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NATS Math Challenge
(Grades 6 to 8)
 
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 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.  Neha enlarged a picture proportionally. Her original picture is 4 cm wide and 6 cm long. If the new, larger picture is 10 cm wide, what is its length? Mark your answer.
 A  8 cm  B  12 cm
 C  15cm  D  20 cm

2.  The vice president of sales took a client out to lunch. If the lunch was $44.00 and she gave a 20% tip, how much money did she spend on lunch? Mark your answer.
 A  $46.80  B  $54.00
 C  $52.80  D  $64.00

3.  What is the greatest common divisor of 54, 36, and 24? Mark your answer.
 A  6  B  2
 C  3  D  9

4.  Anisha had some change in her pocket. After her friend gave her $0.45, Anisha had $1.35 altogether. Which equation can she use to find the original amount of money, m, she had in her pocket? Mark your answer.
 A  m = 1.35 + 0.45  B  m + 0.45 = 1.35
 C  m - 0.45 = 1.35  D  m = 1.35 x 0.45

5.  Which equation could be used to find the area (in square inches) of a circle with a diameter of 8 inches? Mark your answer. (PI is denoted as π)
 A  Area = 2 × π × 4  B  Area = 2 × π × 8
 C  Area = π × 82  D  Area = π × 42

6.  Anjali earned a score between 83 and 94 on all of her previous math tests. She earned a score of 100 on her next test. Which of the following statements is true? Mark your answer.
 A  The mode will increase.  B  The mode will decrease.
 C  The mean will increase.  D  The mean will decrease.

7.  A snack bar sells 5 items with a mean (average) price of $0.60, as shown below..
Snack Menu
Chips $0.50
Energy Bar $0.80
Apple $0.60
Candy $0.70
Banana $0.40

Which pair of items could be added to the menu without changing the average price? Mark your answer.
 A  Gum ($0 60) and Soda ($0 75)  B  Gum ($0 60) and Cookie ($0 50)
 C  Juice ($0 45) and Cookie ($0 50)  D  Juice ($0 45) and Soda ($0.75)

8.  Which of the following is complementary to the angle 35°? Mark your answer.

 A  45°  B  55°
 C  145°  D  155°


9.  Which rule can be used to find the value of any term in the sequence below where n represents the position of the term? Mark your answer.
Position Value of Term
1 4
2 7
3 10
4 13
5 16
n  
 A  2n + 2  B  4n
 C  3n + 1  D  5n - 1

10.  Rectangular cake pans X and Y are similar. The ratio of the width of pan X to the width of pan Y is 3 : 4. The length of pan X is 10 inches, and its width is 5 inches. What is the perimeter of pan Y? Mark your answer.
 A  40 inches  B  20 inches
 C  50 inches  D  30 inches

11.  In gymnastics, each athlete receives 6 scores. The highest and lowest scores do not count, and the final score is determined by the mean of the remaining scores. After a balance beam performance, a gymnast receives the following scores:

9.8, 9.9, 9.8, 9.7, 9.5, 9.6

What is the gymnast’s final score? Mark your answer.

 A  9.70  B  9.50
 C  9.725  D  9.8

12.  Hanna’s class took a survey of 25 students’ favorite foods. Ten of the 25 students chose hot dogs, 28% chose hamburgers, and the rest chose pizza. What percent of the students chose pizza? Mark your answer.

 A  32%  B  38%
 C  62%  D  68%

13.  Ameya's average score for her first four English exams is 83. What score must she get on the fifth exam so that her average for the five exams is 85? Mark your answer

 A  93  B  84
 C  97  D  87

14.  Which of the following is an irrational number? Mark your answer.
 A  √
3
 B  3.0
 C  32  D  0.03

15.  The sum of the digits of a two-digit number is 9. When the digits are reversed, the number is increased by 45. What is the number? Mark your answer.
 A  36  B  45
 C  18  D  27

16.  The length of a football field is 7 yards more than twice the width. If the perimeter of the football field is 230 yards, What is the width of the football field? Mark your answer.

 A  34 yards  B  36 yards
 C  63 yards  D  72 yards

17.  The ratio of boys to girls in a class room is 8 to 7. If there are 105 boys and girls in the class room altogether then how many girls are there? Mark your answer.
 A  59  B  64
 C  49  D  54

18.  Which of following is the equation of a straight line that passes through the point (-6, -3) and is perpendicular to the line passing through the points (-7, 5) and (5, 4)?

 A  Y = 6X + 19  B  Y = 12X + 69
 C  Y = -6X + 19  D  Y = -12X + 69

19.  Which of the following is a factor of x2 - 11x + 24?

 A  (x - 4)  B  (x - 3)
 C  (x + 4)  D  (x + 3)

20.  Two airplanes left the same airport traveling in opposite directions. If one airplane averages 400 miles per hour and the other airplane averages 250 miles per hour, in how many hours will the distance between the two planes be 1625 miles?. Mark your answer.
 A  2 hours  B  2.5 hours
 C  4 hours  D  4.5 hours

21.  How many times does the graph of y = 2x2 - 2x + 3 intersect the x-axis?
 A  none  B  one
 C  two  D  three

22.  Lisa will make punch that is 25% fruit juice by adding pure fruit juice to a 2-liter mixture that is 10% pure fruit juice. How many liters of pure fruit juice does she need to add? Mark your answer.
 A  0.1 liter  B  0.2 liter
 C  0.3 liter  D  0.4 liter

23.  Which ordered pair is the solution to the system of equations below?

   3x - 4y = -8
   x - 7y = 20


 A  (8, 4)  B  (-8, -4)
 C  (-4, -8)  D  (4, 8)

24.  How many sides does a regular polygon have if the sum of its interior angles is 1440 degrees. Mark your answer.
 A  7  B  8
 C  9  D  10

25.  Which of the following is NOT a Pythagorean triple? Mark your answer.
 A  3, 4, 5  B  5, 12, 13
 C  7, 23, 24  D  8, 15, 17

Click Submit button to finish the test: