# 2016 Grade 9 Math Challenge – Elimination Round with answer key – Part I

Below are the 2016 Grade 9 Math Challenge – Elimination Round questions and answers – Part I. More reviewers can be found on the Past Tests and All Posts pages.

1.) Solve for x in $\sqrt {2 - x} - 4 = 0$.

2.) Find $sin \theta$ if $tan \theta - \frac{3}{4}$ and $cos \theta < 0.$

3.) What is the value of
$tan \left( -\dfrac{17}{6}\pi\right)?$

4.) Solve for x in
$\dfrac{5}{x + 2} - \dfrac{2}{x + 1} = \dfrac{1}{2}.$

5.) Solve for x in $x^4 - 4x^2 - 5 = 0$.

6.) Find the sum of the first 20 positive odd numbers.

7.) Solve for x in $x^2 + 12 < 7x.$

8.) Find all possible values of x if one of the interior angles of a square is $(2x^2 - 8x)^\circ.$

9.) What is the sum of the interior angles of a pentagon?

10.) The supplement of an angle is four times its complement. Find the angle.

11.) What is the shortest side of $\bigtriangleup PQR if \angle P = 57^\circ$ and $\angle Q = 67^\circ?$

12.) Rationalize the denominator and simplify:
$\dfrac{2\sqrt{2}}{\sqrt{6} + \sqrt{2}}$

13.) Find the 25th term of the arithmetic sequence whose first 3 terms are 4, 7, and 10.

14.) Solve for x in $\sqrt{2x + 1} - \sqrt{x} = 1.$

15.) For what value/s of x is $x^2 - 8x + 18 \geq 0?$

16.) In $\bigtriangleup ABC, \angle B = 90^\circ$ and $sin A = \frac{3}{4}.$ Determine the value of tan C.

17.) The angle bisector at vertex B of $\bigtriangleup ABC$ meets AC at D. If BC = 6, AC = 40,and CD = 15, find AB.

18.) Find the equation of the line parallel to $4x + 3y = 12$ and passing through (-12, 4).

19.) Express in terms of sines or cosines of $\theta$ and simplify: $cot \theta sec^2 \theta$

20.) Find the common ratio of a geometric sequence whose first term is -2 and the 7th term is -1458.

21.) Solve for x in $4 \sqrt{3x + 1} = 4x + 3.$

22.) Find the 7th term of the geometric sequence 8, 12, 18, …

23.) Triangle ABC is a righttriangle with $C = 90^\circ$. If $A = 60^\circ$ and $a = 50$, find b.

24.) Two of the exterior angles of a regular polygon measure $(6x - 30)^\circ$ and $(114 - 10x)^\circ$. How many sides does this regular polygon have?

25.) Solve for x in:
$\dfrac{3}{2x - 1} - \dfrac{2}{x} = 0.$

1.) -14
2.) $-\dfrac{3}{5}$
3.) $\dfrac{\sqrt{3}}{3}$
4.) 0 or 3
5.) $\pm i, \pm \sqrt{5}$
6.) 400
7.) 3 < x < 4
8.) -5, 9
9.) $540^\circ$
10.) $60^\circ$
11.) PQ
12.) $\sqrt {3} - 1$
13.) 76
14.) 0 or 4
15.) all real numbers or $(-\infty, +\infty) or \mathbb {R}$
16.) $\dfrac{\sqrt{7}}{3}$
17.) 10
18.) 4x + 3y = -36
19.) $\dfrac{1}{sin \theta cos \theta}$
20.) $\pm 3$
21.) $x = \dfrac{7}{4} or -\dfrac{1}{4}$
22.) $\dfrac{729}{8}$
23.) $\dfrac{50 \sqrt{3}}{3}$
24.) 15
25.) 2

View Part II here: 2016 Grade 9 Math Challenge – Elimination Round with answer key – Part II

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