Study Guide
MoGEA Mathematics Subtest
Sample Questions
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?
- 230
- 276
- 310
- 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 , 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 triangle ABC is similar to right triangle GHJ, with AB = 5, BC = 3, and GH = 10. What is the area of triangle GHJ?
- 12 square units
- 15 square units
- 24 square units
- 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?
- the mode and the median
- the mean and the range
- the mean and the median
- the mode and the range
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B. The mean is the average, . 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, . 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.