# 2015 Grade 8 MTAP Math Challenge – Division Orals

Below are the 2015 Grade 8 MTAP Math Challenge Division Oral Competition questions with answers.

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

1.) What is the slope of the line that passes through the points (-1, 0) and (1, -6)?

Answer: -3

2.) Which one is the largest, 3.2, 10/3, π?

Answer: 10/3

3.) A furniture shop offers a 15% discount in all its terms, and a sala set was marked Php 14, 000. What was the selling price of the sala set?

Answer: Php 11, 900

4.) Solve for *x* in the equation |1 – *x*| = 8.

Answer: 9, -7

5.) If , what is ?

Answer: 4

6.) Factor completely the algebraic expression .

Answer:

7.) Find the least integer that satisfies the inequality .

Answer: 0

8.) Given an angle A, what is the supplement of the complement of A?

Answer: 90° + A

9.) The operation is defined as . What is ?

Answer: -6

10.) What is the quotient when is divided by ?

Answer:

11.) Ana can paint their bedroom in 4 hours, while her older sister, Carla, can paint it in 3 hours. If they work together, what part of the bedroom can they paint in half an hour?

Answer: 7/24

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

1.) A man started walking at a constant rate of 50 meters per minute. After 30 minutes, from the same point where the first man started, another man started jogging at a constant rate of 120 meters per minute. After 20 minutes more, who is ahead? By how many meters?

Answer: First man, by 100 meters.

2.) How far from the origin is the point midway between the points (1, 2) and (-3, 6)?

Answer: √17 units

3.) When is divided by , what is the remainder?

Answer:

4.) Find the equation of the line, in slope-intercept form, that passes through the points (-1, 0) and (1, -6).

Answer: *y* = -3*x* – 3

5.) Triangle ABC has sides 13, 13, and 10 cm long. What is the area of the triangle?

Answer: 60 sq. cm.

6.) Find all integers x that satisfy the inequality

Answer: -6, -5, -4, 6, 7, 8

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

1.) Find the point of intersection of the lines and .

Answer: (-1; 4)

2.) Simplify: .

Answer: 0

3.) What is the area of the region described by the inequalities *x* ≥ 0, *y* ≤ 2x, and 2*y* + 6 ≥ *7*x?

Answer: 3 square units

4.) Find the domain of the function

Answer: {x| – 3/2 ≤ x < 0 or x > 0}

5.) State the inverse of the statement “If P(x) ≥ 0 for all x ∈ R, then x < 0 for some x ∈ R.”

Answer: If P(x) < 0 for some x ∈ R, then x ≥ 0 for all x ∈ R.

6.) The sides of a right triangle are x, x + y, and x + 2y, where x and y are positive numbers. What is the ratio of y to x? Answer: 1:3

**Clincher Question**

1.) What is the sum of the x- and y-intercepts of line ?

Answer: 7

2.) In ∆ABC, half of ∠A is 30° less than ∠B, and ∠C is twice the complement of ∠A. What kind of triangle is ∆ABC?

Answer: Equilateral or equiangular.

3.) In tossing a pair of dice and a pair of coins simultaneously, what is the probability of getting a sum of 6, a tail, and a head?

Answer: 5/72

**Do or Die Question**

In the equations and , where , what is the least possible integral value of ?

Answer: 2

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