Study Guide

MoGEA Mathematics Subtest
Sample Questions

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Competency 0005
Understand numbers and algebra.

1. At a particular school, the ratio of students who arrive by bus, to students who walk, to students who are driven by a family member is 7:5:3. If 161 students arrive by bus, how many students attend this school?

  1. 230
  2. 276
  3. 310
  4. 345
Enter to expand or collapse answer.Answer expanded
Correct Response: D. Seven out of every group of 15 students (7 + 5 + 3) arrives by bus. Set up the proportion seven over fifteen equals one hundred and sixty one over x, where x represents the total number of students in the school. Then 7x = (15)(161) and x = 345.

Competency 0006
Understand measurement and geometry.

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

right angle triangle ABC has a lenth of 3 and a hypotenuse of 5, triangle GHJ has a hypotenuse of 10

Right triangle ABC is similar to right triangle GHJ, with AB = 5, BC = 3, and GH = 10. What is the area of triangle GHJ?

  1. 12 square units
  2. 15 square units
  3. 24 square units
  4. 30 square units
Enter to expand or collapse answer.Answer expanded
Correct Response: C. Use the Pythagorean theorem to find the length of side AC: AC2 + 32 = 52, so AC2 = 16 and AC = 4. Since the triangles are similar, their corresponding sides have the same ratio, with the scale factor of 5:10, or 1:2. Thus JH = 6 and GJ = 8. The area of triangle GHJ = (0.5)(6)(8) = 24 square units.

Competency 0007
Understand statistics and data analysis.

3. For a certain 10-day period, police in a particular city reported the following number of car thefts: 10, 7, 3, 9, 5, 9, 5, 9, 4, 9. Which of the following pairs of statistics has the same value for this set of statistics?

  1. the mode and the median
  2. the mean and the range
  3. the mean and the median
  4. the mode and the range
Enter to expand or collapse answer.Answer expanded
Correct Response: B. The mean is the average, 10 plus 7 plus 3 plus 9 plus 5 plus 9 plus 5 plus 9 plus 4 plus 9 over 10 equals 7. The median is found by ordering the data from least to greatest, finding the middle two values (since the number of data points is even), and averaging those, 7 plus 9 over 2 equals 8. The mode is the most common value, 9. The range is the difference between the largest and the smallest values, 10 – 3 = 7. The mean and the range are each equal to 7.