Practice Math Challenge Question for 3rd Year – Orals

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Easy Round – 2 points

  1. How many diagonals does regular nonagon have?     [27]
  2. The interior angle of a regular polygon is 170°. How many sides does the polygon have?     [36]
  3. What is the larger value of x in x^2-x-6=0?     [3]
  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?     [12]
  5. What is the area in square centimeter of a kite with diagonals measuring 20 cm and 10 cm?     [100]
  6. What is the last two digit of 5^{2013}?     [25]
  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]
  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?    [54]
  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?     [6]
  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?     [22]
  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]
  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.    [1536]
  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]

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