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Georgia GACE Mathematics (6-12) Assessment Practice Test

The Georgia GACE Mathematics (6-12) Assessment practice page focuses on secondary-level mathematics, including algebraic expressions and functions, coordinate geometry, trigonometry, matrices, probability, and statistics. Practice problems call for accurate computation and mathematical reasoning, from finding a function’s inverse or a line’s slope to interpreting a data set or calculating a probability.

Exam overview

Exam providerGeorgia Professional Standards Commission
Exam code711
CategoryTeacher Certification

About the Georgia GACE Mathematics (6-12) Assessment Exam

Working through these problems exercises several connected skills: manipulating polynomial and algebraic expressions, solving quadratic equations, and interpreting features of functions such as symmetry and inverses. Geometry and trigonometry tasks involve applying circle formulas, angle measures, and right-triangle ratios. Matrix problems require organizing entries and computing determinants, while probability questions rely on counting possible outcomes and identifying events. Statistics practice includes finding measures such as the median and interpreting numerical data. For teaching mathematics in grades 6–12, these skills support clear explanations of procedures, checking whether a result is reasonable, and connecting symbolic methods with graphs, diagrams, and real-world quantities.

Sample Practice Questions

Review a selection from this exam's published US Practice Tests practice bank.

Question 1

For the function f(x) = (x − 3)² + 2, what is the axis of symmetry of its graph?

  1. Ax = −3
  2. Bx = 2
  3. Cx = 3
  4. Dy = 2
Show answerCorrect answer: C

The function is in vertex form, f(x) = (x − h)² + k, whose axis of symmetry is x = h. Here h = 3, so the axis is x = 3.

Question 2

What is the inverse of the function f(x) = 3x − 8?

  1. Af⁻¹(x) = (x − 8)/3
  2. Bf⁻¹(x) = (x + 8)/3
  3. Cf⁻¹(x) = 3x + 8
  4. Df⁻¹(x) = (8 − x)/3
Show answerCorrect answer: B

Write y = 3x − 8, swap x and y to get x = 3y − 8, then solve for y: y = (x + 8)/3.

Question 3

What is the slope of a line perpendicular to the line y = (2/3)x − 5?

  1. A−3/2
  2. B−2/3
  3. C2/3
  4. D3/2
Show answerCorrect answer: A

The given line has slope 2/3. A perpendicular line has slope equal to the negative reciprocal, −3/2.

Question 4

A circle has radius 6 units. What is the area of a 60° sector of the circle?

  1. A3π square units
  2. B6π square units
  3. C12π square units
  4. D36π square units
Show answerCorrect answer: B

A 60° sector is 60/360 = 1/6 of the circle. The full area is π(6)² = 36π, so the sector area is (1/6)(36π) = 6π square units.

Question 5

The data values 3, 5, 7, and 9 have what median?

  1. A5
  2. B6
  3. C7
  4. D24
Show answerCorrect answer: B

With four values in order, the median is the mean of the two middle values: (5 + 7)/2 = 6.

Question 6

A right triangle has an acute angle θ with adjacent side 8 and hypotenuse 17. What is cos θ?

  1. A8/17
  2. B15/17
  3. C8/15
  4. D17/8
Show answerCorrect answer: A

Cosine is the ratio of the adjacent side to the hypotenuse. Therefore, cos θ = 8/17.

Question 7

What are the solutions to x² − 5x + 6 = 0?

  1. Ax = 1 and x = 6
  2. Bx = −2 and x = −3
  3. Cx = 2 and x = 3
  4. Dx = −1 and x = −6
Show answerCorrect answer: C

Factor the quadratic as (x − 2)(x − 3) = 0. Setting each factor equal to zero gives x = 2 or x = 3.

How to use this practice test

Access is free. A practice session presents up to 20 random questions from the available bank of 50, covering the mathematical skills represented in its items. After the session, review the results to identify which problem types merit more work—for example, function transformations, trigonometric ratios, matrix calculations, or probability.

Preparation tips

  • For quadratic functions, connect vertex form to the vertex and axis of symmetry, then verify by completing the square or comparing graph features.
  • Practice rewriting linear functions as inverses and checking your result by composing the original and inverse functions.
  • Keep geometry formulas and units visible in your work; distinguish a sector’s fraction of a circle from the full-circle area.
  • For right-triangle trigonometry, label opposite, adjacent, and hypotenuse relative to the stated angle before selecting a ratio.
  • Use organized outcome lists or tables for two-event probability problems, and check that the counted outcomes match the sample space.
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