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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2014 Grade 8 Math Challenge Elimination Questions with answers – Part 2

This is the 2014 MTAP Grade 8 Math Challenge questions 26 to 50 with answer key. More reviewers can be found on the Past Tests and All Posts pages.

26.) If the sum of two consecutive angles of a regular polygon is 312^\circ, how many sides does it have?

27.) The length a trapezoid is 52 cm^2. If its bases are 8 cm apart, find the sum of their lengths.

28.) The base angles of an isosceles triangle are (50 - x)^\circ and (30x - 12)^\circ. What is the vertex angle?

29.) What is the area of the circle inscribed inside an equilateral triangle whose are is 4\sqrt{3} cm^2?

30.) Factor: x^2 + x^3 - y^2 - xy^2

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2014 Grade 8 Math Challenge Elimination Questions with answers – Part 1

This is the 2014 MTAP Grade 8 Math Challenge questions 1 to 25 with answer key. More reviewers can be found on the Past Tests and All Posts pages.

1.) Simplify: 1 – 2 +3 – 4 + … + 49 – 50 + 49 – 48 + 47 – 46 + … + 1

2.) Simplify:
\left( \dfrac{1}{2} - 1 \right) - \left( \dfrac{1}{3} - 1 \right)

3.) In the proportion x : 12 = 18 : x^2, what is x?

4.) Between what two consecutive integers does \sqrt [3]{-100} lie?

5.) What is the area of a rectangle whose sides are twice as long as the sides of a smaller rectangle whose area is 17 cm^2?

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