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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