = (j,i);
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| − | }
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| − | }
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| − | for (int i = 0; i < 5; ++i) {
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| − | for (int j = 0; j < 6; ++j) {
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| − | if (j != 5) {
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| − | draw((j,i)--(j+1,i));
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| − | }
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| − | if (i != 4) {
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| − | draw((j,i)--(j,i+1));
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| − | }
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| − | }
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| − | }
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| − | </asy>
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| − | <math>\textbf{(A) } 4 \qquad \textbf{(B) } 5 \qquad \textbf{(C) } 6 \qquad \textbf{(D) } 7 \qquad \textbf{(E) } 8</math>
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| − | ==Problem 10==
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| − | The functions <math>\sin(x)</math> and <math>\cos(x)</math> are periodic with least period <math>2\pi</math>. What is the least period of the function <math>\cos(\sin(x))</math>?
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| − | <math>\textbf{(A)}\ \frac{\pi}{2}\qquad\textbf{(B)}\ \pi\qquad\textbf{(C)}\ 2\pi \qquad\textbf{(D)}\ 4\pi \qquad\textbf{(E)} </math> The function is not periodic.
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| − | ==Problem 11==
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| − | Let <math>x</math> and <math>y</math> be two-digit positive integers with mean <math>60</math>. What is the maximum value of the ratio <math>\frac{x}{y}</math>?
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| − | <math>\textbf{(A)}\ 3 \qquad \textbf{(B)}\ \frac{33}{7} \qquad \textbf{(C)}\ \frac{39}{7} \qquad \textbf{(D)}\ 9 \qquad \textbf{(E)}\ \frac{99}{10}</math>
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| − | ==Problem 12==
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| − | A frog sitting at the point <math>(1, 2)</math> begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length <math>1</math>, and the direction of each jump (up, down, right, or left) is chosen independently at random. The sequence ends when the frog reaches a side of the square with vertices <math>(0,0), (0,4), (4,4),</math> and <math>(4,0)</math>. What is the probability that the sequence of jumps ends on a vertical side of the square?
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| − | <math>\textbf{(A)}\ \frac12\qquad\textbf{(B)}\ \frac 58\qquad\textbf{(C)}\ \frac 23\qquad\textbf{(D)}\ \frac34\qquad\textbf{(E)}\ \frac 78</math>
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| − | ==Problem 13==
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| − | What is the minimum number of digits to the right of the decimal point needed to express the fraction <math>\frac{123456789}{2^{26}\cdot 5^4}</math> as a decimal?
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| − | <math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 104</math>
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| − | ==Problem 14==
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| − | The sequence
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| − | <math>\log_{12}{162}</math>, <math>\log_{12}{x}</math>, <math>\log_{12}{y}</math>, <math>\log_{12}{z}</math>, <math>\log_{12}{1250}</math>
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| − | is an arithmetic progression. What is <math>x</math>?
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| − | <math> \textbf{(A)} \ 125\sqrt{3} \qquad \textbf{(B)} \ 270 \qquad \textbf{(C)} \ 162\sqrt{5} \qquad \textbf{(D)} \ 434 \qquad \textbf{(E)} \ 225\sqrt{6}</math>
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| − | ==Problem 16==
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| − | All the numbers <math>2, 3, 4, 5, 6, 7</math> are assigned to the six faces of a cube, one number to each face. For each of the eight vertices of the cube, a product of three numbers is computed, where the three numbers are the numbers assigned to the three faces that include that vertex. What is the greatest possible value of the sum of these eight products?
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| − | <math>\textbf{(A)}\ 312 \qquad
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| − | \textbf{(B)}\ 343 \qquad
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| − | \textbf{(C)}\ 625 \qquad
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| − | \textbf{(D)}\ 729 \qquad
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| − | \textbf{(E)}\ 1680</math>
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| − | ==Problem 17==
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| − | Jesse cuts a circular disk of radius 12, along 2 radii to form 2 sectors, one with a central angle of 120. He makes two circular cones using each sector to form the lateral surface of each cone. What is the ratio of the volume of the smaller cone to the larger cone?
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| − | <math>\textbf{(A)}\ \frac{1}{8}\qquad\textbf{(B)}\ \frac{1}{4}\qquad\textbf{(C)}\ \frac{\sqrt{10}}{10}\qquad\textbf{(D)}\ \frac{\sqrt{5}}{6}\qquad\textbf{(E)}\ \frac{\sqrt{5}}{5}</math>
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| − | ==Problem 18==
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| − | Rhombus <math>ABCD</math> has side length <math>2</math> and <math>\angle B = 120</math>°. Region <math>R</math> consists of all points inside the rhombus that are closer to vertex <math>B</math> than any of the other three vertices. What is the area of <math>R</math>?
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| − | <math> \textbf{(A)}\ \frac{\sqrt{3}}{3} \qquad\textbf{(B)}\ \frac{\sqrt{3}}{2} \qquad\textbf{(C)}\ \frac{2\sqrt{3}}{3} \qquad\textbf{(D)}\ 1 + \frac{\sqrt{3}}{3} \qquad\textbf{(E)}\ 2</math>
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| − | [[Category: Introductory Geometry Problems]]
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| − | ==Problem 19==
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| − | ==Problem 20==
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| − | ==Problem 21==
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| − | ==Problem 22==
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| − | ==Problem 23==
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| − | ==Problem 24==
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| − | ==Problem 25==
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| − | Stop trying to cheat!
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| − | ~ TRX74x94Planet9
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| | ==See also== | | ==See also== |
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| | * [[Mathematics competitions]] | | * [[Mathematics competitions]] |
| | * [[Mathematics competition resources]] | | * [[Mathematics competition resources]] |
| − | {{MAA Notice}}
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