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 2*x* + 2 cm ad height 2*x* + 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 and ?

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

**Average**

1.) If , evaluate .

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 and their greatest common factor is . 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 , solve for x:

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: , , , .

**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 3*x* + 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.) .

**Answers**

Easy

1.) -106

2.) sq. cm.

3.) 55

4.) 93°

5.)

6.) decrease by 10.9%

7.) 13

8.) 100n

9.) 21

10.) 6

11.) 11

Average

1.) 5

2.)

3.) 18 sq. units

4.) 81°

5.) 6π + 30 cm

6.)

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.)

Do or Die

1.) 1/8