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Teacher Certification · 5163

Praxis Geometry Practice Test

Praxis Geometry (5163) practice covers geometric reasoning and quantitative problem solving involving lines, triangles, circles, polygons, and three-dimensional figures. The available questions ask you to interpret equations, apply geometric relationships, calculate measurements, and track how transformations change coordinates. These tasks connect symbolic representations with diagrams and numerical results.

Exam overview

Exam providerETS Praxis
Exam code5163
CategoryTeacher Certification

About the Praxis Geometry Exam

Geometry work often requires selecting a useful relationship before calculating. For triangles, that can mean using the Pythagorean theorem, classifying angles from side lengths, or applying proportionality when a segment is parallel to one side. Circle problems call for connecting radius, chord distance, tangent length, and area. Coordinate geometry links equations to intercepts, while transformations such as dilations require comparing corresponding coordinates to determine scale. Questions also involve polygon properties and solid measurement, including perimeter and cone volume. For teaching-related practice, explain why a relationship applies, identify the known and unknown quantities, and check whether the resulting measurement and units are reasonable. Sketching a labeled figure can help distinguish perpendicular distances from slanted segments and separate lengths from areas or volumes.

Sample Practice Questions

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

Question 1

A line has equation 3x + 2y = 12. What is its y-intercept?

  1. A(0, 6)
  2. B(0, 12)
  3. C(4, 0)
  4. D(6, 0)
Show answerCorrect answer: A

At the y-intercept, x = 0. Substituting gives 2y = 12, so y = 6; the y-intercept is (0, 6).

Question 2

A cone has radius 3 cm and height 8 cm. What is its volume?

  1. A24π cm³
  2. B48π cm³
  3. C72π cm³
  4. D216π cm³
Show answerCorrect answer: B

The volume of a cone is V = (1/3)πr²h. Substituting r = 3 and h = 8 gives V = (1/3)π(9)(8) = 24π cm³. Correction: this calculation equals 24π cm³, so option A is correct.

Question 3

A circle has radius 10 cm. A chord is 6 cm from the center, measured perpendicularly. What is the chord's length?

  1. A8 cm
  2. B12 cm
  3. C16 cm
  4. D20 cm
Show answerCorrect answer: C

A perpendicular from a circle's center to a chord bisects the chord. Each half forms a right triangle with hypotenuse 10 and one leg 6, so half the chord is √(10² − 6²) = 8 cm. The full chord is 16 cm.

Question 4

A triangle has side lengths 6, 8, and 10 units. Which classification describes the triangle by its angles?

  1. AAcute
  2. BRight
  3. CObtuse
  4. DEquilateral
Show answerCorrect answer: B

Since 6² + 8² = 36 + 64 = 100 = 10², the side lengths satisfy the converse of the Pythagorean theorem, so the triangle is right.

Question 5

A point is 13 units from the center of a circle. The circle's radius is 5 units. What is the length of a tangent segment from the point to the circle?

  1. A8 units
  2. B10 units
  3. C12 units
  4. D18 units
Show answerCorrect answer: C

The radius to a tangent point is perpendicular to the tangent, forming a right triangle. The tangent length is √(13² − 5²) = √144 = 12 units.

Question 6

A circle is inscribed in a square of side length 10 cm. What is the area inside the square but outside the circle?

  1. A100 − 10π cm²
  2. B100 − 25π cm²
  3. C100 − 50π cm²
  4. D100 − 100π cm²
Show answerCorrect answer: B

The inscribed circle has diameter 10 cm, so its radius is 5 cm and its area is 25π cm². The square area is 10² = 100 cm², so the region outside the circle but inside the square has area 100 − 25π cm².

Question 7

A dilation centered at the origin maps point (−2, 3) to (−6, 9). What is the scale factor?

  1. A1/3
  2. B2
  3. C3
  4. D6
Show answerCorrect answer: C

A dilation centered at the origin multiplies both coordinates by the scale factor. Since −2 becomes −6 and 3 becomes 9, each coordinate is multiplied by 3.

How to use this practice test

Access the free practice bank for a session of up to 20 randomly selected questions from the 50 available. Work through each item, then use the displayed results to identify which geometric relationships or calculations need more attention. The questions sample the bank’s subject vocabulary and are useful for targeted review.

Preparation tips

  • For line equations, rewrite them in slope-intercept form and identify the y-intercept from the constant term.
  • Draw and label circle diagrams; use a perpendicular radius-to-chord segment to form a right triangle before finding chord length.
  • For similar-triangle problems, mark corresponding sides and set up proportions before solving for an unknown segment.
  • Check triangle side relationships with the Pythagorean theorem, and distinguish a right triangle from acute or obtuse cases.
  • Keep units and dimensions explicit: perimeter uses linear units, area uses square units, and volume uses cubic units.
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