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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.

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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.

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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.

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2015 Grade 10 Math Challenge – Elimination Round with answer key – Part II

Below are the 2015 Grade 10 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the Past Tests and All Posts pages.

26.) Solve the inequality: 3^{2x^2 + 3x - 2} > 1

27.) Two non-congruent circles have centers at C_1 and C_2. Diameter \overline {AB} of circle C_1 and diameter \overline {CD} of circle C_2 are perpendicular to \overline {{C_1}{C_2}} . If {C_1}{C_2} = 10, what is the area of the quadrilateral determined by A, B, C and D?

28.) Find the area of a triangle whose vertices have coordinates (2, 3), (-4, 2) and (10, 1).

29.) A jar contains only red and green balls. Ten red balls are added and the green balls now constitute 20% of the total. In addition, ten green balls are added, making the percentage of green balls equal to 40% of the total. How many balls were originally in the jar?

30.) If p + q = 22, what is the smallest value of p^2 + q^2?

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2015 Grade 10 Math Challenge – Elimination Round with answer key – Part I

Below are the 2015 Grade 10 Math Challenge – Elimination Round questions and answers – Part I. More reviewers can be found on the Past Tests and All Posts pages.

1.) An item was already discounted by 10% but had to be discounted by another 10% to make the price even more attractive to the customers. Overall, by how many percent was the item discounted?

2.) If the numbers x – 4, 4 – x, and x form an arithmetic progression, what is x?

3.) Two sides of a triangle have lengths 15 and 25. If the thirds side is also a whole number, what is its shortest possible length?

4.) Find the equation of a line that passes through (5, 4) and is parallel to 3x + y = 1.

5.) What is the area of a triangle with sides 10, 10 and 12.

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