Difference between revisions of "Lcz's Mock AMC 10A Problems"
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Revision as of 18:14, 3 July 2020
- 1 Instructions
- 2 Sample Problems lol
- 3 Problem 1
- 4 Problem 2
- 5 Problem 3
- 6 Problem 4
- 7 Problem 5
- 8 Problem 6
- 9 Problem 7
- 10 Problem 8
- 11 Problem 9
- 12 Problem 10
- 13 Problem 11
- 14 Problem 12
- 15 Problem 13
- 16 Problem 14
- 17 Problem 15
- 18 Problem 16
- 19 Problem 17
- 20 Problem 18
- 21 Problem 19
- 22 Problem 20
- 23 Problem 21
- 24 Problem 22
- 25 Problem 23
- 26 Problem 24
- 27 Problem 25
- 28 Rough ordering of problems...
1. All rules of a regular AMC 10 apply.
2. Please submit your answers in a DM to either Superagh or Lcz
3. Don't cheat.
Here's the problems!
Sample Problems lol
Given that , can be expressed as , where the are an increasing sequence of positive integers. Find .
NOTE THAT THESE PROBLEMS ARE DEFINETELY NOT ORDERED BY DIFFICULTY YET LMAO
Find the value of .
If , and , find the sum of all possible values of .
What is ?
Find the sum of all ordered pairs of positive integer and such that
Find if .
Given that is prime, find the number of factors of .
Evaluate , where is the sum of all products when .
Given that , evaluate
Find the number of solutions to .
Jack and Jill play a (bad) game on a number line which contains the integers. Jack starts at , and Jill starts at . Every turn, the judge flip a standard six sided die. If the number rolled is a square number, Jack moves to the right units. Otherwise, Jill moves to the left units. Find the probability for which Jack and Jill pass each other for the first time in moves.
A circle has points , , , , , on the circumference, in that order. , , and meet at the point . intersects at . Given that is similar to , , , . Find .
WE ARE DEFINETELY GOING TO THROW THIS PROBLEM AWAY
How many ways can the number be written as a sum of at least 2 consecutive integers?
What is the maximum amount of acute angles in a -gon?
Sally is going home from school. First, she visits the river to the east of her school, and must take that water to the farm. The school and the farm are on the same side of the river, which runs north to south, but the school is 5 miles from it and the farm is 2 miles from the river. The school and the farm are 5 miles apart. After visiting the farm, she must visit another river that runs east to west. The farm is on the same side of the river as her house, and the farm is 3 miles from the river and her home is 9 miles. She must go to the river to get water then go back home. Her home and the farm are 10 miles apart. What is the shortest distance Sally has to go?