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 45 selected-response questions. The content areas covered by the first test are number and quantity; algebra; and discrete mathematics and calculus. Some of the topics covered by the number and quantity subarea are: the properties of exponents; the properties of rational and irrational numbers and the interactions between those sets of numbers; operations on matrices and how to use matrices in applications; and how complex numbers and operations on them are represented in the complex plane. Some of the topics covered by the algebra subarea are: algebraic expressions in equivalent forms; arithmetic operations on polynomials; equations and inequalities that describe relationships; and how to find the zero(s) of functions. The topics covered by the discrete mathematics and calculus subarea are: how to model and solve problems using vertex-edge graphs, trees, and networks; basic terminology and symbols of logic; how to show that a particular function is continuous; and the relationship between continuity and differentiability.

The second test consists of 45 selected-response questions. The content areas covered by the second test are functions, geometry, probability, and statistics. The topics covered by the functions subarea are: how functions and relations are used to model relationships between quantities; how periodic phenomena are modeled using trigonometric functions; and how to solve trigonometric, logarithmic, and exponential equations. The topics covered by the geometry subarea are: transformations in a plane; congruence and similarity in terms of transformations; theorems about circles; and how to apply geometric concepts in real-world situations. The topics covered by the probability and statistics subarea are: how to summarize, represent, and interpret data collected from measurements on two variables, either categorical or quantitative; how to create and interpret linear regression models; statistical processes and how to evaluate them; and how to make informed decisions using probabilities and expected values.

The examination must be completed within four hours. Test-takers will 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.

GACE Mathematics 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.

GACE Math Practice Questions