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

2.) Solve for *x* in

3.) Simplify:

4.) Solve for *x* in

5.) Simplify

6.) Solve for *x *in

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 and 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 and

13.) Find the hypotenuse of a right triangle with legs and

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

15,) In and and If *AB *= *PQ *= 16, *BC* = 11 and *AC* = 8.6, find *QR*.

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

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

18.) In side *AB *is longer than the other two sides. if what is the range of possible measures of angle *B*?

19.) What is the longest side of if and

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 and *AB* = *DE*. Find

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*.

Answer key:

1.)

2.) *x* = 52

3.)

4.) *x* = 9

5.)

6.) *x* = 8

7.) 70°

8.) 110°

9.) 100°

10.) *k* = 13

11.) 16 : 11

12.) 30

13.) 20

14.)

15.) 11

16.) 20

17.) 2 < *x* < 9

18.)

19.) *AC* or *CA*

20.) *PD*

21.) *c* or

22.) 20°

23.) 144°

24.) 12

25.) 30

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