2015 MMC Grade 9-Orals Questions

To those who are looking for the 2015 Grade 9 oral question, here it comes. For those who wanted to send a copy of reviewer for grade 7 and grade 8. Please send it to techiemathteacher@gmail.com. I will take care to to type and post it here.

15-sec: 1 point each
1. Determine all positive number x that satisfy 5x^2-10x. [x=2]
2. What is the fourth power of sqrt(2+sqrt(2))? [6+4*sqrt(2)]
3. Simplify: 4^(-k/2) * 8^(k-1)/3 [ 3/2^k]
4. If a*b=sqrt(a^2+b^2). What is the value of (3*4)*12 [13]
5. Suppose that x,y, and z are positive integers such that xy=6, xz=10, and yz=15. What is the value of xyz? [30]
6. The yearly changes in the population of a certain town for two consecutive years are 20% increase on the first yead and 20% on the second year.
What is the net change in percent over the two-year period? [4% decrease]
7. What is the slope of the line perpendicular to 2x+5y+2=0 [-2/5]
8. The area of a triangle is 100 cm^2. What will be its area if its altitude is increased by 10% and its base is decreased by 10%? [99 cm^2]
9. The sum of two consecutive numbers is 2015. If 9 is added to each of the numbers and then each of the resulting number is doubled, what is the sum
of the final two numbers? [4066]
10. A square and a triangle has have the same perimeter. If the square has area of 144 cm^2, what is the area of triangle? [64*sqrt(3) cm^2]
11. Let r and s be the solution of x^2-3x+1=0. What is the value of (r+1)(s+1)? [5]

30-second question: 3 points each

1. If f(x)=x^2=x+1, find the sum of all number that y satisfies f(2y)=2. [1/2]
2. A man walks 1 km east and then 1 km northwest. How far is he from his strating point? [sqrt(2-sqrt(2))]
3. Four men working for four days can paint 4 cars. How many cars can 6 men working for 6 days paint? [9 cars]
4. The longer base of a trapezoid measures 10 cm and the line segment joining the midpoint of the diagonals measures 3 cm. What is the lenght of the shorter base? [4 cm]
5. What is the least possible value for x^2+3x+2 if x^2-3x-2=0? [6]
6. The point D is the midpoint of the side BC of equilateral triangle and E is the midpoint of AD. How long is BE if a side of triangle ABC measures 8 cm? [2sqrt(7)]

1-minute question: 5 points each

1. If the root of x^2+nx+m=0 are twice those of x^2+mx+1=0, what is the value of n? [8]
2. The lengths of the sides of a traingle are 10,17 and 21 cm. How long is the altiture of the triangle to the longest side? [4*sqrt(70)/5]
3. Traingle ABC is isoceles if Angle A is 50 degrees, what are the possible measures of angle B? [50 deg, 80 deg]
4. The medians AD and BE and triangle ABC are perpendicular. Find the length of AB if BC=3 cm and AC= 4 cm. [sqrt(5) cm]
5. The product of three consecutive positive integers is 16 times their sum, What is the sum of the three numbers? [21]
6. Point E is on the side AC of triangle ABC and points D and F are chosen on the side AB such that DE||BC and EF||CD. Find the length of BD if AF=FD=3 cm [6 cm]

Clincher Questions:
1. In triangle ABC, angle C=30 deg. If D is the foot of the altiture from A to BC and E is the midpoint of AC, find the measure of angle EDC. [30 deg]
2. One candle will burn completely at a uniform rate in 4 hours while another in 3 hours. At what time should the two candles be simlutanously lighted so that the one will be half the lentgth of the other at 6:00 PM [3:36 PM]
3. Points P and Q are drawn on the sides BC and AC of triangle ABC such that angle AQB and angle APB measures 110 deg and 80 deg respectively. If point R is chosen inside triangle ABC such that AF and BR bisects angle CAp and CAQ respectively, what is the measure of angle ARB? [95 deg]

Do or Die Question:
Point E is the midpoint of side BC of triangle ABC and F is the midpoint of AE. The line thru BF intersects AC at D. Find the area of triangle AFD if the area of the triangle is 48 cm^2? [4 cm^2]

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