# 2004 Grade 8 Math Challenge Elimination Level Questions – Part 2

This is the 2004 Grade 8 Math Challenge Elimination Level Questions – Part 2. Solutions will be posted later. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

26.) If n is an integer, find the solution set of $-5 < 2n - 1 < 5.$

27.) For what value of n will $\dfrac{5n + 2}{7n + 1}$ reduce to $\dfrac{3}{4}?$

28.) Solve for x: $3x^2 + 13x - 10 = 0$

29.) Find the positive root of $2x^2 - 5x - 8 = 0.$

30.) Find an equation with an integral coefficients such that the roots are $\dfrac{3}{2}$ and $\dfrac{2}{5}.$

31.) Simplify:
$\dfrac{4x^2 - 9y^2}{10x^3 + 15x^2y}$

32.) Multiply and simplify:
$\dfrac{a^2 - 9}{3x - 3y} \cdot \dfrac{x^2 - y^2}{a^2 - 6a + 9}$

33.) Perform the indicated operations: $\dfrac{ab + ac}{ab - ac} \cdot \dfrac{b}{b + c} \div \dfrac{b}{b - c}$

34.) Factor completely: $xy^3 + 2xy^2 - xy - 2$

35.) If a – 2 is one factor of $a^3 - 8,$ what is the other?

36.) If 28(32) is written as the difference of two squares, $a^2 - b^2,$ what is $a^2?$

37.) If y varies directly as x and y = 2 when x = 3, what is the equation of variation?

38.) If z varies jointly as $x^2$ and y, and z = 24 when x = 2 and y = 3, find z when x = 4 and y = 2.

39.) If y varies inversely as x and y = 12 when x = 6, and x if $y = \dfrac{1}{2}$

40.) Simplify: $\sqrt{18} - \sqrt{8} + \sqrt{50}$

41.) Multiply and simplify: $(2\sqrt{5} + 3\sqrt{2})(2\sqrt{5} - 3\sqrt{2})$

42.) Rationalize the denominator: $\dfrac{3\sqrt{7} + 2\sqrt{2}}{2\sqrt{7} - 3\sqrt{2}}$

43.) Solve for x: $\sqrt{11 - x} - \sqrt{x + 6} = 3$

44.) Divide $\sqrt{ab^2}$ by $\sqrt[3]{2a^2b}$

45.) If the roots of $2x^2 + 7x - 5 = 0$ are r and s, find an equation with integral coefficients whose roots are equal to 3r and 3s:

46.) The sum of the numerator and denominator of a certain fraction is 104. The value of the fraction reduces to $\dfrac{9}{17}.$ Find the fraction.

47.) Twenty-four men are engaged to do a piece of work in 38 days. After 10 days, 8 men stop working. In how many days can the rest finish the work?

48.) For what values of k will the roots of $x^2 + 5x + k = 0$ be real?

49.) If $2x - y = 1$ and $4y = 8x + c,$ for what value(s) of c will the system be dependent?

50.) If z varies directly as the square of x and inversely as y, what is the effect on z of doubling x and tripling y?

View Part 1 here: 2004 Grade 8 Math Challenge Elimination Level Questions – Part 1

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