Central Arizona College2017 Pinal County High School Math Competition

Level I

1.) David gets to work in 20 minutes when he drives his car. Riding his bike (by the same route) takes him 45 minutes. His average driving speed is 4.5 mph greater than his average bike speed. How far does he travel to work?

A.) 2.0 miles D.) 2.6 miles

B.) 2.2 miles E.) None of the above.

C.) 2.4 miles

2.) Charlotte, a chemist, needs a 20% solution of alcohol. How many liters of a 15% solution should be added to 3 liters of a 30% solution to obtain a 20% solution?

A.) 5.5 L D.) 7.0 L

B.) 6.0 L E.) None of the above.

C.) 6.5 L

3.) Solve for W.S = 2HW + 2LW + 2LH

A.) W =S+2LH

2H+2LD.) W =

S−2LH

2L−2H

B.) W =S−2LH

2H+2LE.) None of the above.

C.) W =S+2LH

2L−2H

4.) What is the minimum value of the expression 3x2-6x+6?

A.) 3 D.) 𝑥 +1

8

2− 3

B.) 𝑥 +3

2

2+ 6 E.) None of the above.

C.) 𝑥 −9

4

2+ 15

5.) Which of the following expressions is equivalent to 5

8

3?

A.) 53

83D.)

8

5

1

3

B.) 53

8E.) None of the above.

C.) 5

83

6.) For a Saturday matinee, adult tickets cost $5.50 and kids under 12 pay only $4.00. If 70 tickets are sold for a total of $310, how many tickets were adult and how many were kids?

A.) 50 kids, 20 adults D.) 20 kids, 50 adults

B.) 40 kids, 30 adults E.) None of the above.

C.) 30 kids, 40 adults

7.) Factor completely.a – 3b 2 – 6(a – 3b) + 9

A.) (a – 3b)(a – 3b + 3) D.) a – 3b – 3 2

B.) (a – 3b)(a – 3b – 3) E.) None of the above.

C.) a – 3b + 3 2

8.) Kevin saves 2 dollars during the month of January. Each month, he plans to save twice the amount saved during the previous month. With this plan, how much will he have saved after 18 months?

A.) $218,174 D.) $524,286

B.) $262,144 E.) None of the above.

C.) $478,195

9.) If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes?

A.) 5

𝑝D.)

𝑝

5

B.) 𝑝 − 5 E.) None of the above.

C.) 𝑝 + 5

10.) If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A.) 2 hours and 24 minutes D.) 4 hours and 10 minutes

B.) 3 hours and 12 minutes E.) None of the above.

C.) 3 hours and 44 minutes

11.) Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?

A.) $280.90 D.) $306

B.) $287 E.) None of the above.

C.) $292.50

12.) Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

A.) 4 D.) 13

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

C.) 12

13.) You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back?

A.) $5.20 D.) $19.95

B.) $7.35 E.) None of the above.

C.) $13.40

14.) Solve for x:x4 − 13x2 = −36

A.) {-2, -3} D.) {2i, -2i}

B.) {2, 3} E.) None of the above.

C.) {-2, -3, 2, 3}

15.) Simplify the expression 4𝑥+22𝑥

2𝑥

A.) 6 D.) 2𝑥+1

B.) 2 + 2𝑥 E.) None of the above.

C.) 2 ∙ 2𝑥

16.) A baseball is thrown up in the air from an initial height of 6 feet. Its height above the ground (in feet) t seconds after being thrown is given by the function ℎ(𝑡) = −16𝑡2 + 46𝑡 + 6. How long will it take (in seconds) for the baseball to hit the ground?

A.) 2 seconds D.) 4 seconds

B.) 5

2seconds E.) None of the above.

C.) 3 seconds

17.) The average of six numbers is 4. If the average of two of those numbers is 2, what is the average of the other four numbers?

A.) 5 D.) 8

B.) 6 E.) None of the above.

C.) 7

18.) Elijah drove 45 miles to his job in an hour and ten minutes in the morning. On the way home in the evening, however, traffic was much heavier and the same trip took an hour and a half. What was his average speed in miles per hour for the round trip?

A.) 30 D.) 321

2

B.) 44 E.) None of the above.

C.) 333

4

19.) If 5 ounces is equal to 140 grams, then 2 pounds of ground meat is equal to how many grams?

A.) 863 g D.) 915 g

B.) 878 g E.) None of the above.

C.) 896 g

20.) Derek is purchasing lunch meat for the class picnic. There are 300 people attending the picnic. Derek expects that for every 10 people 11 sandwiches will be eaten and that 20 pounds of meat will make 90 sandwiches. How much lunch meat should Derek buy?

A.) 731

3lbs. D.) 330 sandwiches

B.) 672

3lbs. E.) None of the above.

C.) 110 lbs.