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 
3.) What should be the value of 
4.) What is the reciprocal of ![\sqrt[3]{9}- 2](http://s0.wp.com/latex.php?latex=%5Csqrt%5B3%5D%7B9%7D-+2&bg=ffffff&fg=000&s=0 "\sqrt[3]{9}- 2")
5.) If 
6.) What is the smallest positive integer n which satisfies 
7.) Find 
8.) Find the value of 
![[0^\circ, 180^\circ]](http://s0.wp.com/latex.php?latex=%5B0%5E%5Ccirc%2C+180%5E%5Ccirc%5D&bg=ffffff&fg=000&s=0 "[0^\circ, 180^\circ]")
9.) The cube of a number 
10.) Find the smallest positive value of 
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 
5.) A linear function 
6.) If 
Difficult
1.) The numerical value of 
2.) Evaluate the sum 
3.) The roots of 
4.) Solve for
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 
Do or Die Question
1.) Find all possible values of 
Answers
Easy
1.) 56
2.) 
3.) -1
4.)
5.) 1/4
6.) 12
7.) -4
8.) 45°
9.)
10.)
11.)
![3 \sqrt[3]{3}+ 2 ^3\sqrt[3]{9} + 4](http://s0.wp.com/latex.php?latex=3+%5Csqrt%5B3%5D%7B3%7D%2B+2+%5E3%5Csqrt%5B3%5D%7B9%7D+%2B+4&bg=ffffff&fg=000&s=0 "3 \sqrt[3]{3}+ 2 ^3\sqrt[3]{9} + 4")
Average
1.) (0, 8) ∪ (8, inf)
2.) 1/19
3.) -1/6
4.) 4
5.) 360
6.) 
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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Good morning can i have detailed solutions for this? Thanks, please email it here masterjed7262@gmail.com