# 2014 Grade 8 Math Challenge Elimination Questions with answers – Part 2

This is the 2014 MTAP Grade 8 Math Challenge questions 26 to 50 with answer key. More reviewers can be found on the Past Tests and All Posts pages.

26.) If the sum of two consecutive angles of a regular polygon is $312^\circ$, how many sides does it have?

27.) The length a trapezoid is $52 cm^2$. If its bases are 8 cm apart, find the sum of their lengths.

28.) The base angles of an isosceles triangle are $(50 - x)^\circ$ and $(30x - 12)^\circ.$ What is the vertex angle?

29.) What is the area of the circle inscribed inside an equilateral triangle whose are is $4\sqrt{3} cm^2?$

30.) Factor: $x^2 + x^3 - y^2 - xy^2$

31.) Simplify the expression: $\dfrac{(x - 1)(x + 2)(2x + 3) + x + 6}{x^2}.$

32.) If $5x + 2y = 4$ and $-4 < x \leq 4,$ find the range of values of y.

33.) Solve the system: $2x + y = 1$ and $2y = x + 7.$

34.) The sum of two numbers is 88. If one number is divided by the other, the quotient and the remainder are 5 and 10, respectively. What is the product of the numbers?

35.) Marlu starts walking along around at 3km/hr. Two hours later, from where Marlu started, Lulu starts in the same direction at 4.5 km/hr. How far from the starting point will Lulu overtake Marlu?

36.) Find the fraction such that if 2 is subtracted from both its numerator and denominator, it is equivalent to $\frac{1}{4},$ but if 4 is added to both of them, it is equivalent to $\frac{1}{2}.$

37.) In how many ways can Php 500 be made up both Php 5 coins and Php 20 bills?

38.) What is the area of the region of solutions of the system: $x + y \leq 1, y + 2 \geq 2x,$ and $x \geq 0?$

39.) Let f be a linear function such that f(2) = 17 and $f \frac{1}{3} = 3$

40.) Solve for x in the equation |1 – x| = 2x – 3.

41.) What is the largest number of acute angles that a convex hexagon can have?

42.) For how many three-element sets of positive integers is it true that their product is 2013?

43.) Solve for x in the inequality $2 < |3 - 2x| \leq 3.$

44.) Simplify: $\dfrac{(2012)(2015)(4029) + 2019}{2013^2}$

45.) The sum of the lengths of all edges of a rectangular box is 140 dm, and the distance from one corner of the box to the farthest corner is 21 dm. What is the total surface area of the box?

46.) If $2x^2 + 2 = 7x$, what is $x^2 + \frac{1}{x^2}$

47.) The lengths of the sides of a triangle are 11 cm, 15 cm, and k cm, where k is an integer. For how many values of k is the triangle acute?

48.) If $x = \sqrt{5} - 2$, find the value of $\dfrac{x^3 + 6x^2 + 13x + 10}{x^3 + 6x^2 + 9x + 2}.$

49.) A list of five positive integers has mean 12 and range 18. The mode and the median are both 8. How many different values are possible for the second largest element of the list?

50.) Albert Einstein was born on 14 March 1879. Which day of the week was he born?

Answer key:

26.) 15
27.) 13 cm
28.) $84^\circ$
29.) $\frac{4}{3} \pi cm^2$
30.) $(x + 1)(x + y)(x - y)$
31.) 2x + 5
32.) $-8 \leq y < 12$
33.) x = -1 and y = 3
34.) 975
35.) 18 km
36.) $\frac{5}{14}$
37.) 24
38.) $\frac{3}{2} square units$
39.) 11
40.) 2
41.) 3
42.) 4
43.) $0 \leq x < \frac{1}{2}$ or $\frac{5}{2} < x \leq 3$
44.) 4031
45.) $784 dm^2$
46.) $\frac{41}{4}$
47.) 8
48.) 3
49.) 6
50.) Friday.

View Part 1 here: 2014 Grade 8 Math Challenge Elimination Questions with answers – Part 1

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