Below are the 2017 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.) Find the value of *c* that will make a perfect square.

2.) Solve for *x* in

3.) A number and its reciprocal have a sum of . Find the larger of these two numbers.

4.) Solve for *x* in

5.) Solve the inequality for *x*.

6.) Let *r* and *s* be the roots of Find *rs* + *r *+ *s*.

7.) Find the range of values of the constant *k* so that has no real roots.

8.) Find the value of the constant n so that has two equal roots.

9.) One of the roots of is twice the other, where *b* > 0. Find the value of* b*.

10.) Find the vertex of the graph of

11.) Find *c* if the directrix of the graph of is the line

12.) The graph of is shifted 5 units to the left and 4 units up. Find the corresponding quadratic function (in the form ) for the resulting graph.

13.) A rectangular pen is to be constructed with one of its sides along a straight river bank. If 40 m of fencing will be used to surround the three other sides, so that the pen has the largest possible area, how long is the side parallel to the river?

14.) Suppose that *m* varies directly as *n*. If *m* = 4 when *n* = 6; find *m* when *n* =

15.) Suppose that *q* varies directly as *r*, and inversely as the square of *s*. If *q* = 12 when *r* = 1 and *s* =

16.) Supposethat *x*, *y* and *z* are positive quantities such that *x* varies directly as *y* and *y* varies inversely as *z*. If *z* decreseases, will *x* increase or decrease?

17.) Rewrite with nonnegative exponents and simplify:

18.) Simplify:

19.) Rationalize the denominator of and simplify.

20.) If 4 < *x* < 7, simplify

21.) Simplify

22.) Solve for *x* in

23.) Solve for *x* in

24.) If *r* : *s* = 7 : 4 and *s* : *t* = 2 : 5, find *r* : *t*.

25.) If , find

Answer key:

1.) 100

2)

3.)

4.)

5.) or [-5, 7]

6.) 16

7.) -12 < *k* < 12 or (-12, 12)

8.)

9.) 12

10.) (2, 3)

11.) 6

12.)

13.) 20 m

14.)

15.) 54

16.) increase

17.)

18.) 80

19.)

20.) 3

21.)

22.) 25

23.) 16

24.) 7 : 10

25.)

View Part II here: 2017 Grade 9 Math Challenge – Elimination Round with answer key – Part II