# Practice Math Challenge Question for 3rd Year – Orals

Easy Round – 2 points

1. How many diagonals does regular nonagon have?     
2. The interior angle of a regular polygon is 170°. How many sides does the polygon have?     
3. What is the larger value of x in $x^2-x-6=0$?     
4. Adjacent sides of a triangle are 6 and 7. What is the maximum length of the third side if it is an integer value?     
5. What is the area in square centimeter of a kite with diagonals measuring 20 cm and 10 cm?     
6. What is the last two digit of $5^{2013}$?     
7. Find the equation of the line with 2 and 3 as its x- and y-intercept respectively     [3x+2y-6=0]
8. What is the geometric mean of 3 and 27?     
9. What is the area of a triangle with side 6 cm?    [9 $\sqrt{3} cm^2$]
10. The perimeter of rectangle is 24 cm. The length is twice the measure of the width. What is the dimension of the rectangle?     [4cm x 6 cm]

Average Round – 3 points

1. The ball rolled for a distance of 32 cm in the first second, 16 cm after second seconds, 8 cm in the third seconds and so on. What the distance that the ball travelled before it stops?     [64cm]
2. In triangle ABC, $\angle{A} = 2\angle{B} = 3\angle{C}$. What is the measure of $\angle{B}$ in degrees?    
3. ABC is a right triangle with right angle at B. AB=3, BC=4 and AC=5. D is on AC such that AD=DC. How long is BD?     [5/2 or 2.5]
4. For what value/s of k does the line $kx-9y-1=0$ is perpendicular to $(k-12)x+4y-6=0$?     
5. Segment AB is divided by P such that AP:BP = 1:3, point A is on (3,1) and B is on (7,5) what is the coordinate of point P?     [(4,2)]

Difficult Round – 5 points

1. The sum of the squares of two numbers is 4 and their product is 9. What is the square of the sum of the numbers?     
2. ABCD is an isosceles trapezoid with $\overline{BC}$ parallel to $\overline{AD}$ and $\angle{A}$ = 60°. $\overline{BC}= 6 cm$ and $\overline{AD} =10 cm$. What is the area of the trapezoid in square centimeter?     [16√3]
3. 20! = 20x19x18x17x…x2x1 has k zeroes at the end of it. What is the value of k?    
4. Find the surface area of the cube in cm2 with a volume equivalent to a rectangular prism with dimension 8cm by 16 cm by 32cm.    
5. Find the area of a circle inscribed in a triangle with sides 5,12,13 in cm. Give the answer in terms of π.     [ 4π sq. cm]