IM Unit 2 End of Module Review

IM Unit 2 End of Module Review

by Jaworski Sartin

Multiple Choice

Consider the inequality

$$\frac{x+3}{6}>\frac{x}{4}+1$$  . Which value of x is a solution to the inequality?

• $$x=-10$$  

• $$x=-6$$  

• $$x=6$$  

• $$x=10$$  

​Solution

​The correct answer is A.

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​Students who choose B have found the value of x that makes the expressions on the two sides equal.

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Students who choose C may also have solved the related equation and missed a negative sign.

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Students who choose D may have switched the direction of the inequality when substituting 10 for x, or when testing points after solving the related equation.

Multiple Select

The gardening club at school is growing vegetables. The club has 300 square feet of planting beds. Cucumber plants require 6 square feet of growing space, and tomato plants require 4 square feet of growing space. The students want to plant some of each type of plant and have at least 60 plants.

Select all the equations or inequalities that could describe this situation. Let c represent the number of cucumber plants and t represent the number of tomato plants.

• $$c>0$$  

• $$t<0$$  

• $$c+t=300$$  

• $$c+t\ge60$$  

• $$6c+4t\le300$$  

​Solution

​The correct answers are A, D, and E.

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​Students selecting B may not realize that t < 0 indicates that the number of tomato plants is negative, which is impossible in the scenario.

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Students selecting C may not have recognized that c and t represent the number of plants.

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Students selecting F do not recognize that the amount of available space is a constraint for the situation, so total space needed must be less than or equal to space available. It is also possible that incorrect answers are due to consistent misreading of the inequality sign.

Multiple Choice

Which graph represents the solution to this system of inequalities?

$$3x-5y\le15$$  

$$y>-\frac{2}{3}x+1$$  

​Solution

​The correct answer is B.

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​All four answer choices correctly display the graphs of the related equations and mark the boundary lines properly. The work here is to identify which side of each line contains the solutions to the related inequality.

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Students choosing A have correctly identified the solution region for the first inequality, but not the second.

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Students choosing C are correct about the second inequality, but not the first.

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Students choosing D have incorrectly identified both solution regions.

Open Ended

​Solution

Sample Response: (25, 0); (25, 2)

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​Students should select any point in the region where the two shaded planes intersect.