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NATS Math Challenge
(Grades 9 to 12)
Please read each question and select the best answer. After answering the questions, select the submit button at the bottom of the page. The time limit is 60 minutes for this test.
You don't have to answer all the questions as you are competing with your own grade students and wrong answers carry -4 points.

1.  How many sides does a regular polygon have if the sum of its interior angles is 1440 degrees. Mark your answer.
 A  9  B  10
 C  11  D  12

2.  Which method listed below could NOT be used to prove that two triangles are congruent? Mark your answer.
 A  Prove all three sets of corresponding sides congruent.
 B  Prove that two sides and an included angle of one triangle are congruent to two sides and an included angle of the other triangle.
 C  Prove that two angles and an included side of one triangle are congruent to two angles and an included side of the other triangle.
 D  Prove all three sets of corresponding angles congruent.

3.  A classroom globe has a diameter of 18 inches. Which of the following is the approximate surface area, in square inches, of the globe?

 A  98.4  B  107.4
 C  987.4  D  1017.4

4.  The measures of the interior angles of a pentagon are 2x, 6x, 4x-6, 2x-16, 6x+2. What is the measure, in degrees, of the largest angle? Mark your answer.
 A  64  B  170
 C  108  D  120

5.  The following expression

(1 + Sinβ)(1 - Sinβ)

can be simplified to which of the following?
 A  Cos2β  B  Csc2β
 C  Sec2β  D  Cot2β

6.  Which figure best describes the graph of

2x2 - 5y2 - 2x - 10y - 15 = 0

Mark your answer.

 A  Circle  B  Ellipse
 C  Parabola  D  Hyperbola

7.  A monthly cell phone plan charges $5.00 for the first 300 text messages used and $0.15 for each additional message. On this plan, what is the number of text messages that must be used in a month in order to make the average cost per message $0.05? Mark your answer.
 A  900  B  750
 C  600  D  400

8.  A restaurant manager bought 20 packages of bagels. Some packages contained 6 bagels each, and the rest contained 12 bagels each. There were 168 bagels in all. How many packages of 12 bagels did the manager buy? Mark your answer.
 A  6  B  8
 C  9  D  12

9.  Julia wants to create several different 7-character screen names. She wants to use arrangements of the first 3 letters of her first name (jul), followed by arrangements of 4 digits in 1987, the year of her birth. How many different screen names can she create in this way? Mark your answer.

 A  576  B  288
 C  144  D  72

10.  A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could NOT be the length of the fence in feet? (12 inches = 1 foot)? Mark your answer.

 A  28  B  35
 C  39  D  50

11.  At what point does the graph of 5x + 4y = 12 intersect the y-axis? Mark your answer.

 A  (3, 3)  B  (0, -3)
 C  (0, 3)  D  (0, 5)

12.  If (3x + 2) (2x - 5) = ax2 + bx + c then What is the value of a - c + b? Mark your answer.
 A  4  B  5
 C  6  D  7

13.  If x2 - y2 = 55, and x - y = 11 then what is the value of y? Mark your answer.
 A  5  B  -5
 C  3  D  -3

14.  Two equal circles are cut out of a rectangle of card of dimensions 16 cm by 8 cm. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out? Mark your answer.

 A  104 sq. cm  B  78 sq. cm
 C  54 sq. cm  D  27 sq. cm

15.  A certain radioactive substance has a half life of 6 hours. If you start with 200 grams of the substance, how much will you have after 12 hours?
 A  25 grams  B  50 grams
 C  75 grams  D  100 grams

16.  A projectile launched at a speed of 60 meters per second from the ground, is modeled by the equation y = -2t2 + 38t + 10 where t is the time, in seconds, and y is height, in meters. How long will it take for the object to reach its maximum height? Mark your answer.
 A  7.5 seconds  B  9.5 seconds
 C  12.5 seconds  D  15.5 seconds

17.  A bookstore sold 18,000 paperbacks one month. This was 10% less than the number of paperbacks the store sold the previous month. How many paperbacks did the store sell in both the months combined? Mark your answer.

 A  34,200  B  35,990
 C  38,000  D  39,600

18.  Trini’s car breaks down on a highway. Trini estimates that she is 20 to 30 miles from the nearest car repair shop. She calls a towing company that charges a fee of $80 plus $3 per mile to tow a car. If Trini uses this towing company, which is the best estimate for the amount of money, m, she will pay for the company to tow her car? Mark your answer.

 A  103 ≤ m ≤ 113  B  120 ≤ m ≤ 140
 C  160 ≤ m ≤ 170  D  140 ≤ m ≤ 170

19.  Given log 2 = 0.3010, and log 3 = 0.4771. What is the value of log 6? Mark your answer.
 A  0.7781  B  0.5436
 C  0.1761  D  0.6751

20.  Two cars are racing at a constant speed around a circular racetrack. Car A requires 15 seconds to travel once around the racetrack, and car B requires 25 seconds to travel once around the racetrack. If car A passes car B, how many seconds will elapse before car A once again passes car B ? Mark your answer.
 A  49.5 seconds  B  32.5 seconds
 C  41.5 seconds  D  37.5 seconds

21.  The value of y increased by 12 is directly proportional to the value of x decreased by 6. If y = 2 when x = 8, what is the value of x when y = 16 ? Mark your answer.
 A  16  B  10
 C  36  D  64

22.  The average (arithmetic mean) of a particular set of seven numbers is 12. When one of the numbers is replaced by the number 6, the average of the set increases to 15. What is the number that was replaced? Mark your answer.

 A  -10  B  -12
 C  -15  D  -20

23.  Which of the following is the factored form of 3x2 - 22x -16? Mark your answer

 A  (3x - 2)(x - 8)  B  (x + 8)(3x - 2)
 C  (3x - 8)(x + 2)  D  (x - 8)(3x + 2)

24.  M is the mid point of a line segment QR. Q has coordinates (-3, 5), and M has coordinates (7, -9). Find the coordinates of R. Mark your answer.
 A  (17, -23)  B  (12, -2)
 C  (10, -14)  D  (11,-12))

25.  The coordinates of X are (a-5, -2a). The coordinates of Y are (a+1, 2a). If the distance between X and Y is 10, which of the following is a possible value of a? Mark your answer.

 A  1  B  2
 C  3  D  4

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