##### 1. Given the triangle shown in the figure, what is the length of the side *A*?

- C/2
- A/2
- (A+C)/2
- 2A
- 2C

##### 2. A circle is inscribed within a square, as shown. What is the difference between the area of the square and that of the circle, where *r* is the radius of the circle?

- 2πr
^{2} - 4/3 πr
^{3} - r
^{2}(4-π) - 2π
*r* - 2r
^{2}

##### 3. Two angles of a triangle measure 15 and 70 degrees, respectively. What is the size of the third angle?

- 90 degrees
- 80 degrees
- 75 degrees.
- 125 degrees
- 95 degrees

##### 4. A rectangle is divided into two squares, each with a perimeter of 20. What is the perimeter of the rectangle?

- 20
- 30
- 40
- 50
- 60

##### 5. The diagram shows the outline of a racetrack for skaters, which consists of two long straight sections and two semi-circular turns. Given the dimensions shown, which of the following most closely measures the perimeter of the entire track?

- 180 yards
- 360 yards
- 395 yards
- 425 yards

##### 6. A tire on a car rotates at 500 RPM (revolutions per minute) when the car is traveling at 50 km/hr (kilometers per hour). What is the circumference of the tire, in meters?

- 50,000/2π
- 50,000/(60*2π)
- 50,000/(500*2π)
- 50,000/60
- 10/6

##### 7. Which of the following expressions represents the ratio of the area of a circle to its circumference?

- πr
^{2} - πr
^{2}/2π - 2πr/r
^{2} - 2πr
^{1/2} - r/2

##### 8. Lines AC and BD intersect at point E. Angle BEC is 45^{0}. What is the measure of angle AEB?

- Angle AEB is 90
^{0} - Angle AEB is 115
^{0} - Angle AEB is 135
^{0} - Angle AEB is 180
^{0} - Angle AEB is 360
^{0}

##### 9. Which of the following are complementary angles?

- 71
^{0}and 19^{0} - 18
^{0}and 180 - 90
^{0}and 90^{0} - 90
^{0}and 45^{0} - 15
^{0}and 30^{0}

##### 10. Which of the following letters has a vertical line of symmetry?

- A
- B
- C
- D
- E

##### Answers & Explanations

###### 1. A

Since the two angles shown add up to 90 degrees, and the remaining angle must therefore be 90 degrees, this is a right triangle. For a right triangle, the length of a side is related to the hypotenuse by the sine of the opposite angle. Thus, A=Csin(30^{0}) and since the sine of a 30-degree angle is 0.5 or 1/2, A=C/2 .

###### 2. C

The side of the square is equal to the diameter of the circle, or twice the radius: 2*r. *The area of the square is this quantity 2*r* squared, or 4r^{2}. The area of the circle is πr^{2}. Subtracting gives the difference between the two areas: 4r^{2}-πr^{2}=r^{2} (4-π)

###### 3. E

The sum of angles in a triangle equals 180 degrees. Therefore, solve for the remaining angle by subtracting the sum of the two given angles from 180 degrees: 180 – (15 + 70) = 95 degrees.

4. B

The perimeter of a square is four times the length of any one of its sides. If a square’s perimeter is 20, the length of any side is 5. The perimeter of the rectangle described in this problem is six times the length of a side of the square, which is 6*5=30.

###### 5. C

First, add the two straight 150 yard portions. Also, note that the distance around the two semi-circle turns combine to form the circumference of a circle. The radius (*r*) of that circle is half of the dimension shown as the width of the track, or 15 yards. Now, taking the formula for the circumference of a circle, 2πr (with r = 15), and adding it to the length of the two straight portions of the track, we have:Length=(2π*15)+(2*150)=394.25.

###### 6. E

It is not necessary to use the circle circumference formula to solve the problem. Rather, note that 50 km/hr corresponds to 50,000 meters per hour. We are given the car tire’s revolutions per minute and the answer must be represented as meters; therefore, the speed must be converted to meters per minute. This corresponds to a speed of meters 50,000/60 per minute, as there are 60 minutes in an hour. In any given minute, the car travels 50,000/60 meters/min, and each tire rotates 500 times around, or 500 times its circumference. This corresponds to 50,000/(60*500)=10/6 meters per revolution, which is the circumference of the tire.

###### 7. E

The area of the circle is πr^{2} while the circumference is 2πr. Taking the ratio of these two expressions and reducing gives: io=(πr^{2})/2πr=r/2.

###### 8. C

Note that angles AEB and BEC are supplementary and so their sum is 180^{0}. Subtract to solve: 180^{0} – 45^{0} = 135^{0}.

###### 9. A

Complementary angles are two angles that equal 90^{0} when added together.

###### 10. A

If you draw a vertical line down the center of the letter A, the two sides will be symmetrical.

##### Additional Practice Questions

by Enoch Morrison | Last Updated: December 31, 2018