Study Guide

Field 242: Multi-Subject: Secondary Teachers
(Grade 7–Grade 12)
Part Two: Mathematics

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Sample Selected-Response Questions

The following reference material will be available to you during the test:

Formulas PDF document

Competency 0001
Number and Quantity

1. Grapes are 80% water by weight and raisins are 15% water by weight. If 100 pounds of grapes are dried to make raisins, which weight is closest to the weight of the raisins?

  1. 24 pounds
  2. 32 pounds
  3. 75 pounds
  4. 85 pounds
Correct Response: A. This question requires the examinee to use proportional relationships to solve a multistep ratio and percent problem. If grapes are 80% water by weight, then 20% of the weight is not water, so 100 pounds of grapes contain 20 pounds of non-water matter. These 20 pounds must make up the non-water matter in the raisins. Since raisins are 15% water by weight, the non-water matter is 85% of the weight, so 20 = 0.85 (total weight) and total weight of the raisins is 20 ÷ 0.85 or about 24 pounds.

Competency 0002
Algebra and Functions

2. Use the graph below to answer the question that follows.

The graph shows a function of the form y = f(x) = for constant c and x > 0. What is the inverse function of y = f(x) for x > 0?

  1. y =

  2. y = 2x2

  3. y =

  4. y =
Correct Response: C. This question requires the examinee to build new functions from existing functions. Since the graph contains the point (1, 2), substituting 1 for x and 2 for y calculates c = 2. Then y = . Inverse functions reverse the roles of x and y, so an equation for the inverse is x = . Squaring both sides, x2 = x2y = 4 → y = .

Competency 0003
Geometry and Statistics

3. Use the diagram below to answer the question that follows.

The fuselage of an airplane is modeled as a right circular cylinder with a diameter of 20 feet and a length of 200 feet. A platform is built into the cylinder to serve as a floor for cargo, as shown in the cross-section diagram. How much floor space, in square feet, is provided if the platform is positioned 4 feet above the bottom of the fuselage?

  1. 2400 ft2
  2. 3200 ft2
  3. 4800 ft2
  4. 9600 ft2
Correct Response: B. This question requires the examinee to analyze the shape of a two-dimensional cross section of a three-dimensional object. The floor in question is a rectangle of length 200 feet, whose width must be calculated. Using the diagram below, AB is the width of the floor and also a chord of the circular cross section whose diameter is 20 feet and radius is 10 feet. A radius drawn perpendicular to a chord bisects it, so (AD)2 + 62 = 102, AD = 8, and AB = 16. The area of the floor is 16 200 = 3200 square feet.