Category Archives: Grade 9-10

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.

Continue reading

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.

Continue reading

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.

Continue reading

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.

Continue reading

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.

Continue reading