# Practice Math Challenge Question for 3rd Year – Orals

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Easy Round – 2 points

- How many diagonals does regular nonagon have? [27]
- The interior angle of a regular polygon is 170°. How many sides does the polygon have? [36]
- What is the larger value of x in ? [3]
- Adjacent sides of a triangle are 6 and 7. What is the maximum length of the third side if it is an integer value? [12]
- What is the area in square centimeter of a kite with diagonals measuring 20 cm and 10 cm? [100]
- What is the last two digit of ? [25]
- Find the equation of the line with 2 and 3 as its x- and y-intercept respectively [3x+2y-6=0]
- What is the geometric mean of 3 and 27? [9]
- What is the area of a triangle with side 6 cm? [9]
- 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

- 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]
- In triangle ABC, . What is the measure of in degrees? [54]
- 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]
- For what value/s of k does the line is perpendicular to ? [6]
- 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

- 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? [22]
- ABCD is an isosceles trapezoid with parallel to and = 60°. and . What is the area of the trapezoid in square centimeter? [16√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 cm
^{2}with a volume equivalent to a rectangular prism with dimension 8cm by 16 cm by 32cm. [1536] - 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]

### Dan

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