**Announcement!**

*As of September 2019, the content of the Praxis Core mathematics test has changed. Learn more here.*

On the Math test in Praxis Core, you’ll be asked a handful of geometry questions. While the subset of geometry questions is not the largest category on the exam, there will still be a significant number of geometry questions on test day. You can expect geometry answers to be about 15% of your final Core Math score.

So obviously you’re going to want to do well on the types of geometry questions seen in Praxis Core math. Geometry problems on this exam fall into three broad categories: coordinate plane geometry, geometry with two dimensional shapes (squares, cubes, triangles, circles, etc..), and geometry with three dimensional shapes (cylinders, cones, angular blocks, and so on). Below, you can test your Praxis Core Math geometry skills with one practice question from each category. An answer key is available at the very bottom of this post.

## Practice coordinate plane geometry question

*Note: *I almost considered including this question type in the practice set for numbers and quantity. This is because coordinate plane geometry on the Praxis Core always boils down to addition or subtraction. However, doing these problems efficiently and correctly does require a keen sense of geometric space. So I’m going to count these as true geometry questions.

If rhombus *ABCD *in the *xy*-plane is shifted 3 units down and 5 units to the left, what would be the coordinates of point *D* after the shift?

A) (-3, 10)

B) (-3, 0)

C) (10, 3)

D) (0, -3)

E) (5, -3)

## Practice two-dimensional geometry question

The rectangle above is four centimeters high and 8 centimeters wide. What is the approximate length of each diagonal (diagonals *AC* and *BD*)?

A) 7

B) 3

C) 9

D) 10

E) 5

## Practice three-dimensional geometry question

The figure above shows a three dimensional object comprised of a cylinder with a radius of 4 feet and a height of 5 feet, topped by a right cylinder cone with a radius of 4 feet and a height of 3 feet. What is the approximate total volume of this object? (The volume of a right cylinder cone with a base radius *r* and height *h* is 1/3 pi(*r^2*)*h*.)

A) 200 cubic feet

B) 300 cubic feet

C) 335 cubic feet

D) 415 cubic feet

E) 610 cubic feet

** **

## Answer Key

- D
- C
- B

## Notes about the answers:

The answer to question 1 is a simple matter of correctly subtracting 3 from the *y* coordinate, and 5 from the *x* coordinate. Answer two requires you to know and correctly apply the Pythagorean theorem, which states that in a right triangle where *a* and *b* are the lengths of the sides of the right angle, and *c* is the length of the side opposite the right angle, *a*^2 + *b*^2 = *c*^2. The answer to the third question gives you the formula for the volume of a right circular cone, but it also requires you to know and use the formula for cylinder volume: *V* =pi(*r*^2)*h*.

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