Lcz's Mock AMC 10A Problems

Instructions

1. All rules of a regular AMC 10 apply.

2. Please submit your answers in a DM to me (Lcz).

3. Don't cheat.

Here's the problems!

Sample Problems lol

Given that $729=1011011001_2$ , $2021^2$ can be expressed as $2^{a_1}+2^{a_2}+2^{a_3} . . . +2^{a_k}$ , where the $a_i$ are an increasing sequence of positive integers. Find $k$ .

$\textbf{(A)}\ 10 \qquad\textbf{(B)}\ 11 \qquad\textbf{(C)}\ 12 \qquad\textbf{(D)}\ 13 \qquad\textbf{(E)}\ 14$

Problem 1

Find the value of $2^{0+2+1}+2+0(2+(1))+20(21)$ .

$\textbf{(A)}\ 8 \qquad\textbf{(B)}\ 426 \qquad\textbf{(C)}\ 428 \qquad\textbf{(D)}\ 430 \qquad\textbf{(E)}\ 432$

Problem 2

If $|x-2|=0$ , and $|y-3|=1$ , find the sum of all possible values of $|xy|$ .

$\textbf{(A)}\ 0 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 8 \qquad\textbf{(D)}\ 12 \qquad\textbf{(E)}\ 16$

Problem 3

What is $1*2+2*3+3*4+4*5+5*6+6*7+7*8$ ?

$\textbf{(A)}\ 84 \qquad\textbf{(B)}\ 120 \qquad\textbf{(C)}\ 138 \qquad\textbf{(D)}\ 150 \qquad\textbf{(E)}\ 168$

Problem 4

Find the sum of all ordered pairs of positive integer $x$ and $y$ such that

(1) $|x-y| \geq 0$

(2) $x,y \leq 3$

(3) $xy \leq 8$

$\textbf{(A)}\ 24 \qquad\textbf{(B)}\ 27 \qquad\textbf{(C)}\ 30 \qquad\textbf{(D)}\ 36 \qquad\textbf{(E)}\ 39$

Problem 5

Find $x$ if $x^3-3x^2+3x-1=x^3-2x^2+15x+35$ .

$\textbf{(A)}\ -6 \qquad\textbf{(B)}\ -4 \qquad\textbf{(C)}\ 0 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 6$

Problem 6

Given that $5101$ is prime, find the number of factors of $104060401+20402+1$ .

$\textbf{(A)}\ 2 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 6 \qquad\textbf{(E)}\ 8$

Problem 7

Find $\sum_{i,j,k=1}^{7} ijk=1*1*1+1*1*2+1*1*3 . . . 1*1*7+1*2*1+1*2*2+1*2*3 . . . 2*1*1+2*1*2 . . .7*7*7 \pmod{5}$

$\textbf{(A)}\ 0 \qquad\textbf{(B)}\ 1 \qquad\textbf{(C)}\ 2 \qquad\textbf{(D)}\ 3 \qquad\textbf{(E)}\ 4$

Problem 8

Problem 9

Problem 10

Jack and Jill play a (bad) game on a number line which contains the integers. Jack starts at $-1$ , and Jill starts at $18$ . Every turn, the judge flip a standard six sided die. If the number rolled is a square number, Jack moves to the right $10$ units. Otherwise, Jill moves to the left $5$ units. Find the probability for which Jack and Jill pass each other for the first time in $3$ moves.

$\textbf{(A)}\ 4/27 \qquad\textbf{(B)}\ 2/9 \qquad\textbf{(C)}\ 1/3 \qquad\textbf{(D)}\ 4/9 \qquad\textbf{(E)}\ 2/3$

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Lcz's Mock AMC 10A Problems

Contents

Instructions

Sample Problems lol

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25