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NATS Math Challenge
(Grades 9 to 12)
 
Directions:
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 30 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.  The sum of three consecutive even numbers is 174. What is the largest of these 3 numbers? Mark your answer.
 A  56  B  58
 C  60  D  62

2.  The base of a triangle is 3 inches less than twice its height. If the area of the triangle is 126 square inches, which of the following equations can be used to find h, the height of the triangle in inches? Mark your answer.
 A  2h2 - 3h - 126 = 0  B  2h2 - 3h + 126 = 0
 C  2h2 - 3h - 252 = 0  D  2h2 - 3h + 252 = 0

3.  When viewed from above, the base of a water fountain has the shape of a hexagon composed of a square and 2 congruent isosceles right triangles, as represented in the diagram below.



Which of the following measurements best represents the perimeter of the water fountain’s base in feet? Mark your answer.
 A  (40 + 20√2) ft  B  (40 + 40√2) ft
 C  (20 + 40√2) ft  D  (20 + 20√2) ft

4.  What are the x-intercepts of the graph of

   y = 2x2 + 7x - 4
 A  0.5 and 4  B  0.5 and -4
 C  -0.5 and -4  D  -0.5 and 4

5.  In 1997 the population of a small town was 700. If the annual rate of increase is about 0.8%, which value below expresses the population five years later? Mark your answer.
 A  (5)(700)(0.008)  B  (5)(700)(1.008)
 C  (700)(1.008)5  D  (700)(0.008)5

6.  Which of the following is the equation of a line that passes through the point (8, 1) and is perpendicular to the line passing through the points (2, -2) and (7, 3)?
 A  y = 2x + 9  B  y = -x + 9
 C  y = -x - 9  D  y = -2x - 9

7.  A point P (-7, 4) is rotated by an angle 270° about the origin. What are the coordinates of the rotated point P1? Mark your answer.
 A  (4, 7)  B  (4, -7)
 C  (-4, 7)  D  (-4, -7)

8.  A bag contains tomatoes that are either green or red. The ratio of green tomatoes to red tomatoes in the bag is 4 to 3. When five green tomatoes and five red tomatoes are removed, the ratio becomes 3 to 2. How many red tomatoes were originally in the bag? Mark your answer.

 A  15  B  18
 C  24  D  30

9.  M is a set of six consecutive even integers. When the least three integers of set M are summed, the result is x. When the greatest three integers of set M are summed, the result is y. Which of the following is true?
 A  y = 2x + 4  B  y = 2x - 4
 C  y = x + 18  D  y = x - 18

10.  An integer is subtracted from its square. The result could be which of the following?
 A  A negative integer.
 B  The product of two consecutive even integers.
 C  The product of two consecutive odd integers.
 D  The product of two consecutive integers.

11.  The first term of a sequence is the number n, and each term thereafter is 5 greater than the term before. Which of the following is the average (arithmetic mean) of the first nine terms of this sequence? Mark your answer.
 A  n + 20  B  n + 180
 C  2n + 40  D  9n + 20

12.  If (x + 1)2 = 4 and (x - 1)2 = 16, what is the value of x? Mark your answer.
 A  -1  B  -3
 C  1  D  3

13.  Let x and y be positive integers such that one-third of x is y less than one-half of x. Which of the following is a possible value of x?
 A  22  B  24
 C  26  D  28

14.  If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that of the original area of the square. Find the longest side of the rectangle.
 A  14  B  24
 C  10  D  16

15.  A square is inscribed in a large circle. A small circle is inscribed in the square. If the area of the small circle is 1, what is the area of the large circle?

 A  √2  B  √3
 C  2√2  D  2

16.  230 + 230 + 230 + 230 = ?
 A  830  B  8120
 C  2120  D  232

17.  Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
 A  12  B  10
 C  8  D  6

18.  The quantity 1212 is NOT divisible by which of the following?
 A  24  B  27
 C  30  D  36

19.  A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?.

 A  30  B  24
 C  16  D  12

20.  Three apples and five oranges cost 85 cents, and five apples and three oranges cost 83 cents. How much will it cost to buy one apple and one orange?
 A  17 cents  B  19 cents
 C  21 cents  D  23 cents

21.   If the population of bacteria in a culture flask doubles every 20 minutes, the population after 3 hours and 20 minutes will be how many times the population at the start?

 A  1024  B  2048
 C  512  D  256

22.  An object is launched at 19.6 meters per second (m/s) from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is given by the equation

   s(t) = -4.9t2 + 19.6t + 58.8

  where s is in meters. How long will it take for the object to strike the ground?
 A  3 seconds  B  6 seconds
 C  12 seconds  D  24 seconds

23.  A committee consisting of 3 boys and 4 girls is to be formed from a group of 5 boys and 6 girls. How many different committee can be formed from the group?

 A  100  B  120
 C  150  D  180

24.  On a certain day the chance of rain is 80% in San Francisco and 30% in Sydney. Assume that the chance of rain in the two cities is independent. What is the probability that it will not rain in either city? Mark your answer.

 A  25%  B  14%
 C  50%  D  7%

25.  If four distinct lines lie in a plane, and exactly two of them are parallel, what is the least possible number of points of intersection of the lines?
 A  2  B  3
 C  4  D  5

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