2016 Grade 8 Math Challenge – Elimination Round with answer key – Part II

Below are the 2016 Grade 8 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the Past Tests and All Posts pages.

26.) Liza ran 200 meters in only 45 seconds. What was Liza’s speed in kilometers per hour?

27.) Suppose f(x) is a linear function such that f(\frac{1}{2}) = -7 and f(1) = -3. What is f(3)?

28.) Ana has four cardboard squares, each of which has side of length 6 cm. She decides to form a trapezoid by putting three squares side-by-side, cutting one square along a diagonal, discarding one-half and putting the other half at one end of three squares. What is the area of the trapezoid?

29.) What is the perimeter of the trapezoid in #28?

30.) The number 9,979 is a four-digit number the sum of whose digits is equal to 34. How many such number exist?



31.) If 10^{10} + 10^{10} +10^{10} +10^{10} +10^{10} +10^{10} +10^{10} +10^{10} +10^{10} +10^{10} = 10^x  , what is x?

32.) If the sum of the reciprocals of the roots are the equation 3x^2 + 7x + k is -\frac {7}{3}, what is k?

33.) If x = 1 + \sqrt{3}, find the value of
\dfrac{2x^2 - 4x + 8}{3x^2 - 6x + 10}.

34.) The sum of the angles of regular polygon is 2,160^\circ. How many sides does it have?

35.) An iron cube of side 16 cm is melted down and is used to make eight smaller iron cubes of the same size. What is the length of the sides of the smaller iron cubes?

36.) The sum of two numbers is 20. If one of the numbers is three times the other, what is their product?

37.) Determine how many ordered pairs (x, y) satisfy the system
x^2 + y^2 = 25
x - y = 5

38.) A 400 mL flask containing 40% alcohol mixture and a 600 mL flask containing 60% alcohol mixture are put together in a single large flask. How many percent alcohol is the resulting mixture?

39.) For what values of k will the equation y = x^2 + kx + k cross the x-axis twice?

40.) A certain farmer only raises chickens and pigs. Altogether, the animals have 57 heads and 158 legs. How many chickens does he have?

41.) Solve for x: |x – 4| = |2x + 1|

42.) The sum of 100 numbers is 34 278. The teacher write all the numbers on the board and proceeds as follows: he adds 1 to the first number, 2 to the second, 3 to the third, and so on, and adds 100 to the last. What is the sum of the new set of numbers?

43.) Express the answer in lowest terms
\dfrac{6a - 2}{9a} \times \dfrac{9a^2}{24a - 8}

44.) The sum of the roots of the quadratic function x^2 - 4x + 3 is 4. If all the coefficients of the quadratic function are increased by 2, what is the sum of the roots of the new function?

45.) What is the constant term in the expansion of \left (2x^2 + \dfrac{1}{2x} \right)^6

46.) Suppose that a is a positive number such thatthe roots x^2 - ax + 1 = 0 differ by exactly 1. What is the value of a?

47.) Two positive integers are relatively prime if they have no common factor other than 1. How many two digit numbers are relatively prime with 24?

48.) A motorist travelled a distance of 180 km. If he had driven 30km/h faster, he could have travelled the same distance in 1 hour less time. How fast did he drive?

49.) Solve for x in the inequality: 5 < |1 - 2x| \leq 7

50.) Joey draws a line on the board and marks five points on that line. He then marks two points on the board that lie on the same side of the line obtaining a total of seven points. How many different triangles can be drawn using the seven points as vertices?

Answer key:

26.) 16 km/hr
27.) -\frac{41}{3}
28.) 126 cm^2
29.) 48 + 6\sqrt{2} cm
30.) 10
31.) 11
32.) 3
33.) \frac{3}{4}
34.) 14
35.) 8 cm
36.) 75
37.) 2
38.) 52%
39.) k < 0 or k > 4
40.) 35
41.) x = 5 or x = 1
42.) 39 337
43.) \frac{a}{4}
44.) \frac{2}{3}
45.) \frac{15}{4}
46.) \sqrt{5}
47.) 30
48.) 60 km/h
49.) -3 \leq x < -2 or 3 < x \leq 4
50.) 25

View Part I here: 2016 Grade 8 Math Challenge – Elimination Round with answer key – Part I

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