25 - AMC 12 Problems and Solutions (Free)
You can access 25 AMC 12 Practice Questions from MyExamCloud Exam Simulator AMC 12A 2015 Practice ExamAMC 12 Practice Exam 1
for American Mathematics Competition
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The American Mathematics Competition (AMC) is a series of exams offered to High School and Middle School Students. These exams include;
Students across the United States of America and Canada in grades 10 and below usually take part in the first AMC 10. In addition, all USA embassy and foreign students can also participate. This is the new American Mathematics Competition contest for middle and high school students. The new contest enhances the two currently offered competitions. This is the American High School Mathematics exam which is called the AMC 12 and the American Junior High School Mathematics Exam which is known as AMC 8. The students who are in grade 8 and lower can participate in the AMC 12 whereas all the middle and high school students can take the AMC 12.
The remaining exams are by invitation. The AIME is a 15 question exam which takes 3 hours in which each answer is an integer number from 0-999. This exam is usually much more difficult. The difference between the AIME and the AMC 10 and AMC 12 is that all the problems in the latter can be solved by pre-calculus methods.
These exams provide the students with a great chance to compare their skills in mathematics competitively with other students nationwide. The students who perform exceptionally well in this tests are usually invited to take part in the state ARML team. This series of exams is also used in the picking of the team that represents the United States of America in the International Olympiads.
The American Mathematics Competition exams are sponsored by a number of organizations which include the National Council of Teachers of mathematics and the Mathematical Association of America.
The AMC 12 is usually a 25-question exam which takes up to 75 minutes to complete. It is a multiple choice exam containing problems which can be understood and solved with pre-calculus concepts. In the recent years the exams used to consist of 30 questions with a time limit of 90 minutes but that was changed. The AMC 12 and the AMC 10 normally take place on the same day. The rules are clear and a student is not allowed to take more than one of them.
The AMC 12 has 25-question, 75-minute, multiple choice examination in high school mathematics designed to promote the development and enhancement of problem-solving skills.
The students who qualify for the AIME invitations are the ones who are lucky to score at least 100 on the AMC 12. In addition, the top 1% of the AMC 10 participants qualify for the AIME.
Improve problem-solving skills. Students with a passion for problem-solving who are in grade 12 or below and under 19.5 years of age on the day of the contest can take the AMC 12
The following practice question is taken from MyExamCloud AMC 12 Study Plan.
Goldbach's conjecture states that every even integer greater than 2 can be written as the sum of two prime numbers (for example, 2016=13+2003 ). So far, no one has been able to prove that the conjecture is true, and no one has found a counterexample to show that the conjecture is false. What would a counterexample consist of?
Choice A: an odd integer greater than 2 that can be written as the sum of two prime numbers
Choice B: an odd integer greater than 2 that cannot be written as the sum of two prime numbers
Choice C: an even integer greater than 2 that can be written as the sum of two numbers that are not prime
Choice D: an even integer greater than 2 that can be written as the sum of two prime numbers
Choice E: an even integer greater than 2 that cannot be written as the sum of two prime numbers
Answer and Explanation:
Choice E is correct
A counterexample would be to find an even integer that would prove Goldbach's Conjecture false. Thus, the counterexample consist of an even integer greater than 2 that cannot be written as the sum of two prime numbers (Answer E)
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