## 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.

## 2017 Grade 9 Math Challenge – Division Level with answer key

Below are the 2018 MTAP Grade 6 Math Challenge Division level questions and answers. Solutions will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Easy

1.) How many ten thousands are there in 2 234 188?

2.) Ana’s house is the fifth from one end of a street, and eighth from the other end. How many houses are there along this street?

3.) The base of an isosceles triangle is 10 cm and one of its legs is 18 cm. What is its perimeter?

4.) What number is 27 less than the sum of 50 and 15?

5.) Arnold can walk 19.5 km in 3 hours. How many kilometers can we walk in 4 hours?

## 2019 Grade 10 Math Challenge – Division Level with answer key

Below are the 2019 MTAP Grade 10 Math Challenge Division level questions and answers. Solutions will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Easy

1.) Find the solution set of the inequality $x(x + 1) < x.$

2.) A circle, centered at the origin, passes through the points (-2, 3) and (3, k). What is k?

3.) The 4th and 10th terms of an arithmetic sequence are 48 and 68. What is the 1st term?

4.) If -1 is a root of the equation $2x^4 + 2x^3 = 3x^2 + kx + 2$, what is k?

5.) A 3 cm chord is 3 cm away from the center of the circle. What is the exact area of the circle?

## 2018 Grade 10 Math Challenge Questions 26-50 (with PDF)

This is the 2018 MTAP Grade 10 Math Challenge questions 26 to 30. Questions 1-25 including can be found here. The pdf can be downloaded here. Solutions and answer will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Questions

26.) Find the radius of the circle with equation $x^2 + y^2 + 4x - 3y + 5 = 0$.

27.) Give the equation (in center-radius form) of the circle having as a diameter the segment with endpoints $(-2, 10)$ and $(4, 2)$.

28.) The center of a circle is on the x-axis. If the circle passes through $(0,5)$ and $(6,4)$, find the coordinates of its center.

29.) If $\theta$ is an angle in a triangle and $\sec \theta = \frac{7}{5}$, find $\tan \theta$Continue reading