## 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?

## 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 $x^2 + y^2$?

## 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 $p^2 + q^2$?

## 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.

## 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?