The solving equtions test is divided up into 3 sections. These sections have problems over the 3 topics covered in this unit.
Problems 1 and 2 ask students to demonstrate how to solve an algebraic equation. The students struggle with problem 2. Most mistakes are made when multiplying (2x+1)(2x-1) the students also drop negatives. Some students will find common denominator while other students will just multiply both sides by the common denominator so they can get rid of the fractions.
The next section tests students over inequalities. Both inequalities require factoring. The second problem includes some of the endpoints. This helps me verify that the students understand when points are included in the solution and when they are not included.
The last 4 problems are trigonometric equations. The first 3 are just using algebra techniques to solve. I will have some student divide by tan x on question 6 which will cause them to lose some solutions. Question 7 will mess students up that are not good at factoring. I try to make the factor portion of the test not have numbers with a large number of factors since I am determining whether they see the underlying structure of the problem.
Question 7, gives the students a contextual problem. This problem also requires students to understand how to work with trigonometric function with a multiply angle in this case 120(pi)t.