Difference between revisions of "2021 Mock AMC 8 Problems"
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<math>\mathrm{(A)}\ 4 | <math>\mathrm{(A)}\ 4 | ||
− | \qquad\mathrm{(B)}\ | + | \qquad\mathrm{(B)}\ 16 |
− | \qquad\mathrm{(C)}\ | + | \qquad\mathrm{(C)}\ 256 |
− | \qquad\mathrm{(D)}\ | + | \qquad\mathrm{(D)}\ 288 |
− | \qquad\mathrm{(E)}\ | + | \qquad\mathrm{(E)}\ 576</math> |
https://artofproblemsolving.com/wiki/index.php/2021_Mock_AMC_8_Problems/Problem_2 | https://artofproblemsolving.com/wiki/index.php/2021_Mock_AMC_8_Problems/Problem_2 | ||
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==Problem 6== | ==Problem 6== | ||
− | Hexagon <math>ABCDEF</math> has side length <math>4</math>. What is the area of this hexagon rounded to the nearest tenth | + | Hexagon <math>ABCDEF</math> has side length <math>4</math>. What is the area of this hexagon rounded to the nearest tenth? |
<math>\textbf{(A) } 40.8 \qquad \textbf{(B) } 41.5 \qquad \textbf{(C) } 41.6 \qquad \textbf{(D) } 42.4 \qquad \textbf{(E) } 44.3</math> | <math>\textbf{(A) } 40.8 \qquad \textbf{(B) } 41.5 \qquad \textbf{(C) } 41.6 \qquad \textbf{(D) } 42.4 \qquad \textbf{(E) } 44.3</math> | ||
==Problem 7== | ==Problem 7== | ||
+ | The number <math>N</math> is a positive <math>3</math> digit integer. | ||
+ | |||
+ | •When <math>N</math> is divided by <math>80</math>, the remainder is <math>4</math> | ||
+ | |||
+ | •When <math>N</math> is divided by <math>3</math>, the remainder is <math>1</math> | ||
+ | |||
+ | •<math>N</math> is a perfect square. | ||
+ | |||
+ | What is the sum of the digits of <math>N</math>? | ||
+ | |||
+ | <math>\textbf{(A) }8\qquad\textbf{(B) }10\qquad\textbf{(C) }12\qquad\textbf{(D) }14\qquad \textbf{(E) }16</math> | ||
+ | |||
+ | ==Problem 8== | ||
+ | How many many zeros are at the right of the last nonzero digit of the number <math>1020!</math>? | ||
+ | |||
+ | <math>\textbf{(A) }204\qquad\textbf{(B) }244\qquad\textbf{(C) }252\qquad\textbf{(D) }253\qquad \textbf{(E) }254</math> | ||
+ | |||
+ | ==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 isosceles triangle <math>FCD</math>. 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> | ||
+ | |||
+ | ==Problem 10== | ||
+ | Maddie picks <math>2</math> numbers between <math>0</math> and <math>1</math>. The probability that both numbers are less than <math>\frac {2}{3}</math> can be expressed in the form <math>\frac {a}{b}</math> where <math>a</math> and <math>b</math> are relatively prime positive integers. What is <math>a</math> + <math>b</math>? | ||
+ | |||
+ | <math>\text{(A)}\ 5 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 18</math> | ||
+ | |||
+ | ==Problem 11== | ||
+ | Which of the following numbers is the smallest? | ||
+ | |||
+ | <math>3 \sqrt 2</math>, <math>\frac {21}{5}</math>, <math>\frac {5}{2} \sqrt 3</math>, <math>2 \sqrt 5</math>, <math>\frac {5}{3} \sqrt 7</math> | ||
+ | |||
+ | <math> \textbf{(A)}\ 3 \sqrt 2 \qquad\textbf{(B)}\ \frac {21}{5} \qquad\textbf{(C)}\ \frac {5}{2} \sqrt 3 \qquad\textbf{(D)}\ 2 \sqrt 5 \qquad\textbf{(E)}\ \frac {5}{3} \sqrt 7 </math> | ||
+ | |||
+ | ==Problem 12== | ||
+ | Isosceles <math>\triangle ABC</math> has <math>\angle ABC</math> = <math>80</math> degrees. What is the sum of all possible values for <math>\angle CAB</math>? | ||
+ | |||
+ | <math>\textbf{(A)} ~80 \qquad\textbf{(B)} ~100 \qquad\textbf{(C)} ~130 \qquad\textbf{(D)} ~140 \qquad\textbf{(E)} ~150</math> | ||
+ | |||
+ | ==Problem 13== | ||
+ | Real numbers <math>x</math> and <math>y</math> has these following conditions: | ||
+ | |||
+ | <math>x \cdot y</math> = <math>43</math> | ||
+ | |||
+ | <math>x + y = 37</math> | ||
+ | |||
+ | What is the product of the roots of the equation? |
Latest revision as of 17:33, 9 November 2023
Contents
Problem 1
What is the value of ?
https://artofproblemsolving.com/wiki/index.php/2021_Mock_AMC_8_Problems/Problem_1
Problem 2
Aaron has a rectangular yard measuring feet by
feet. How many
inch by
inch rectangular bricks can he fit in his yard?
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 choices for what they wear on day
of the camping trip. How many different arrangements of what they wear are possible on day
of the camping trip?
Problem 4
A rectangle with positive integer side lengths has area . In how many ways is this possible?
Problem 5
Fiona leaves her house to go to the airport. She drives for minutes at a constant rate of
miles per hour, then walks for
minutes at a constant rate of
miles per hour. She then goes on a train going 50 miles per hour for 12 minutes. How far has she traveled?
Problem 6
Hexagon has side length
. What is the area of this hexagon rounded to the nearest tenth?
Problem 7
The number is a positive
digit integer.
•When is divided by
, the remainder is
•When is divided by
, the remainder is
• is a perfect square.
What is the sum of the digits of ?
Problem 8
How many many zeros are at the right of the last nonzero digit of the number ?
Problem 9
Isosceles trapezoid has
. Point
is on
such that
is perpendicular to
and that
=
.
and
are extended to point
to make isosceles triangle
. Point
is
units away from the midpoint of
. What is the area of isosceles trapezoid
?
Problem 10
Maddie picks numbers between
and
. The probability that both numbers are less than
can be expressed in the form
where
and
are relatively prime positive integers. What is
+
?
Problem 11
Which of the following numbers is the smallest?
,
,
,
,
Problem 12
Isosceles has
=
degrees. What is the sum of all possible values for
?
Problem 13
Real numbers and
has these following conditions:
=
What is the product of the roots of the equation?