Difference between revisions of "Lcz's Mock AMC 10A Problems"

Revision as of 13:50, 30 June 2020

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!

Problem 1

Find the value of $2^{0+1+2}+2+0(1+(2))+20(12)$ .

$\textbf{(A)}\ 8 \qquad\textbf{(B)}\ 248 \qquad\textbf{(C)}\ 250 \qquad\textbf{(D)}\ 252 \qquad\textbf{(E)}\ 254$

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

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.

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

@@ Line 23: / Line 23: @@
 ==Problem 3==
-Jack and Jill play a (bad) game on a number line which contains the integers. Jack starts at <math>-2</math>, and Jill starts at <math>18</math>. Every turn, the judge flip a standard six sided die. If the number rolled is a square number, Jack moves to the right <math>10</math> units. Otherwise, Jill moves to the left <math>5</math> units. What is the probability that it takes exactly <math>3</math> moves for Jack and Jill to be on the same unit?
+What is <math>1*2+2*3+3*4+4*5+5*6+6*7+7*8</math>?
- oops gotta go eat lol
-<math>\textbf{(A)}\  \qquad\textbf{(B)}\ 248 \qquad\textbf{(C)}\ 250 \qquad\textbf{(D)}\ 252 \qquad\textbf{(E)}\ 254</math>
+<math>\textbf{(A)}\ 84 \qquad\textbf{(B)}\ 120 \qquad\textbf{(C)}\ 138 \qquad\textbf{(D)}\ 150 \qquad\textbf{(E)}\ 168</math>
+==Problem 4==
+Jack and Jill play a (bad) game on a number line which contains the integers. Jack starts at <math>-1</math>, and Jill starts at <math>18</math>. Every turn, the judge flip a standard six sided die. If the number rolled is a square number, Jack moves to the right <math>10</math> units. Otherwise, Jill moves to the left <math>5</math> units. Find the probability for which Jack and Jill pass each other for the first time in <math>3</math> moves.
+<math>\textbf{(A)}\ 4/27 \qquad\textbf{(B)}\ 2/9 \qquad\textbf{(C)}\ 1/3 \qquad\textbf{(D)}\ 4/9 \qquad\textbf{(E)}\ 2/3</math>

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