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MENTAL MATH 2016 FAMAT STATE CONVENTION
10  10 
10 
      ...   ?
0 1
10 
________1.
________2.
11! ?
________3.
4315  ______ 10
________4.
92 108  ?
________5. Express
9 1
+
11 2
1 1
+
3 4
________21. What is the 10th pentagonal number?
________22. What is the area of a regular hexagon with
sides of length 2?
________23. A circle is inscribed in a square, which is
then inscribed in another circle. What is the
ratio of the radius of the larger circle to the
radius of the smaller circle?
________24.
as an improper fraction.
________6. What is the sum of the coefficients of the
expansion of
________20. What is the sum of the first 5 triangular
numbers?
( x  y  z )1337 ?
________7. How many factors does 144 have?
________8. What is the sum of the squares of the
solutions of
95 2  ?
________25. Is 145911387 divisible by 11?
________26. What is the sum of the reciprocals of the
roots of
x1337  2 x  1  0 ?
________27. What is the area of a triangle with side
lengths 4, 6, and 8?
x -3 = 4?
________28. What is the sum of the roots of
________29.
1 1 1
  ?
2 3 6
________30.
1  2  3  ...  50  ?
________31.
312  ?
________32.
2 x  32 and x 2 z  25 , then
x2  z2  ?
________12. In how many ways can 5 people sit around
_a round table?
________33.
33 121  ?
________13. How many permutations are there of the
letters of the word “MENTAL”?
________34.
4134
?
3
________14. What is the average of 4,9,5,2?
________35. Write 104 (base 10) in base 5.
________15. How many terms are there in
________36.
x1337  2 x1336  2 x1335  1337  0 ?
________9. How many diagonals does a convex 12-gon
have?
________10.
________11.
1
3
3 2  ?
5
16
1  8  27  ....  729  ?
( x  3 y  z) 4 ?
________16.
________17.
143  9999  ?
114  ?
________18. Joe does a job in 10 minutes. John does the
same job in 5 minutes. How long (in
minutes) does it take them to complete 3
jobs working together?
2013  (a)(b) , a  b  ?
(a and b are
both prime positive integers)
________37. What is the units digit of the expansion
1337
of 5
?
________38. What is the maximum number of regions
that 5 lines can divide the interior of a
circle into?
________39. What is the area of the triangle with sides
of length 4 and 6 and an included angle of

________19. How many positive prime numbers are
there that are less than 50?
________40.
?
3
x
2  32 , so x  ?