## 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 $x^4 - 4x^2 - 5 = 0$.

## 2017 Grade 9 Math Challenge – Elimination Round with answer key – Part II

Below are the 2017 Grade 9 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the Past Tests and All Posts pages.

26.) Find all possible values of x in the proportion (x – 3) : (x – 1) = (x + 6) : 20.

27.) An angle in a quadrilateral has measures $60^\circ$, while the others have degree measures in the ration 3 : 5 : 7. Find the measure of the largest angle.

28.) In rhombus $PQRS, \angle QPR = 4 \angle QSR$. Find $\angle PQS.$

29.) The diagonals of rhombus STAY intersect at X. If $AX = m + n, YX = 12, SX = 4m - n,$ and $TX = 4n,$ find the length (in units) of the shorter diagonal.

30.) Find the perimeter (in units) of the rhombus STAY in the previous problem.

## 2017 Grade 9 Math Challenge – Elimination Round with answer key – Part I

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 $x^2 - 20x + c$ a perfect square.

2.) Solve for x in $16x^2 - 10 = 15.$

3.) A number and its reciprocal have a sum of $\frac{13}{6}$. Find the larger of these two numbers.

4.) Solve for x in $(x^2 + 1)^2 + 2(x^2 + 1) - 35 = 0.$

5.) Solve the inequality $x^2 - 2x - 35 \leq 0$ for x.

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

Below are the 2013 Grade 9 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the Past Tests and All Posts pages.

26.) A right trangle has legs $4 \sqrt{5}$ and $2 \sqrt{5}$. How long is the hypotenus?

27.) Quadrilateral PQRS has right angles at P and R. If PQ = 9, PS = 12 and QR = 10, find RS.

28.) What is the area of quadrilateral PQRS from the previous problem?

29.) The shortest legs of two similar triangles are 5 and 7.5. If the bigger triangle has perimeter 33, find the perimeter of the smaller triangle.

## 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.