2018 Grade 9 Math Challenge Elimination Level Questions – Part 1

This is the 2018 Grade 9 Math Challenge Elimination Level Questions – Part 1 with answers. 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.) Find the value of k that will make x^2 + 16x + k a perfect square.

2.) A number and its reciprocal have a sum of \dfrac {34}{15}. Find the smaller of these two numbers.

3.) Solve for x in 9x^2 - 10 = 6.

4.) Solve for x in (x^2 - 4)^2 - 2(x^2 - 4) = 15.

5.) Solve the inequality x^2 + 2x - 15 \geq 0 for x.

6.) Let r and s be the roots of x^2 + 10x - 7 = 0. Find rs + r + s.

7.) Find the range of values of k so that 5x^2 + kx + 20 = 0 has no real roots.

8.) Find the values of the constant n so that 4x^2 - 6(n + 1)x + 9n + 4 = 0 has 2 equal roots.

9.) One of the roots of x^2 - bx + 48 = 0 is three times the other, where b > 0. Find the b.

10.) Find the vertex of the graph y = x^2 - 4x + 5.

11.) Find an equation of the parabola having its vertex at (-1, 3) and directrix at y = 1. Give the answer in the form y = ax^2 + bx + c.

12.) The graph of y = x^2 + 5 is shifted 3 units to the right and 4 units down. Find the corresponding quadratic function (in the form y = ax^2 + bx + c) for the resulting graph.

13.) A rectangular pen is to be constructed with one of its sides along a straight river bank. If 50m of fencing will be used to enclose the three remaining sides, how long is the side parallel to the river, so that the pen has the largest possible area?

14.) Suppose that m varies inversely as n. If m = 5 when n = 7, find n when m = 35/3.

15.) Suppose q varies directly as r and inversely as the cube of s. If q = 5 when r = 1 and s = 1/2, find q when r = 2 and s = 3.

16.) Suppose m, n, and p are positive quantities such that m varies directly as n and n varies inversely as p. If m increases, will p increase or decrease?

17.) Rewrite the nonnegative exponents and simplify:
\dfrac{(x^3y^{-2})^2}{(x^{-2}y)^{-1}}

18.) Simplify:
\left( 7^{\frac{1}{2}}3^{\frac{3}{4}} \right)^{\frac{4}{5}} 7^{\frac{1}{5}} 3^{\frac{7}{5}}

19.) Rationalize the denominator and simplify:
\dfrac{4 + 3\sqrt{2}}{2 - 2\sqrt{2}}

20.) If 3 < x < 5, simplify \sqrt{x^2 - 10x - 25}.

21.) Simplify: \sqrt{32} + 5\sqrt{8} - 4\sqrt{18}.

22.) Solve for x in: 5\sqrt{x} - 5 = 3\sqrt{x} + 7.

23.) Solve for x in: \sqrt{2x + 7} = \sqrt{x} + 2.

24.) If q : r = 3 : 5 and r : t = 5 : 13, find t : q.

25.) If \dfrac {p - q}{3q} = \dfrac{5}{2}, find \dfrac{q}{p}.

Answer key:

1.) k = 64
2.) \dfrac{3}{5}
3.) x = \dfrac{4}{3} or x = -\dfrac{4}{3}
4.) x = \pm 1, x = \pm3
5.) x = \leq -5 or x \geq 3
6.) -17
7.) -20 < k < 20
8.) n = \dfrac{7}{3}, -\dfrac{1}{3}
9.) b = 16
10.) V(2, 1)
11.) y = 8x^2 - 16x + 1
12.) y = x^2 + 6x + 18
13.) 25m
14.) m = 21
15.) q = \dfrac{5}{108}
16.) p will decrease
17.) \dfrac{1}{x^2}
18.) 63
19.) \dfrac{-10 - 7\sqrt{2}}{2} or -5 - \dfrac{7\sqrt{2}}{2}
20.) 5 – x
21.) 2 \sqrt{2}
22.) x = 36
23.) x = 1 or 9
24.) 13 : 3
25.) \dfrac{q}{p} = \dfrac{2}{7}



View Part 2 here:2018 Grade 9 Math Challenge Elimination Level Questions – Part 2

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