Difference between revisions of "2021 Mock AMC 8 Problems"

Revision as of 15:33, 23 October 2021

Problem 1

What is the value of $1-2+3-4+5-6+7-8+9$ ?

$\mathrm{(A)}\ 4 \qquad\mathrm{(B)}\ 5 \qquad\mathrm{(C)}\ 6 \qquad\mathrm{(D)}\ 7 \qquad\mathrm{(E)}\ 25$

https://artofproblemsolving.com/wiki/index.php/2021_Mock_AMC_8_Problems/Problem_1

Problem 2

Aaron has a rectangular yard measuring $4$ feet by $10$ feet. How many $2$ inch by $5$ inch rectangular bricks can he fit in his yard?

$\mathrm{(A)}\ 4 \qquad\mathrm{(B)}\ 12 \qquad\mathrm{(C)}\ 24 \qquad\mathrm{(D)}\ 72 \qquad\mathrm{(E)}\ 144$

https://artofproblemsolving.com/wiki/index.php/2021_Mock_AMC_8_Problems/Problem_2

Problem 3

Amy, Bob, Cassie, and Darren are on a camping trip. Each of them has $4$ choices for what they wear on day $1$ of the camping trip. How many different arrangements of what they wear are possible on day $1$ of the camping trip?

$\textbf{(A) } 16 \qquad \textbf{(B) } 32 \qquad \textbf{(C) } 64 \qquad \textbf{(D) } 256 \qquad \textbf{(E) 500}$

Problem 4

A rectangle with positive integer side lengths has area $2021$ . In how many ways is this possible?

$\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 3 \qquad \textbf{(D) } 4 \qquad \textbf{(E) } 5$

Problem 5

Fiona leaves her house to go to the airport. She drives for $30$ minutes at a constant rate of $40$ miles per hour, then walks for $20$ minutes at a constant rate of $3.6$ miles per hour. She then goes on a train going 50 miles per hour for 12 minutes. How far has she traveled?

$\textbf{(A) } 31.2 \qquad \textbf{(B) } 32.2 \qquad \textbf{(C) } 32.4 \qquad \textbf{(D) } 33.8 \qquad \textbf{(E) } 35.9$

Problem 6

Hexagon $ABCDEF$ has side length $4$ . What is the area of this hexagon rounded to the nearest tenth?

$\textbf{(A) } 40.8 \qquad \textbf{(B) } 41.5 \qquad \textbf{(C) } 41.6 \qquad \textbf{(D) } 42.4 \qquad \textbf{(E) } 44.3$

Problem 7

The number $N$ is a positive $3$ digit integer.

•When $N$ is divided by $80$ , the remainder is $4$

•When $N$ is divided by $3$ , the remainder is $1$

• $N$ is a perfect square.

What is the sum of the digits of $N$ ?

$\textbf{(A) }8\qquad\textbf{(B) }10\qquad\textbf{(C) }12\qquad\textbf{(D) }14\qquad \textbf{(E) }16$

Problem 8

How many many zeros are at the right of the last nonzero digit of the number $1020!$ ?

$\textbf{(A) }204\qquad\textbf{(B) }244\qquad\textbf{(C) }252\qquad\textbf{(D) }253\qquad \textbf{(E) }254$

Problem 9

Isosceles trapezoid $ABCD$ has $AB = 8$ . Point $E$ is on $DC$ such that $AE$ is perpendicular to $DC$ and that $AE$ = $9$ . $BC$ and $AE$ are extended to point $F$ to make an isosceles triangle. Point $F$ is $18$ units away from the midpoint of $AB$ . What is the area of isosceles trapezoid $ABCD$ ?

$\text{(A)}\ 60 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 90 \qquad \text{(D)}\ 108 \qquad \text{(E)}\ 162$

@@ Line 60: / Line 60: @@
 ==Problem 9==
-Isosceles trapezoid <math>ABCD</math> has <math>AB = 8</math>. Point <math>E</math> is on <math>DC</math> such that <math>AE</math> is perpendicular to <math>DC</math> and that <math>AE</math> = <math>9</math>. <math>BC</math> and <math>AE</math> are extended to point <math>F</math> to make an isosceles triangle. What is the area of isosceles trapezoid <math>ABCD</math>?
+Isosceles trapezoid <math>ABCD</math> has <math>AB = 8</math>. Point <math>E</math> is on <math>DC</math> such that <math>AE</math> is perpendicular to <math>DC</math> and that <math>AE</math> = <math>9</math>. <math>BC</math> and <math>AE</math> are extended to point <math>F</math> to make an isosceles triangle. Point <math>F</math> is <math>18</math> units away from the midpoint of <math>AB</math>. What is the area of isosceles trapezoid <math>ABCD</math>?
+<math>\text{(A)}\ 60 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 90 \qquad \text{(D)}\ 108 \qquad \text{(E)}\ 162</math>

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