2013 Grade 9 Math Challenge – Elimination Round with answer key – Part I

Below are the 2013 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.) Simplify:
\dfrac{(-2x^{-3}y^4)^{-2}}{x^5y{-3}} \times (3x^{-2}y^{-1})^4

2.) Simplify:
\dfrac{6\sqrt{2}}{\sqrt{7} - 2}

3.) Simplify:
-2 \sqrt{75} + 5 \sqrt{12} - 4 \sqrt{27}

4.) Simplify:
6mn^4 \sqrt[3]{8m^{11}n^4}- 2m^3n \sqrt[3]{m^5n^{13}}

5.) Simplify:
xy^2 \sqrt{16x^3y^5} - 7y \sqrt{x^5y^7} + 4y^3 \sqrt{4x^5y^3}, if x > 0 and y > 0.

6.) Simplify:
\dfrac{x^2 - 3x - 28}{x^2 + 3x - 28} \div \dfrac{x^2 - 16}{x^2 - 49}

7.) Simplify:
\dfrac{x - 2}{x^2 - x - 6} + \dfrac{x + 5}{x^2 + 2x - 15}

8.) Solve: x(6x – 1) = 12

9.) Find the equation of the line with x-intercept 3 and y-intercept -7.

10.) Find the equation of the line passing through (2, 3) and perpendicular to 7x – 5y = 40.

11.) Find the constant s so that the lines (2s + 4)x + 5y = -7 and (s + 4)x + 3y = s are parallel.

12.) Find the point of intersection of the lines 5x + 2y = 16 and 10x – 3y = 46.

13.) Find the supplement of an angle measuring 76 {\frac{2}{7}}^\circ

14.) If \angle X = (6x + 5k)^\circ and \angle Y = (158 - 3k)^\circ are supplementary, find the complement of \angle X.

15.) Find x.

16.) Find y.

17.) Find RS.

18.) Find PQ.

19.) The four points A(-6, 2), B(-3, 3), C(9, 7) and D form Rectangle ABCD, what are the coordinates of D?

20.) How many circles of radius 9 cm can be cut from a rectanglular sheet 3.7 m by 1.05 m?

21.) In Parallelogram PARK, \angle P = 7x^\circ, \angle A = (3x - 20)^\circ, and \angle K = (5y - 10)^\circ. What is x + y?

22.) The angles of a triangle are in the ratio 11 : 12 : 13. Find the measure in degrees of its largest angle.

23.) The vertex angle of an isosceles triangle is 63 degrees. Find the measure of a base angle.

24.) A regular polygon has 15 sides. Find the measure in degrees of each of its interior angles.

25.) An equilateral triangle has perimeter 27 cm. What is its area?

Answer key:

1.) \dfrac{81}{4x^7y^9}
2.) 2 \sqrt{14} + 4 \sqrt{2}
3.) -12 \sqrt{3}
4.) 10m^4n^5 \sqrt[3]{m^2n}
5.) 5x^2y^4 \sqrt{xy}
6.) \dfrac{x^2 - 14x + 49}{x^2 - 8x + 16}
7.) \dfrac{2x}{x^2 - x - 6}
8.) -\dfrac{4}{3} and \dfrac{3}{2}
9.) y = \dfrac{7}{3} x - 7
10.) y = {-\dfrac{5}{7}}x + \dfrac{31}{7}
11.) 8
12.) x = 4 and y = -2
13.) 103 {\dfrac{5}{7}}^\circ
14.) 44^\circ
15.) 15
16.) 20
17.) 12
18.) 6
19.) (6, 11)
20.) 100
21.) 30
22.) 65^\circ
23.) 58.5^\circ
24.) 156^\circ
25.) \dfrac{81 \sqrt{3}}{4} cm^2

View Part II here: 2013 Grade 9 Math Challenge – Elimination Round with answer key – Part II

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