2022 amc10a

For more detailed information about AMC 10, please refer to this article.

The AMC 10 and AMC 12 are both question, minute, multiple-choice examinations in high school mathematics designed to promote the development and enhancement of problem-solving skills. The AMC 10 is for students in 10th grade and below and covers the high school curriculum up to 10th grade. Students in grade 10 or below and under The AMC 12 covers the entire high school curriculum, including trigonometry, advanced algebra, and advanced geometry, but excluding calculus. Students in grade 12 or below and under The only differences are the competition dates and that each version has a distinct set of questions, although the two examinations are designed to be equal in difficulty and distribution of topics. Schools can order one or both versions of the tests, so long as they pay the appropriate registration fee for each competition date and purchase the competition bundles for each date.

2022 amc10a

Scroll down and press Start to try the exam! Or, go to the printable PDF , answer key , or solutions. Used with permission of the Mathematical Association of America. We can simplify this expression as follows:. Assume he cycled at a constant speed throughout. We can set up a proportion to solve this problem:. What is the absolute value of the difference between the first and second numbers? The conditions from the problem give us the following relations:. We can do the following conversions to get the desired answer. We can rationalize this fraction to get. This value can equal any of the terms in the set, so we can case on what it equals.

Let 2022 amc10a guide you on your journey to success in the AMC 10! Consequently, the diligent completion of mock exams by students, considering both quality and quantity of the mock exams, can significantly enhance their familiarity and readiness, thereby ultimately contributing to their success during the actual AMC 10 examination. To prepare effectively, we recommend that students begin taking mock exams approximately six months prior to the actual exam date, 2022 amc10a, starting in April.

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Problems used with permission of the Mathematical Association of America. Scroll down to view solutions, print PDF solutions , view answer key , or:. We can simplify this expression as follows:. Assume he cycled at a constant speed throughout. We can set up a proportion to solve this problem:. What is the absolute value of the difference between the first and second numbers? The conditions from the problem give us the following relations:. We can do the following conversions to get the desired answer.

2022 amc10a

Isosceles trapezoid has parallel sides and with and There is a point in the plane such that and What is. Consider the reflection of over the perpendicular bisector of , creating two new isosceles trapezoids and. Under this reflection, , , , and. Since and are isosceles trapezoids, they are cyclic. Using Ptolemy's theorem on , we get that , so Then, using Ptolemy's theorem again on , we get that , so Thus, and ; dividing these two equations and taking the reciprocal yields. Extend and to a point as shown, and let. Then let and. Notice that by similar triangles.

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Competition managers must administer competitions during their valid competition window. In past exams, the first ten questions were generally straightforward, allowing most students to score points easily. Thus, E is the correct answer. Although we discourage a change in date because of potential confusion, a date change is permitted under certain circumstances. Only competition manager proctoring is allowed. Instead, it primarily assessed knowledge commonly encountered in previous years. The principal asked everyone the same three questions in this order. Furthermore, the last five questions, renowned for their challenging nature, exclusively featured three geometry problems, without any number theory or algebra questions. The comprehensive nature of the algebra module necessitated a deep understanding and proficiency in various algebraic skills, often requiring candidates to apply multiple concepts in combination. The exam also tested arithmetic sequences, quadratic functions, absolute value inequalities of functions, polynomial division, and more. Search form Search.

For more detailed information about AMC 10, please refer to this article. The AMC 10A placed significant emphasis on algebraic computation skills. The exam tested various knowledge points, including continued fraction calculations, exponent computations, averages, unit conversions, estimations, simplifications of algebraic expressions, arithmetic, and geometric sequences.

Additionally, question 13 tested the concept of similarity, question 18 involved geometric transformations, question 21 assessed solid geometry, and question 25 dealt with lattice point problems. Used with permission of the Mathematical Association of America. The ability to quickly identify breakthroughs in problem-solving is crucial for success in this exam. Schools can order one or both versions of the tests, so long as they pay the appropriate registration fee for each competition date and purchase the competition bundles for each date. Students in grade 12 or below and under Thus, D is the correct answer. Additionally, we highly recommend candidates to take both Exam 10A and 10B. If our testing sites are not conveniently located for you, please visit this link to find the nearest exam location, and register for exam on the MAA official website. Skip to main content. Completing these first 10 questions guarantees a score of Although we discourage a change in date because of potential confusion, a date change is permitted under certain circumstances. For the first question, the truth-tellers will respond yes, the liars will respond yes, and the alternaters who decided to lie first will say yes. However, the proportion of each module may vary between the two exams.