2015 Grade 8 MTAP Sectoral Level

This is the 2015 Metrobank-MTAP-NCR Math Challenge Sectoral Level for  Grade 8. Please inform me if you see any errors.

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Easy

1.) What is the slope of the line with equation 4x + 3y - 2 = 0?

2.) Arnold is 7 years older than her sister Rica. If Arnold will turn 36 seven years from now, how old is Rica now?

3.) Solve for x in the equation 2(x + 2) + x = 2x + 3.

4.) Find the area of the triangle bounded by the line 2x + y = 4 and the coordinate axes.

5.) Factor completely: x^3y - zy^3.

6.) If the base angles of an isosceles triangle measure 2x and 3x - 20 degrees, find the measure of the vertex angle.

7.) If f(x) = x^2 - 3x + 1, what is f(-1) + f(0)?

8.) If the sides of a triangle have integral lengths, and its perimeter is 13 cm, what is the largest possible length of one side?

9.) What is the probability of getting a sum of 5 in rolling a pair of dice?

10.) If zy = 13 and x + y = 10, what is x^2 + y^2?

11.) Find the distance between the points (2, 1) and (-3, 4).

Average

1.) Find the measure of the acute angle between the hour and the minute hands of 12:15 PM.

2.) If \displaystyle \frac {1}{x + 1} + \frac {1}{(x + 1)^2} + \frac {1}{(x + 1)^3} = \frac {A}{(x + 1)^3}, what is A?

3.) Christine can paint a whole table in 50 minutes, while Vicky can do it twice as fast as Christine. If they continuously work together, how ling will it take them to finish 15 such tables?

4.) If ab = 3 and a - b = 7, what is a^4b^2 - 2a^3b^3 + a^2b - ab^2?

5.) One leg of an isosceles right triangle measures 12 cm. What is the area of the circle that passes through the vertices of the triangle?

6.) Which integer values of x satisfy 3x + 1 < 2x + 11 \leq  4x - 3?

Difficult

1.) If x is the largest negative integer that satisfies 17 < |2x - 1| < 20, what is 2 - 3x>

2.) What is the equation (in the form y = mx + b) of the perpendicular bisector of the segment joining the points (4, -2) and (-1, 4)?

3.) James jogs every morning, while Dina cycles on the same route. If Dina’s speed is 3.5 times that of James, and Dina starts 2 hours after James, how many minutes does Dina cycle before she overtake James?

4.) With what polynomial must 6x^4 - 2x^3 + x^2 + x - 5 be divided to get the quotient 2x^2 + 5 and a remainder of 6x + 30?

5.) Let ABCD be a square, and let E, F, G and H be the midpoint of sides CD, AD, AB and BC, respectively. The segments AE, BF, CG, and DH create a smaller square inside ABCD. If the area of this smaller square is 1.5 sq. units, what is the area of ABCD?

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

Clincher 

1.) What is the equation of the line (in the form y = mx + b) that passes through (2, -3) and the origin?

2.) Two consecutive interior angles of a parallelogram measure 7x + 48 and 2x + 90 degrees. What is 6x?

3.) A chemist has two alcohol solutions of the same kind but of different strengths, one with 35% alcohol and another with 50% alcohol. How many liters of each solution must be mixed to produce 60 liters of solution with 40% alcohol?

Do or Die Question

1.) Find all positive integers a, b, c and d that satisfy the equation a = b^2, c^3 = d^2, and c - a = 49.

Answers:

Easy
1.) -\frac {4}{3}
2.) 22 years old
3.) -1
4.) 4 sq. units
5.) xy(x – y)(x + y)
6.) 100°
7.) 6
8.) 6 cm
9.) -\frac {1}{9}
10.) 74
11.) \sqrt{34} units

Average
1.) 82.5°
2.) x^2 + 3x + 5
3.) 250 min
4.) 462
5.) 72π sq. cm.
6.) 7, 8, 9

Difficult
1.) 29
2.) y\frac {5}{6}x - \frac {1}{4}
3.) 48
4.) 3x^2 - x - 7
5.) 7.5 sq. units
6.) 1 : 3

Clincher
1.) y\frac -{3}{2}x
2.) 28
3.) 40 L of 35% alcohol, 20 L of 50% alcohol

Do or Die
1.) a = 24^2, b = 24,c = 25^2, d = 25^3

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