2014 Grade 9 Math Challenge Elimination Level Questions – Part 2

This is the 2014 Grade 9 Math Challenge Elimination Level Questions – Part 2 with answers. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

26.) (Figure 3) Find z.

27.) (Figure 4) The figure shoes a segment joining the midpoints of two sides of a triangle. Find x.

28.) Find the equation of the line passing through (-12, 6) and perpendicular to 6x + 7y = 3.

29.) Find the equation of the line having half the x-intercept and twice the y-intercept of 3x + 5y = 15.

30.) Find all values of the constant k so that the line (k² – 10)z + ky = 10 and (k – 4)x + 3y = 7 are parallel.

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2014 Grade 9 Math Challenge Elimination Level Questions – Part 1

This is the 2014 Grade 9 Math Challenge Elimination Level Questions – Part 1 with answers. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

1.) Rationalize the denominator of
\dfrac{7 + \sqrt{5}}{3 + \sqrt{5}}.

2.) Solve for x in 9 \sqrt{x - 3} - 3 = 5 \sqrt{x - 3} + 25.

3.) Simplify: 2y^3 \sqrt[3]{27x^7y^2}- x^2 \sqrt[3]{xy^8}.

4.) Solve for x in \sqrt{5x + 4} = \sqrt{x} + 4.

5.) Simplify \sqrt{45} + 4\sqrt{20} - \sqrt{125}.

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2018 Grade 10 Math Challenge Elimination Level Questions – Part 2

This is the 2018 Grade 10 Math Challenge Elimination Level Questions – Part 2 with answers. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

26.) If \theta is an angle in a triangle and cos \theta = \dfrac{5}{13}, find csc \theta.

27.) In \triangle ABC, BC = 6, CA = 7, and AB = 8. Find \dfrac{sin C}{sin A}.

28.) In \triangle ABC, AB= 3, AC = 7, and \angle A = 60^{\circ}. Find BC.

29.) In a circle, chord PQ is bisected by chord RS and T. If RT = 3 and ST = 6, find PQ.

30.) A line through a point A outside a circle is tangent to the circle at D. Another line through A intersects the circle at points B (closer to A) and C. If BC/AB = 2 and AD = 6, AC.

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2018 Grade 10 Math Challenge Elimination Level Questions – Part 1

This is the 2018 Grade 10 Math Challenge Elimination Level Questions – Part 1 with answers. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

Give all fractions and ratios in lowest terms and all expressions in expanded form.

1.) Ten percent of 450 is 20% of what number?

2.) Let r and s be the roots of x^2 - 9x + 7 = 0. Find r + s + rs.

3.) How many integers between 60 and 600 are divisible by 7?

4.) Simplify:
\dfrac{8!}{6!}

5.) If A = {2, 3, 5, 7}, B = {2, 4, 6, 8, 10}, and C = {3, 6, 9}, find (A \bigcup B) \bigcap C.

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2018 Grade 9 Math Challenge Elimination Level Questions – Part 2

This is the 2018 Grade 9 Math Challenge Elimination Level Questions – Part 2 with answers. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

26.) Find all possible values of n in the proportion (n – 5) : (n – 3) = (n + 3) : 20.

27.) An angle in a quadrilateral has measures 45°, while the others have degree measures in the ratio 5 : 7 : 9. Find the measure of the largest angle.

28.) In rhombus QRTS, \angle RQS = 5 \angle QRT. Find angle RTS.

29.) The diagonals of the rhombus PRAY intersect at G. If AG = 3n, PG = 6, RG = 3m – 2n, and YG = m + 2n, find the length (in units) of the shorter diagonal.

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

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