2017 Grade 8 Math Challenge Elimination Round (Questions 26-50) with PDF

This is the 2017 MTAP Grade 8 Math Challenge questions 26 to 30. Questions 1-25 including can be found here. The pdf can be downloaded here. Solutions and answer will be posted later.

26.) Perform the indicated operations and simplify:

\dfrac{2x - 3}{6x} \cdot \dfrac{4}{6x - 9} \div \dfrac{8}{x}

27.) What is the difference between the mean and the median of 2, 3, 3, 4, 6, 7, 8, 15?

28.) The surface area of a cube is 50% more than its volume. Find the total length of the edges of the cube.

29.) What is the slope of the line with y-intercept 6 and x-intercept -4?

30.) If the standard deviation of a set of 20 numbers is 0, what is its range?

31.) A date is randomly chosen from the month of February 2017. What is the probability that the date chosen is a prime number greater than 10?

32.) Solve for x: (x - 3) + 2( x-3) + 3(x-3)+ \cdots + 200(x-3)=1809004

33.) Donna’s age is 1/5 her grandfather’s age. In 35 years, the grandfather will be 100 years old. In how many years’ time will Donna be 1/3 as old as her grandfather?

34.) Find the greatest possible perimeter of an isosceles triangle with sides 10 cm and 8 cm.

35.) If line l passes through the origin and the point P(-3,8), what is the equation of l in slope- intercept form?

36.) In △ACE, ∠A = 42◦ and ∠C = 88◦. Arrange the sides of △ACE from the shortest to the longest.

37.) If Liza is half as old as Paul and Paul will be x years old in five years, what is Liza’s age 10 years ago?

38.) If two dice are rolled, what is the probability that the sum of the numbers showing is 7 or 11?

39.) For what values of a and b will the system be inconsistent:

40.) Mark and Marry left home together and drove to their mother’s house which was 84 km away. Mary drove at 60 kph and Mark drove 20 kph faster than Marry. After travelling 2/7 of the journey, Mark stopped and wait for Marry. How long did Mark wait?

41.) Solve for x and y: (12)^{3x+2} = (18)^{2y - 1}.

42.) James and John can finish a job in 51 hours. If James can finish the job in 3 hours less time 7 than John, how long will each one finish the job alone?

43.) The number of girls in a school is 160 more than 1/3 of the total enrolment in the school. The number of boys is 280 more than 1/7 of the total enrolment in the school. How many pupils in the school are girls?

44.) The graph of two linear functions f(x) = ax + b and g(x) = bx - a are perpendicular. If \frac{f(0)}{g(-1)} = \frac{1}{3}, what are the possible values of a + b?

45.) If the sum of two numbers is 7 and their product is 8. What is the sum of their cubes?

46.) The mean of 6 numbers is 28 while the mean of another set of 10 numbers is 36. What is the mean of all the numbers combined?

47.) Find all integers x such that

\dfrac{9x^2 - 36}{3x3 - 6x^2 - 12x+24}

is an integer.

48.) In parallelogram ABCD, ∠A = (8x − 5)◦ and ∠C = (61 − 3x)◦. Find the measure of ∠B and ∠D.

49.) In quadrilateral ABCD, AB = 8, BC = 12, CD = 16 and DA = 21. Find the range of possible lengths of diagonal AC.

50.) If a, b, and c are positive numbers such that a + b + c = 10 and

\dfrac{1}{a + b} + \dfrac{1}{b + c} + \dfrac{1}{a + c} = \dfrac{4}{5},

what is the value of

\dfrac{c}{a + b} + \dfrac{a}{b + c} + \dfrac{b}{a + c}?

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