This is the 2015 Metrobank-MTAP-NCR Math Challenge Sectoral Level for Grade 10. Please inform me if you see any errors.

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**Easy**

1.) What is the next term in the arithmetic sequence whose first two terms are −18 and then 19?

2.) Express as a single logarithm with base .

3.) What should be the value of if the point where attains its maximum, is also a zero of ?

4.) What is the reciprocal of in simplest terms?

5.) If , what is ?

6.) What is the smallest positive integer n which satisfies ?

7.) Find such that the circle intersects the parabola in exactly three points.

8.) Find the value of in assuming

9.) The cube of a number equals . What is the product of and the square of ?

10.) Find the smallest positive value of such that .

11.) Which real number is not attained by the function ?

**Average**

1.) Find the domain of

2.) Find the 12th term of the harmonic sequence 3/2, 3/7, 4, …

3.) What is the numerical value of ?

4.) An isosceles right triangle, with area sq. cm, has a hypotenuse which also measures cm. Find .

5.) A linear function is such that . What is ?

6.) If , what is ?

**Difficult**

1.) The numerical value of is in between which consecutive integers?

2.) Evaluate the sum .

3.) The roots of are prime numbers. Find .

4.) Solve for in the equation

5.) How many positive integers n are there such that 1n and n/3 are three-digit integers?

6.) For n ≥ 2, the nth term of the sequence equals the sum of all the terms before it. If the eight therm is 320, what the first term of the sequence?

**Clincher Questions**

1.) Solve for x: .

2.) For which real x can we sum the geometric series x, −1, 1/x, …to infinity?

3.) If , , are the prime factors of 2015, find

**Do or Die Question**

1.) Find all possible values of so that the sequence , , becomes geometric.

**Answers**

**Easy**

1.) 56

2.) )

3.) -1

4.)

5.) 1/4

6.) 12

7.) -4

8.) 45°

9.)

10.)

11.)

**Average**

1.) (0, 8) ∪ (8, inf)

2.) 1/19

3.) -1/6

4.) 4

5.) 360

6.) or equivalent

**Difficult**

1.) 6 and 7

2.)

3.) 13

4.) -1, -1/9

5.) 67

6.) 5

**Clincher**

1.)

2.) x > 1 or x < −1

3.) 2

Do or Die

1.) -10, 3

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