Middle school students are often prepared for math competitions with a focus on algebra, especially number theory. However, geometry might come as a surprise in the second part of the exam paper, if students don’t practice it as much as algebra. There are several geometry exercises present in math competitions, so check them below so you are not taken by surprise.
Types of geometry exercises in math competitions
By looking at the exam papers published by the American Mathematics Competitions, you can get familiar with the type of exercises that are introduced in math competitions. Keep in mind the fact that AMC exam papers start with easy exercises, then the level of difficulty increases with each exercise. AMC 8, for example, is dedicated to middle school students and by looking at the last years, the most common types of geometry exercises were:
About triangles
Mathematics surrounding triangles is the most common in olympiads or math competitions. During an examination, students are allowed to use scratch or graph papers, rulers, compasses, and protractors, so make sure you benefit from these tools. In 2019, the AMC 8 examiners introduced the following geometry problem:
There are three ways in which this problem can be solved. But, first, try to solve the problem on your own, then check your answers.
About measurements
In 2020, middle school students taking the AMC 8 competition had to solve hybrid geometry problems, just like the ones below:
FInd out the correct answer, then check your answer here.
Do you know how to solve it? Problem-solvers are giving us three ways in which we can reach the ultimate answer.
About logical thinking
Since we’re at the front steps of the 2023 AMC 8 for middle school, it helps to take a look back at the exercises published for the 2022 math competition. Within the last questions of the AMC 8 in 2022, students have to solve the following question:
Check out the solutions here.
A or is placed in each of the nine squares in a -by- grid. Shown below is a sample configuration with three s in a line. How many configurations will have three s in a line and three s in a line?
Check out the solutions here.
Since AMC is about increasing the level of difficulty with each question, the next to last problem in the 2022 math competition was the following:
Are you ready for your next math competition?
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