AMC 8
The AMC 8 is a 25-question, 40-minute, multiple-choice exam regarded as a standard in middle-school extracurricular mathematics. The AMC 8 is designed to promote understanding, interest, and development of problem-solving skills. The AMC 8 covers concepts in mathematics that are commonly taught at the junior high level, but offers a problem-solving experience not found in the standard classroom.
Link: amc.maa.org/e-exams/e4-amc08/amc8.shtml
AP Computer Science
The Advanced Placement Program offers a course and exam in introductory computer science. The course emphasizes object-oriented programming methodology with a concentration on problem solving and algorithm development, and is meant to be the equivalent of a first-semester college-level course in computer science.
Link : http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/4483.html
Continental Math League
Continental Mathematics League is a problem solving competition consisting of 3 meets for 2nd - 3rd grades throughout the year and 5 meets for 4th to 9th graders. Each meet has 6 questions and students work independently within the prescribed time period. Students will be participating with other students on the same grade level from schools all over the United States.
Link: http://www.continentalmathematicsleague.com/
Junior High Math League
The Junior High Math League is for middle school students. The students participate as teams and each team can have a maximum of six students with no more than four eighth graders. The meet topics are based on the MathCounts topics.The teams in each division come together for five meets each season.
Link: http://www.usfamily.net/web/mathleague/
Mathcounts
The MathCounts Competition is a national middle school coaching and competitive mathematics program that promotes mathematics achievement. Outstanding students will advance to the next stage. Each and every round of MathCounts is always exciting and fun. The best contestants will be recognized.
Link: https://mathcounts.org/page.aspx?pid=1828
MOEMS
The MOEMS consist of five monthly contests given from November to March. Teams of up to 35 students may be registered in either Division E (4th to 6th grade) or Division M (6th to 8th grade). Teams may not be split between divisions. Each contest, taken at the participating school, consists of five problems which each student completes alone within a certain time limit.
Link: www.moems.org/
USA Mathematical Talent Search
USAMTS is a competition designed to identify and promote talented math students in middle and high school. Problems span a variety of difficulties and require participants to justify their answers. Each round allows at least a full month for students to work on problems. Top-scoring participants receive prizes, recognition, and a free entrance to the American Invitational Mathematical Examination (AIME).
Link: www.usamts.org/