The majority of the placement test should consist of multiple choice problems. These problems give students different mathematical operations to perform in a quick manner. Students are able to check that their calculations match one of the given solutions. Multiple choice problems allow you to include samples from entire curriculums so any trouble areas students are experiencing stand out. Arrange the problems from intermediate to advanced so that students will work through the easier operations first. Also, require students to show their work so you can ensure that they are using the proper mathematical procedure.
Students must demonstrate their ability to apply their knowledge of mathematics to word problems. Word problems translate mathematical concepts into real-world situations or imagined scenarios. Students are required to interpret the word problems conceptually in order to solve them. This gives you an idea of each student's proficiency in applied mathematics, which should be considered when placing them in the correct math course. Have students show their work so you can see that they understand how to decipher mathematical concepts from word problems.
High school math placement exams should feature numerous algebra questions of varying skill level. Include basic one-variable equations and inequalities and problems dealing with exponents. Further in the test, include more advanced algebra problems featuring two-variable equations, radicals and graphing problems. Also include basic precalculus problems such as problems requiring the use of imaginary numbers, synthetic division and complex equations. This allows students to demonstrate their abilities to solve basic problems taken from the math courses in which they will be placed.
Placement tests aren't always the best reflection of students' knowledge in mathematics. At the beginning of the semester, carefully consider each student's understanding of the material, and evaluate their ability to learn the new concepts of the course. Do so by studying their methods of problem-solving on quizzes and homework assignments. Class participation activities, such as board problems, is another way. If you notice that a student is struggling at the beginning of the semester, it's important to place him in a less-advanced math course before he gets behind in the curriculum.