## 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?

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

Below are the 2013 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: $\left (2 - \dfrac {1}{2} \right) + \left (3 - \dfrac {1}{3} \right) + \left (4 - \dfrac {1}{4} \right)$

2.) Let $A = (a, b, c, d, e), B = (a, e, i, o ,u), C = (e, f, g, h, i).$ Find $(A \cap B ) \cup (B \cap C)$.

3.) Write $\dfrac {1}{50000000}$ in scientific notation.

4.) Nonoy left Butuan City to drive to Cagayan de Oro City at 6:15 PM and arrive 9:15 PM. If he averaged 80 kph and stopped 30 minutes for dinner, approximately how far is Cagayan de Oro from Butuan?

5.) Simplify: $\left (1 - \dfrac {1}{2} \right)^2 - \left (1 + \dfrac {1}{2} \right)^2$

## 2010 4th Year Math Challenge – National Level with answer key

Below are the 2010 MTAP 4th Year Math Challenge – National Level questions and answers. Solutions will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Easy

1.) Ricky has (4a + 1) ₧100 bills and Emil has (2a – 2) Php 50 bills. How much more money has Ricky than Emil?

2.) The graphs of $y = 10 - x^2$ and $y + 1 = 0$ intersect at two points. Find the distance between these points

3.) If r and s are the roots of $x^2 = x + 30$, what is ∣r – s∣?

4.) A triangle has sides with integral length. If its perimeter is 12 cm, what is the longest possible side of the triangle?

5.) If the length of a rectangle is increased by 10% and the area is increased by 120%, by how many percent is the width increased?