2014 Grade 9 Math Challenge Elimination Level Questions – Part 1

This is the 2014 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.) Rationalize the denominator of
$\dfrac{7 + \sqrt{5}}{3 + \sqrt{5}}.$

2.) Solve for x in $9 \sqrt{x - 3} - 3 = 5 \sqrt{x - 3} + 25.$

3.) Simplify: $2y^3 \sqrt[3]{27x^7y^2}- x^2 \sqrt[3]{xy^8}.$

4.) Solve for x in $\sqrt{5x + 4} = \sqrt{x} + 4.$

5.) Simplify $\sqrt{45} + 4\sqrt{20} - \sqrt{125}.$

6.) Solve for x in $\sqrt{x + 1} = x - 5.$

7.) An isosceles triangle has a 55° base angle. What is its vertex angle?

8.) An angle is 40° less than its supplement. Find the larger angle.

9.) The angles of a triangle are in the ratio of 3 : 5 : 10. Find the largest angle.

10.) If $\angle A = (5k + 2)^\circ$ and $\angle B = (2k - 3)^\circ$ are complementary, find k.

11.) If two acute angles of a right triangle are in the ratio of 2 : 7, find the ratio of the exterior angles adjacent to them.

12.) Find x if the angles of a triangle are $(x + 10)^\circ , (2x + 20)^\circ$ and $(3x - 30)^\circ.$

13.) Find the hypotenuse of a right triangle with legs $2 \sqrt{10}$ and $6 \sqrt{10}$

14.) An equilateral triangle has perimeter 18. What is its area?

15,) In $\triangle ABC$ and $\triangle PQR, \angle A = \angle P = 40^\circ, \angle B = 30^\circ$ and $\angle R = 110^\circ.$ If AB = PQ = 16, BC = 11 and AC = 8.6, find QR.

16.) The angle bisector at vertex A of $\triangle ABC$ meets BC at point D. If AB = 30, AC = 24 and BC = 36, find BD.

17.) A triangle has sides 7, 2x and 11. What is the range of values that x can take?

18.) In $\triangle ABC,$ side AB is longer than the other two sides. if $\angle A = 50^\circ ,$ what is the range of possible measures of angle B?

19.) What is the longest side of $\triangle ABC$ if $\angle A = 35^\circ, \angle B = 75^\circ$ and $\angle C = 70^\circ?$

20.) In equilateral ABCD, AB = AD and CD > CB. If the diagonals intersects at P, which one is longer between PB and PD?

21.) (Figure 1) Which of the marked angles is the largest?

22.) (Figure 2) In quadrilateral $ABCD, \angle CBE = \angle CEB = \angle CED = 50^\circ, \angle CAB = 20^\circ,$ and AB = DE. Find $\angle CDE.$

23.) A regular polygon has 10 sides. Find each interior angle.

24.) How many sides does a convex polygon have if the sum of its interior angles is 5 times the sum of all its exterior angle?

25.) (Figure 3) Find x.

1.) $4 - \sqrt{5}$
2.) x = 52
3.) $5x^2y^2 \sqrt[3]{xy^2}$
4.) x = 9
5.) $6 \sqrt{5}$
6.) x = 8
7.) 70°
8.) 110°
9.) 100°
10.) k = 13
11.) 16 : 11
12.) 30
13.) 20
14.) $9 \sqrt{3}$
15.) 11
16.) 20
17.) 2 < x < 9
18.) $0^\circ < \angle B < 80^\circ$
19.) AC or CA
20.) PD
21.) c or $\angle c$
22.) 20°
23.) 144°
24.) 12
25.) 30

View Part 2 here: 2014 Grade 9 Math Challenge Elimination Level Questions – Part 2

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