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.

Answer key:

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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