# 2015 Grade 7 MTAP Sectoral Level

This is the 2015 Metrobank-MTAP-NCR Math Challenge Sectoral Level for  Grade 7. Please inform me if you see any errors.

More past tests can be found here. If you have old tests, kindly send it to mtapreviewers@gmail.com, so we can share it here with answers/solutions.

QUESTIONS

Easy

1.) What number must be added to -5 × -10 to produce -7 × 8?

2.) Find the area of a triangle with base 2x + 2 cm ad height 2x + 1 cm.

3.) The sum of two primes is 16. What is the largest possible value of their product?

4.) In a quadrilateral, 3 interior angles have measures 87°, 89°, and 91°. Find the fourth angle.

5.) What is the sum of $(x + 3) (x - 3)$ and $(x + 3)^2$?

6.) By what percentage will the volume of a cylinder increase or decrease, if the radius is decreased by 10% and the height increased by 10%?

7.) With what integer must -54 be divided by to get a remainder of 11 and a quotient of -5?

8.) The sum of n numbers is 50n. If each number is increased by 50, what is the new sum?

9.) How many integers n are there for which |n – 5| < 11?

10.) The sum of two numbers is 10 and the sum of their reciprocal is 5/3. Find their product.

11.) What is the largest integer smaller than $\sqrt{125}$

Average

1.) If $x^2 - 1 = 4$, evaluate $\displaystyle \frac {x^6 + 3x^4}{x^4 + 2x^2 + 5}$.

2.) The base of a rectangle box has dimensions 30 cm and 45 cm. A cube, with side length 6cm, is submerged in the water inside. By how much will the water level rise?

3.) A rectangle has area 48 sq. units. The midpoints of two adjacent sides, and the common vertex of the other two sides, are connected to form a triangle. Find its area.

4.) The angles of a triangle are (4x – 13)°, (4x + 21)°, (5x – 23)°. Find the largest angle.

5.) A right triangle has legs 5 cm and 12 cm long. A bug, as it travels around it, is always 3 cm away from the triangle. What is the length of the bug’s path?

6.) The product of two numbers is $98,000z^5y^4$ and their greatest common factor is $70x^2y$. What is their least common multiple?

Difficult

1.) A car and a truck, 500 km apart, drive towards each other until they meet, with the car driving at 90 km/hr, and a truck at 60 km/hr. How fast should the car drive for its return trip to take 2 hours?

2.) If n isa a constant such that ||x – 2|-3| = n has exactly 3 distinct roots, what are these roots?

3.) If $p + q \neq 0$, solve for x: $\frac {x - 3p}{q} + \frac {x - 2q}{p} = 5$

4.) The sum of 4 numbers is 75. If the number 4 is added to the first, subtracted from the second, multiplied to the third, and used as the divisor for the fourth, the resulting numbers are all equal. What are the 4 original numbers, in order?

5.) The figure shown is formed by joining 4 semicircles. If AC = 18 and BD = 14, find the area of the enclosed region.

Note: No figure from source

6.) Arrange these numbers in ascending order: $p = 3^{120}$, $q = 4^{96}$, $r = 5^{72}$, $s = 6^{48}$.

Clincher

1.) What number is exactly midway between -35 and 3 on the number line?

2.) What must be multiplied to x + 3 so the product is 10 less than the product of x + 1 and 3x + 4?

3.) The medians to two legs of a right triangle are 6 and 7 units long. How long is the hypotenuse?

Do or Die Question

1.) $\frac {1 + 2}{1 + 2 + 3} \times \frac {1 + 2 + 3 + 4}{1 + 2 + 3 + 4 + 5} \times \cdots \times \frac {1 + 2 + \cdots 14}{1 + 2 +\cdots+ 15}$.

Easy
1.) -106
2.) $2x^2 + 3x + 1$ sq. cm.
3.) 55
4.) 93°
5.) $2x^2 + 6x$
6.) decrease by 10.9%
7.) 13
8.) 100n
9.) 21
10.) 6
11.) 11

Average
1.) 5
2.) $\frac {4}{25} = 0.16 cm$
3.) 18 sq. units
4.) 81°
5.) 6π + 30 cm
6.) $1400x^3y^3$

Difficult
1.) 150 km/hr
2.) -4, 2, 8
3.) x = 3p + 2q
4.) 8, 16, 3, 48
5.) 63π sq. units
6.) s, r, p, q

Clincher
1.) -16
2.) 3x – 2
3.) $2\sqrt{17} or \sqrt{68}$

Do or Die
1.) 1/8