Central Arizona College2017 Pinal County High School Math Competition

Level II

1.) While cycling Margi pedals the crank one and a half complete turns each second. Her gears are set so that each turn on the crank turns the wheel 2 times. If the wheel has a diameter of 70 cm, approximately how fast is she going?

A.) 6.6 m/sec D.) 4.4 m/sec

B.) 7.0 m/sec E.) None of the above.

C.) 2.1 m/sec

2.) All these points are collinear except for one. Which one is it?

A.) (0,7) D.) (2, 2)

B.) (−4, 16) E.) None of the above.

C.) (6, −8)

3.) Twenty unit cubes are glued together to form a 3 x 3 cube with holes through the middle. How many square units is the cubes surface area?

A.) 27 units

B.) 48 units

C.) 64 units

D.) 72 units

E.) None of the above.

4.) Find the area enclosed by the x-axis, the y-axis, and the graph of 𝑥 + 2𝑦 − 1 = 0.

A.) 1

8D.) 1

B.) 1

4E.) None of the above.

C.) 1

2

5.) An equilateral triangle is inscribed in a circle with a 2 inch radius. What is the triangle’s area?

A.) 6 3 D.) 3 𝜋

B.) 3 3 E.) None of the above.

C.) 1.5 2

6.) Considering the graph of the function 𝑓 𝑥 =𝑥2+3𝑥+2

𝑥2−4, which of

the following statements are true:

I. 𝑥 = 2 is a vertical asymptote.II. 𝑥 = −2 is a vertical asymptote.III. 𝑦 = 1 is a horizontal asymptote

A.) I. only. D.) I. and III. only.

B.) II. only. E.) None of the above.

C.) I. and II. only.

7.) In the expansion of 𝑥 − 3 5 , which of the following is the coefficient of 𝑥4:

A.) −15 D.) 5

B.) −5 E.) None of the above.

C.) −1

8.) Suppose that a sphere is inscribed in a cube (meaning the sphere touches all six faces of the cube). How many cubic meters is the volume of the sphere if the volume of the cube is 1 𝑚3 (one cubic meter)?

A.) 𝜋

6D.)

5𝜋

3

B.) 𝜋

3E.) None of the above.

C.) 5𝜋

6

9.) Consider the mobile displayed. Assume it is perfectly balanced, determine the weight 𝑥. Remember sides are balanced if the products of weight and distance from balancing point are equal.

A.) 1 kg.

B.) 4 kg.

C.) 8 kg.

D.) 14 kg.

E.) None of the above.

Do not assume boxes with “?” have the same values.

10.) Marvin earned 81 on his essay, a 91 on his midterm, and an 88 on his homework. The only grade missing is his Final Exam. If the essay and midterm are each worth 25% of his grade, and homework is worth 10%, what grade must he make on his final exam to get an average of 90?

A.) 94.5 D.) 98.6

B.) 95.5 E.) None of the above.

C.) 97.2

11.) If the sum of two numbers is 13 and the sum of their squares is 113, what is their product?

A.) 28 D.) 42

B.) 30 E.) None of the above.

C.) 36

12.) The equation 5𝑥2 − 12𝑥 = 𝑏, has 𝑥 = 3 as a solution. Determine the second value of 𝑥.

A.) −0.6 D.) 9

B.) −3.6 E.) None of the above.

C.) 6

13.) Two chords, 𝐴𝐵 and 𝐶𝐷, in a circle intersect at point P as shown. If the length of chord 𝐶𝐷 is 42 and the lengths of the segments 𝐴𝑃and 𝐶𝑃 are 10 and 12 respectively, what is the length of 𝐴𝐵?

A.) 25 D.) 46

B.) 35 E.) None of the above.

C.) 36

14.) Find the sum of all the solutions to the equation:

3𝑥 + 5 − 𝑥 = 7

A.) −2 D.) 6

B.) 2 E.) None of the above.

C.) 4

15.) A rectangle encloses three mutually tangent circles as shown. If each circle has a radius of 3, what is the height of the rectangle?

A.) 6 + 9

B.) 6 3

C.) 3 3 + 6

D.) 12

E.) None of the above.

16.) The pilot of an airline flying at an altitude of 10 km sees two towns, A and B, directly in view ahead. Suppose the pilot’s line of view makes angles of 30 and 60 respectively with the horizontal. How far are the towns A and B?

A.) 20 3

3

B.) 20

C.) 10

D.) 10 3

E.) None of the above.

17.) Consider the given circle. The chords 𝐴𝐵 and 𝐶𝐷 intersect at 𝑂such that 𝐴𝑂 = 4 𝑐𝑚 and 𝐷𝐶 = 16 𝑐𝑚. If 𝑂𝐶 = 𝐷𝑂, find the length 𝐴𝐵

A.) 16 𝑐𝑚

B.) 20 𝑐𝑚

C.) 4 5 𝑐𝑚

D.) 2 38 𝑐𝑚

E.) None of the above.

18.) In the figure to the right 𝐵𝐸 ∥ 𝐶𝐷, 𝐴𝐸 = 𝑥, ∠𝐸𝐴𝐵 = 90°, 𝐵𝐸 = 𝑦, 𝐶𝐷 = 20, 𝐷𝐸 = 3, 𝐴𝐵 = 12, 𝐵𝐶 = 4. Find the value of 𝑥 + 𝑦.

A.) 17

B.) 32

C.) 37

D.) 28

E.) None of the above.

19.) In the figure, the radius of each circle is 2 units. If a dart is thrown at random at the frame 𝐴𝐵𝐶𝐷, find the probability that it will hit the shaded region.

A.) 2−𝜋

2

B.) 16𝜋

C.) 𝜋

4

D.) 4−𝜋

4

E.) None of the above.

20.) Consider the triangle 𝐴𝐵𝐶 with vertices 𝐴 = 0,0 , 𝐵 = (4,0) and 𝐶 = (0,8). Let triangle 𝐴′𝐵′𝐶′ be the image of triangle 𝐴𝐵𝐶 after the

transformation 𝑥, 𝑦 =1

2𝑥,

1

4𝑦 . Find the area of triangle 𝐴′𝐵′𝐶′.

A.) 16 D.) 2

B.) 8 E.) None of the above.

C.) 4