2014 Grade 7 Math Challenge – Elimination Round with answer key – Part I

Below are the 2014 Grade 7 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 {6}{5} \times \dfrac {1}{4} + 2 \div \dfrac {5}{2}

2.) Simplify:
\dfrac{\dfrac{2}{3} - \dfrac{5}{4}}{\dfrac{1}{2} + \dfrac{4}{3}}

3.) Write in scientific notation:
\dfrac {7}{12500000}

4.) Simplify:
2 - \left( 1 + \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{16} \right)

5.) Julie’s average for the first four tests is 88.5 If she wants an average of at least 90 in the five tests, what score must she get in her last test?

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2016 Grade 8 Math Challenge – Elimination Round with answer key – Part I

Below are the 2016 Grade 8 Math Challenge – Elimination Round questions and answers – Part I. More reviewers can be found on the Past Tests and All Posts pages.

1.) Simplify: (a - b)^2 (a + b)^2 + 2a^2b^2

2.) Simplify: \left( \dfrac {125x^4y^3}{27x^{-2y^6}} \right)^\frac{1}{3}

3.) Solve for x in the equation x^4 - 5x^2 + 4 = 0 .

4.) In the arithmetic sequence 10 + 10\sqrt{3}, 11 + 9\sqrt{3}, 12 + 8\sqrt{3}, ... , what term has no \sqrt{3}?

5.) If x + y = 12 and xy = 50 , what is x^2 + y^2 ?

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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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2013 Grade 7 Math Challenge – Elimination Round with answer key – Part II

Below are the 2013 Grade 7 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the Past Tests and All Posts pages.

26.) In Teacher Ella’s class, a student receives a final grade of A if the student garners an average of at least 92% in the five long test. After four long test, Jonathan got an average of 91%. At least how much should he get in the last long test to get a final grade of A?

27.) What is the largest prime factor of 2013?

28.) A class of 47 students took examinations in Algebra and in Geometry. If 29 passed Algebra, 26 passed Geometry, and 4 failed in both subjects. How many passed both subjects?

29.) A runner started a course at a steady rate of 8 kph. Five minutes later, a second runner started the same course at 10 kph. How long did it take for the second runner to overtake the first?

30.) A rectangle has sides (2x +3) cm and (4x + 5) cm. How many squares of side x cm can be cut from it?

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