NSBE JR TRY-MATH-A-LON

# NSBE JR TRY-MATH-A-LON

## NSBE JR TRY-MATH-A-LON

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1. NSBE JR TRY-MATH-A-LON Regional Competition Round 1

2. Algebra Functions- 10 If x = -6, What is the value of the expression x2 + 3x +3 ?

3. Algebra Functions- 20 If |2x+10| = 36, then what is x?

4. Algebra Functions- 30 If xy = 35 and x2 +y2 = 74 , then (x+y)2 = ?

5. Algebra Functions- 40 If a+b = 16, b +c = 6, and a+c = 8, then what is a+b+c ?

6. Algebra Functions- 50 If 6a=2b=3c, what is the value of 10a+8b, in terms of c?

7. Algebra Functions- 60 If f(x) =x2 +2xh+h2 then f(x-h) = ? Note: Simplify the answer in like terms.

8. Geometry Measure - 10 If 8 and 17 are the lengths of two sides of a triangle, what is the range of the possible lengths of the third side of the triangle?

9. Geometry Measure - 20 In the figure below, if a=5b and c = 3b, what is the value of b? b a c

10. Geometry Measure - 30 The area of a rectangular plot of land is 3,000 square meters. If the length of one side of the plot is 60 meters, what is the perimeter of the plot?

11. Geometry Measure - 40 In a standard (x,y) coordinate plane, point A has coordinates (-4, 14) and point B has coordinates (16, -6). If (c,d) is the midpoint of AB, what is c +d?

12. Geometry Measure - 50 In the x-y coordinate plane, what is the distance between the points with coordinates (2,5) and (-3,-5)?

13. Geometry Measure - 60 If the slope of a line is – 5/3 and a point on the line is (3,5), what is the y intercept?

14. Numbers & Operations - 10 Simplify the problem below.

15. Numbers & Operations - 20 What is the number of distinct prime factors of 200?

16. Numbers & Operations - 30 The sum of all integers between 3 and 48, inclusive, is subtracted from the sum of all integers between 10 and 55, inclusive. What is the result?

17. Numbers & Operations - 40 How many integers between 10 and 500 begin and end in 3?

18. Numbers & Operations - 50 What is the positive difference between the largest and the smallest of the fractions?

19. Numbers & Operations - 60 Nancy’s wire is cut into 3 equal parts. She gives a section to each of her friends, Destiny, Kelly, and Tiffany. Each of them cut their segments into 6, 10, and 15 equal parts, respectively. If each of the resulting segments has an integer length, what is the minimum length of Nancy’s wire?

20. Data Analysis - 10 A fruit salad mixture consists of apples, peaches and grapes in the ratio 5 : 4 : 2 respectively, by weight. If 55 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

21. Data Analysis - 20 On a certain test, a class of 16 students has an average (arithmetic mean) score of 81. A second class of 16 students has an average score of 87. What is the average score of the combined classes?

22. Data Analysis - 30 Natasha, Jason, and Diane made a total of 51 greeting cards. Jason made 4 times as many as Natasha and Diane made 3 times as many as Jason. How many greeting cards did Natasha make?

23. Data Analysis - 40 In a recent poll, 80 percent of the 2,500 union members voted. Of the voting members, 40 percent answered “yes” to a certain yes-no proposal and 125 employees did not respond to that particular proposal. How many employees answered “no” to this proposal?

24. Data Analysis - 50 Flour, sugar, and baking soda are mixed by weight in the ration 6:6:2, respectively, to produce a certain type of cookie. In order to make 7pounds of this dough, what weight of sugar, in pounds, is required?

25. Data Analysis - 60 In an 9x9 checkerboard with 81 unit squares, what is the ratio of all the unit squares that are completely surrounded by other unit squares to all the unit squares on the border?

26. Problem Solving - 10 The tax on a \$275 television is \$22. At the same rate, what is the tax on a \$175 television?

27. Problem Solving - 20 The amount of money a caterer charges for an event is directly proportional to the number of attendees. If the caterer charges \$960 for 80. How much would she charge for an event with 100 attendees?

28. Problem Solving - 30 A company’s copier is broken and it will cost \$450 to fix it. A new toner-efficient copier, costing \$2,150, will save the company \$25 per month on its toner bill. If the company buys the new copier, in m months it will have saved an amount equal to the difference between the cost of the new copier and the cost of fixing the old one. What is the value of m?

29. Problem Solving - 40 On a scaled map, a distance of 10 centimeters represents 5 kilometers. If a street is 750 meters long, what is its length on the map in centimeters? (1 kilometer = 1000 meters)

30. Problem Solving - 50 If the sum of consecutive integers from -36 to n, inclusive is 114, what is the value of n?

31. Problem Solving - 60 A vending machine dispenses gumballs in a regularly repeating cycle of 10 different colors. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent before 6 gumballs of the same color are dispensed?

32. Black Inventors & Scientists - 10 She was the African American woman to receive a patent for her Cabinet Bed Invention.

33. Black Inventors & Scientists - 20 Benjamin Bradley, a slave, was employed at a printing office and later at the Annapolis Navel Academy, where he helped set up scientific experiments. In the 1840s, he developed what device on naval war ships? Note: He was unable to patent his work . He sold it and with the proceeds purchased his freedom.

34. Black Inventors & Scientists - 30 Charles Henry Turner, a native of Cincinnati, OH received a BS (1891) and MS (1892) from the University of Cincinnati and a PhD from the University of Chicago. He was a noted authority in insects. He was the first to prove that insects did what?

35. Black Inventors & Scientists - 40 He was born in Columbus, Ohio, and later settled in Cincinnati. Largely self-educated, he was awarded more than 60 patents. One of his most important inventions was a telegraph that allowed moving trains to communicate with other trains and train stations, thus improving railway efficiency and safety.

36. Black Inventors & Scientists - 50 Dr. Patricia Bath was born in Harlem, New York. She holds a bachelor's degree from Hunter College and an M.D. from Howard University. She is a co-founder of the American Institute for the Prevention of Blindness. She is best known for her invention of the Laserphaco Probe for the treatment of what eye disease?

37. Black Inventors & Scientists - 60 Mark Dean led the team of IBM scientists that developed the ISA bus—a device that enabled computer components to communicate with each other rapidly, which made personal computers fast and efficient for the first time. He also led the design team responsible for creating what important component of a computer that was the first of its kind?