GACE: Mathematics

The Mathematics assessment, offered as part of the Georgia Assessments for the Certification of Educators, is divided into two tests.

The first test consists of 60 selected-response questions (80% of the test score) and 2 constructed-response assignments (20% of the test score). The content areas covered by the first test are number concepts and operations, algebra, precalculus, and calculus. The topics covered by the number concepts and operations subarea are: number operations; the basic principles of number theory; and real and complex number systems. The topics covered by the algebra subarea are: basic algebraic operations and properties of functions and relations; linear equations and linear systems; and the properties of quadratic functions. The topics covered by the precalculus and calculus subarea are: nonlinear functions; trigonometric functions and identities; and calculus.

The second test consists of 60 selected-response questions (80% of the test score) and 2 constructed-response questions (20% of the test score). The content areas covered by the second test are geometry, measurement, data analysis, probability, and mathematical processes and perspectives. The topics covered by the geometry and measurement subarea are: measurement; Euclidean geometry; and coordinate and transformational geometry. The topics covered by the data analysis and probability subarea are: the methods of collecting, organizing, and describing data; theory and applications of probability; and analysis and interpretation of data when making statistical inferences. The topics covered by the mathematical processes and perspectives subarea are: the representations used to communicate mathematical ideas and concepts; and mathematical reasoning, the construction of mathematical arguments, and problem-solving strategies.

The examination must be completed within four hours. The total test score is placed on a scale of 100 to 300, with 220 as the lowest passing score. Scores are based on the number of selected-response questions answered correctly and the scores assigned by judges to the constructed responses. Test-takers will also receive performance indices indicating their success in each subarea of the examination. Scores will be available approximately a month after the date of the examination; unofficial results are posted on the internet, and an official score report is mailed to the test-taker, the Professional Standards Commission, and the institution specified by the test-taker during registration.

Practice Questions

1. In the set of numbers {14, 5, 12, 9, 12, 15, 10}, a is the mean, b is the median, c is the mode, and d is the range. Given this scenario, which of the following statements is true?

A: a > b > c > d
B: d > a > b = c
C: a = c > b > d
D: b = c > a > d

2. A rectangular prism is five inches long, six inches wide, and seven inches long. Which of the following cannot be the surface area in square inches of two sides of the prism?

A: 90
B: 77
C: 70
D: 60

3. If the integer x is a multiple of 12 but not a multiple of 9, which of the following expressions cannot be an integer?

A: x/12
B: x/3
C: x/4
D: x/36

4. Gerald has ten shirts. He needs to pack four of them for a business trip. How many different combinations of shirts could Gerald pack?

A: 150
B: 210
C: 230
D: 240

5. If x - y + z = 15 and x + y = 24, solve the following: 4x + 2z = ?

A: 24
B: 38
C: 78
D: 84

Answer Key

1. D. The median is equal to the mode, so only B or D could be correct. The range is smaller than both the median and the mode, which eliminates B.
2. A. The box will have two sides that are 30 square inches, two sides that are 35 square inches, and 2 sides that are 42 square inches.
3. D. The best way to solve this sort of problem is to plug in values for k, as for instance 12 and 24.
4. B. To solve this factorial problem, you must set up the equation: .
5. C. By adding the two equations together, you can derive: 2x + z = 39. Twice this is: 4x + 2z = 78.