# Tag Archives: mtap reviewers

## 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.

## 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.

## 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.

## 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.