2004 Grade 8 Math Challenge Elimination Level Questions – Part 1

This is the 2004 Grade 8 Math Challenge Elimination Level Questions – Part 1. 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.

1.) If x > 5, which is the largest?
a.) \dfrac{5}{x}
b.) \dfrac{5}{x - 1}
c.) \dfrac{x}{5}

2.) Simplify: 9x - (2y - 3x) - \{y - (2y - x)\} - \{2y + (4x - 3y)\}

3.) Perform the indicated operations:
\dfrac{3x - 2y}{5x - 3} + \dfrac{2x - y}{3 - 5x}

4.) Expand: (2x - 3y)^2

5.) The coordinate of A is -7 and that of B is 21. If M is the midpoint of AB, how long is AM?

6.) A, B and C are collinear with B between A and C. If the coordinate of B is -2, that of C is 6 and AB = 2BC, what is the coordinate of A?

7.) Factor completely: 81x^4 - 16y^8

8.) Simplify: \dfrac{2x^2 - 3x - 14}{2x^2 - 3x - 5} \cdot \dfrac{2x^2 - x - 10}{2x^2 - 5x - 7}

9.) Find two numbers with a product of 60 and a sum of 19.

10.) Expand: (3x^2 - 2y^2)^3

11.) Find the value of 27^{\frac{2}{3}}

12.) Find the value of (2^{-1} + 3{^-1})^2

13.) Write (3x^{-6})(9x^2) in simplest form.

14.) A square has a perimeter 12x + 28 cm. Find its area.

15.) Express the product of two consecutive odd integers as a polynomial.

16.) If the coordinates of the midpoint of the segment joining A(-3, 1) and B(x, y) are M(2, 4), find B(x, y).

17.) Find the least common multiple of: (2x^2 + x - 6) and (2x^2 - 5x + 3).

18.) Find the solution (x, y) in 5x - 4y = 19 and 7x + 3y = 18.

19.) What is the remainder when 2x^3 - 5x + 10 is divided by x – 2?

20.) For what real values of x is -4 < 3x - 2 < 14?

21.) If s = vt - \dfrac{at^2}{2}, solve for a in terms of s, v and t.

22.) Solve for x:
\dfrac{2}{x + 1} = \dfrac{3}{2x - 2}.

23.) Solve for x and y:
\dfrac{4}{x} - \dfrac{1}{y} = 17; \dfrac{2}{x} + \dfrac{3}{y} = 19.

24.) What kind of system is x + y = 3 and 2x = 6 - 3y

25.) Three times a number decreased by 15 is at least 23 and at most 56. What is the biggest integral value that the number can have?

View Part 2 here: 2004 Grade 8 Math Challenge Elimination Level Questions – Part 2

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