2014 Grade 7 Math Challenge – Elimination Round with answer key – Part II

Below are the 2014 Grade 7 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the Past Tests and All Posts pages.

26.) Subtract 2a^2 + 2ab - ac from the product of a + b and 2a - b + c.

27.) A cylindrical container which with radius 10 cm is filled with water to a height of 2 cm. The water is poured into a second cylindrical container with 4 cm radius. How high will the water be in the second container?

28.) Luis can arrange 6 or 9 stickers to a page without any stickers left over. If he arrange his stickers 10 to a page, there are 2 stickers left over. What is the smallest number of stickers Luis can have?

29.) ABCDEFGH is a regular octagon. What is the measure of \angle BAD?

30.) Given a rectangle ABCD, let E be the midpoint of side AB and F be the midpoint of side BC. What part of the rectangle ABCD is triangle DEF?

31.) At a party, married people came with their husbands or wives. If half of the women and \frac{1}{6} of the men in the party were single, what percentage of the people in the room were married?

32.) If the length of a rectangle is x + 5, its width is 2x - 1, and its area is 2x^2 + 5x + 7, what is x?

33.) How many four-digit numbers are multiples of 12?

34.) Simplify: (x^2 - 4)(x - 2) - (x + 3)(x^2 - 4x + 4)

35.) If n and m are positive integers, what is the value of \left[ (-2)^{n^2} + 2^{m+3} - (-2^n)^n\right] \div 2^m?

36.) Simplify:
\dfrac{(\sqrt{x} - \sqrt{2})(\sqrt{x} + \sqrt{2})}{x^2 - 4}.

37.) A rectangle with dimension x by x + 10 has the same area as the square with side x + 3. What is x?

38.) If today is Saturday, what day is 10^{20} days from now?

39.) Which is larger \sqrt{75} + 1 or 8 + \sqrt{3}

40.) Which values of x satisfy |x + 1| = |2x - 4|?

41.) What is the value of:
\left( 1 - \dfrac{1}{2}\right) \left( 1 - \dfrac{1}{3}\right) \left( 1 - \dfrac{1}{4}\right) ... \left( 1 - \dfrac{1}{2013}\right)?

42.) The vase of a pyramid is a square and its other faces are equilateral triangles. Draw all possible nets for the pyramid.

43.) A car leaves A at 8 AM and travels to B at a rate of 60 kph. A bus leaves B at 8:30 AM and travels to A at a rate of 75 kph. If the car and the bus pass each other midway between A and B, at what time will the car pass the bus?

44.) Which integer values of x satisfy 3x + 1 < 2x + 11 \leq 4x - 3?

45.) Find the solution set: 2 < |2x - 3| \leq 5.

46.) In a class of 30, ten students have computers at home and 15 have cellphones. What are the possible number of students who don’t have a computer nor cellphone?

47.) If n is a positive integer, which of the following is a perfect square: 3^{n^2}, (-3)^{3n}, 3(12)^{n^{2-1}}?

48.) If 5n leave a remainder of 8 when divided by 11, what is the remainder when 4n is divided by 11?

49.) With what polynomial must 6x^4 - 2x^3 + x^2 + x - 5 be divided to get a quotient of 2x^2 + 5 and a remainder of 6x + 30?

50.) Give the solution set to |3 - 2x| + |-6 + 1| < 12.

Answer key:

26.) 2ac + bc - ab + b^2
27.) 12.5 cm
28.) 72
29.) 45^\circ
30.) \frac{3}{8}
31.) 62.5%
32.) x = 3
33.) 750
34.) -x^2 + 4x - 4
35.) 8
36.) \dfrac{1}{x + 2}
37.) x = \dfrac{9}{4}
38.) Monday
39.) 8 + \sqrt{3}
40.) x =1 or 5
41.) \frac{1}{2013}
42.)

43.) 10:30 AM
44.) x = 7, 8, or 9
45.) [x | -1 \leq x < \frac{1}{2} or \frac{5}{2} < x \leq 4] or [-1, \frac{1}{2}) \cup (\frac{5}{2}, 4]
46.) from 5 to 15
47.) If n is even, then all of them are perfect squares. If n is odd, then all of them are not perfect squares.
48.) 2
49.) 3x^2 - x -7
50.) [x | -2 < x < 5] or (-2, 5)

View Part I here: 2014 Grade 7 Math Challenge – Elimination Round with answer key – Part I

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