|
|
| (27 intermediate revisions by 10 users not shown) |
| Line 1: |
Line 1: |
| | {{AMC10 Problems|year=2024|ab=A}} | | {{AMC10 Problems|year=2024|ab=A}} |
| | | | |
| − | ==Problem 1==
| + | The AMC 10A Contest will occur on November 6, 2024. |
| − | | |
| − | 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?
| |
| − | | |
| − | <math> \textbf{(A)}\ 9\qquad\textbf{(B)}\ 11\qquad\textbf{(C)}\ 13\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 15 </math>
| |
| − | | |
| − | ==Problem 2==
| |
| − | | |
| − | What is the value of <math>\dfrac{11!-10!}{9!}</math>?
| |
| − | | |
| − | <math>\textbf{(A)}\ 99\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 110\qquad\textbf{(D)}\ 121\qquad\textbf{(E)}\ 132</math>
| |
| − | | |
| − | ==Problem 3==
| |
| − | 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>?
| |
| − | | |
| − | <math>\textbf{(A)}\ 146 \qquad \textbf{(B)}\ 147 \qquad \textbf{(C)}\ 148 \qquad \textbf{(D)}\ 149 \qquad \textbf{(E)}\ 150</math>
| |
| − | | |
| − | ==Problem 4==
| |
| − | What is <math>\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}?</math>
| |
| − |
| |
| − | <math>\textbf{(A)}\ -1 \qquad
| |
| − | \textbf{(B)}\ \frac{5}{36} \qquad
| |
| − | \textbf{(C)}\ \frac{7}{12} \qquad
| |
| − | \textbf{(D)}\ \frac{147}{60} \qquad
| |
| − | \textbf{(E)}\ \frac{43}{3} </math>
| |
| − | | |
| − | ==Problem 5==
| |
| − | 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?
| |
| − | | |
| − | <math>\textbf{(A) }\$35\qquad
| |
| − | \textbf{(B) }\$38.50\qquad
| |
| − | \textbf{(C) }\$40\qquad
| |
| − | \textbf{(D) }\$42\qquad
| |
| − | \textbf{(E) }\$42.50</math>
| |
| − | | |
| − | ==Problem 6==
| |
| − | | |
| − | 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>? | |
| − | | |
| − | <math>\textbf{(A) } 25 \qquad\textbf{(B) } 33 \qquad\textbf{(C) } 44\qquad\textbf{(D) } 66 \qquad\textbf{(E) } 78</math>
| |
| − | | |
| − | ==Problem 7==
| |
| − | | |
| − | 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?
| |
| − | | |
| − | <math>
| |
| − | \textbf{(A) }25\pi \qquad
| |
| − | \textbf{(B) }50\pi \qquad
| |
| − | \textbf{(C) }75\pi \qquad
| |
| − | \textbf{(D) }100\pi \qquad
| |
| − | \textbf{(E) }125\pi \qquad
| |
| − | </math>
| |
| − | | |
| − | ==Problem 8==
| |
| − | | |
| − | 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?
| |
| − | | |
| − | <math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5</math>
| |
| − | | |
| − | ==Problem 9==
| |
| − | | |
| − | 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?
| |
| − | | |
| − | <asy>
| |
| − | import olympiad;
| |
| − | unitsize(25);
| |
| − | filldraw((1,3)--(1,4)--(2,4)--(2,3)--cycle, gray(0.7));
| |
| − | filldraw((2,1)--(2,2)--(3,2)--(3,1)--cycle, gray(0.7));
| |
| − | filldraw((4,0)--(5,0)--(5,1)--(4,1)--cycle, gray(0.7));
| |
| − | for (int i = 0; i < 5; ++i) {
| |
| − | for (int j = 0; j < 6; ++j) {
| |
| − | pair A = (j,i);
| |
| − | }
| |
| − | }
| |
| − | for (int i = 0; i < 5; ++i) {
| |
| − | for (int j = 0; j < 6; ++j) {
| |
| − | if (j != 5) {
| |
| − | draw((j,i)--(j+1,i));
| |
| − | }
| |
| − | if (i != 4) {
| |
| − | draw((j,i)--(j,i+1));
| |
| − | }
| |
| − | }
| |
| − | }
| |
| − | </asy>
| |
| − | | |
| − | <math>\textbf{(A) } 4 \qquad \textbf{(B) } 5 \qquad \textbf{(C) } 6 \qquad \textbf{(D) } 7 \qquad \textbf{(E) } 8</math>
| |
| − | | |
| − | ==Problem 10==
| |
| − | 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>?
| |
| − | | |
| − | <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.
| |
| − | | |
| − | ==Problem 11==
| |
| − | 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>?
| |
| − | | |
| − | <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>
| |
| − | | |
| − | ==Problem 12==
| |
| − | | |
| − | 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?
| |
| − | | |
| − | <math>\textbf{(A)}\ \frac12\qquad\textbf{(B)}\ \frac 58\qquad\textbf{(C)}\ \frac 23\qquad\textbf{(D)}\ \frac34\qquad\textbf{(E)}\ \frac 78</math>
| |
| − | | |
| − | ==Problem 13==
| |
| − | | |
| − | 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?
| |
| − | | |
| − | <math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 104</math>
| |
| − | | |
| − | ==Problem 14==
| |
| − | | |
| − | The sequence
| |
| − | | |
| − | <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>
| |
| − | | |
| − | is an arithmetic progression. What is <math>x</math>?
| |
| − | | |
| − | <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>
| |
| − | | |
| − | ==Problem 16==
| |
| − | | |
| − | ==Problem 17==
| |
| − | | |
| − | ==Problem 18==
| |
| − | | |
| − | ==Problem 19==
| |
| − | | |
| − | ==Problem 20==
| |
| − | | |
| − | ==Problem 21==
| |
| − | | |
| − | ==Problem 22==
| |
| − | | |
| − | ==Problem 23==
| |
| − | | |
| − | ==Problem 24==
| |
| − | | |
| − | ==Problem 25==
| |
| − | Stop trying to cheat!
| |
| − | | |
| − | ~ TRX74x94Planet9
| |
| | | | |
| | ==See also== | | ==See also== |
| Line 150: |
Line 9: |
| | * [[Mathematics competitions]] | | * [[Mathematics competitions]] |
| | * [[Mathematics competition resources]] | | * [[Mathematics competition resources]] |
| − | {{MAA Notice}}
| |
