# 4th Year Sample Math Challenge Questions – Oral

This is not the official reviewer. If you were able to answer most of these questions correctly that means you are ready for the final round. Remember! the winner’s secret is their speed and accuracy to answer the questions. Speed and accuracy is achieve if you are familiar of the problem. Have fun. Please watch this video from the Raytheon Mathcounts Championship.

EASY

1. ABCD is a quadrilateral inscribed in a circle. $\angle{A} = x$ and $\angle{C} =3x$. How many degrees is $\angle{A}?$     [45]
2. What is the maximum of $y=16-x^2$     [16]
3. cos15° =  $\displaystyle\frac{\sqrt{a}+\sqrt{b}}{c}$. Find a+b+c.     [12]
4. The area of hexagon with side 4 cm can be expressed in the form of $a\sqrt{b}$ What is a+b?    [27]
5. The sum of x and y is 10. If x is 2 more than y. What is 2x+y?    [16]
6. If $x^2+3x-1=0$ what is the value of $x^2 +\displaystyle\frac{1}{x^2}$?          [11]
7. What is the 2nd term of the expansion of $(x-2y)^5$?    [-10x4y]
8. Find the quadratic equation with integral coefficients if one root is $\sqrt{3}$      [x2-3=0]
9. ABCD is a square inscribed in a circle with diameter 8. What is the area of the square in sq. units?      [32]
10. What is the sum of the roots of equation $5-2x-x^2=0?$     [-2]

AVERAGE

1. If $f(x) = 2014x^{2014}+2013x^{2013} +2012x^{2012}+\ldots+3x^3+2x^2+x+1$ what is the value of f(-1)?    [1008]
2. If $4sin^2x-1=0$ what is the value of x in degrees in the interval [90°,180°]     [150°]
3. Sam tossed 3 dice, what is the probability of getting a sum of 17 given that the first die shows 6.     [1/18]
4. Evaluate   $\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\ldots}}}}$     [2]
5. Circles A and B have radii 5 and 7, respectively, and the distance between their centers A and B is 6. If the two circles intersect at points M and N, $MN=a\sqrt{b}$ What is a+b?[10]

DIFFICULT

1. Solve for x: $x^3-7x+6=0$    [-3,1,2]
2. John can row in the river downstream 20 km in 2 hours and went back in 5 hours. What is the rate of John in kph?    [7]
3. Given that log3 = 0.477, how many digits are there if we expand 9^50?    [48]
4. ABC is an isosceles triangle, AB=BC=6. $\angle{ABC}=120$. $\overline{AC}=a\sqrt{b}$. What is a+b?    [9]
5. Find the equation of a perpendicular bisector of points (2,3) and (4,1). Express your answer in ax+by+c=0.     [x-y-1=0]