Geometry Practice Questions

Geometry questions are very common on high school exit exams, some nursing entrance exams, and college entrance exams.  Topics vary, but most of the following are covered:

– identifying solid figures
– solving problems with solid and plane figures
– solving problems using Pythagorean principles
– solve problems using scale drawings
– calculating area, circumference, volume and perimeter
– solve problems using geometric transformations

 

 

 

 

 

 

 

 

1. Which of the above points represents the origin?

1. A
2. B
3. C
4. D

 

 

 

 

 

 

 

 

 

 

2. What is measurement of the indicated angle?

1. 45^o
2. 90^o
3. 60^o
4. 30^o

 

 

 

 

 

 

 

 

 

 

3. What is perimeter of the above shape?

1. 12 cm
2. 16 cm
3. 6 cm
4. 20 cm

 

 

 

 

 

 

 

 

 

 

 

4. What is (area of large circle) – (area of small circle) in the figure above?

1. 8 π cm²
2. 10 π cm²
3. 12 π cm²
4. 16 π cm²

 

 

 

 

 

 

 

 

 

 

 

5. What is the length of each side of the indicated square above?

1. 10
2. 15
3. 20
4. 5

 

 

 

 

 

 

 

 

6. Which of the lines above represents the equation 2y – x = 4?

1. A
2. B
3. C
4. D

 

 

 

 

 

 

 

7. What is the measurement of the indicated angle?

1. 45^o
2. 90^o
3. 60^o
4. 50^o

Answer Key

 

1. A
Point A represents the origin.

2. B
The diagonals of a square intersect perpendicularly with each other so each angle measures 90^o
x =90^o

3. B
The square with 2 cm side common to the rectangle apart from 4 cm side. So the perimeter = 2+2+2+4+2+4 = 16 cm

4. C
Given: Two circles with smaller circle (diameter given) exactly half the larger circle (radius given).
Difference = (Area of large circle) – (Area of small large circle)
π 4² – π 2²
= 16π  – 4π
Difference = 12π cm²

5. B
Pythagorean Theorem:

(Hypotenuse)² = (Perpendicular)²  + (Base)²
h² = a²  + b²

a² = 81, b² = 144
h² = a²  + b²
h² = 81+144
h² = 225
h= 15

6. A
Line A represents the equation 2y – x = 4.

7. C
The sum of angles around a point is 360^o
d+300 = 360^o
d = 60^o

 

 Geometry Tutorials

Euclidean geometry  (Wikipedia)
High School Geometry Tutorials (About.com)
Teaching High School Geometry – An excellent article about teaching geometry from HomeSchoolMath