# 2015 Grade 9 MTAP Math Challenge – Division Orals

Below are the 2015 Grade 9 MTAP Math Challenge Division Oral Competition questions with answers.

**15-second question (2 points each)**

1.) Determine all positive number x that satisfy .

Answer: x = 2

2.) What is the fourth power of ?

Answer:

3.) Simplify

Answer:

4.) If a ♠ b = , what is the value of (3 ♠ 4) ♠ 12?

Answer: 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*?

Answer: 30

6.) The yearly changes in population of a certain town for two consecutive years are 20% increase on the first year and 20% decrease on the second year. What is the net change in percent over the two year period?

Answer: 4% decrease

7.) What is the slope of the line parallel to 2*x* + 5*y* + 2 = 0.

Answer: -2/5

8.) The area of a triangle is 100 sq. cm. What will be its area if its altitude is increased by 10% and its base is decreased by 10%?

Answer: 99 sq. cm.

9.) The sum of two numbers is 2015. If 9 is added to each of the numbers and then each of the resulting numbers is doubled, what is the sum of the final two numbers?

Answer: 4066

10.) A square and a triangle have the same perimeter. If the square has area 144 sq. cm., what is the area of the triangle?

Answer: sq cm.

11.) Let r and s be the solutions of . What is the value of ?

Answer: 5

**30-second question (3 points each)**

1.) If , find the sum of all numbers y that satisfies .

Answer: 1/2

2.) A man walks 1 km east then 1 km northwest. How far is he from his starting point?

Answer: 2-√2 km

3.) Four men working for four days can paint 4 cars. How many cars can 6 men working for 6 days paint?

Answer: 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 length of the shorter base?

Answer: 4 cm

5.) What is the least possible value of ?

Answer: 6, -1/4

6.) The point D is the midpoint of the side BC of equilateral triangle ABC and E is the midpoint of AD. How long is BE if a side of ∆ABC measures 8 cm?

Answer: 2√7 cm

**1-minute question (5 points each)**

1.) If the roots of are twice those , what is the value of n?

Answer: 8

2.) The lengths of the sides of a triangle are 10, 17 and 21 cm. How long is the altitude of the triangle to longest side?

Answer:

3.) Triangle ABC is isosceles. If ∠A = 50°, what are the possible measures of ∠B?

Answer: 50°, 80°

4.) The medians AD and BE of ∆ABC are perpendicular. Find the length of AB if BC = 3 cm and AC = 4 cm.

Answer: √5 cm

5.) The product of three consecutive positive integers is 16 times their sum. What is the sum of the three numbers?

Answer: 21

6.) Point E is on the side AC of ∆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.

Answer: 6 cm

**Clincher Question**

1.) In ∆ABC, ∠C = 30°. If D is the foot of the altitude from A to BC and E is the midpoint of AC, find the measure of ∠EDC.

Answer: 30°

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 simultaneously lighted so that one will be half the length of the other at 6:00 PM?

Answer: 3:36 PM

3.) Points P and Q are drawn on the sides BC and AC of triangle ABC such that ∠AQB and ∠APB measures 110° and 80° respectively. If point R is chosen inside ∆ABC such that AR and BR bisects ∠CAP and ∠CAQ respectively, what is the measure if ∠ARB?

Answer: 95°

**Do or Die Question**

Point E is the midpoint of the side BC of ∆ABC and F is the midpoint of AE. The line thru BF intersects AC at D. Find the area of ∆AFD if the area of the triangle is 48 cm^2.

Answer: 4 cm^2

KINDLY INCLUDE THE SOLUTION

I will, soon.

Please kindly include solutions. Thank you

may I ask for the reviewers of grade 7-division orals

.please include the solution.

Good day. Please kindly upload solutions. Thank you

Solutions please😀😀

is this able to download.

kindly post the solutions.thank you..

Give the solution cuz we have mtap finals tomorrow and I really need it til dawn. P.S. I am not cheating. If ever you have the leaked files for 2017, kindly send it to me. P.S. just a friendly request.