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Speed Math
15 minutes
Name: _________________________
School:________________________
Division:_________________________
__________ 1. What is the largest three-digit number
divisible by 3, 4, 5, and 6?
FAMAT State Convention 2010
__________ 14. Find the radius of the circle
2
2
2  x  3  2  y  5  25 .
__________ 15. How many different three-digit area
codes are possible if all three digits
must be different and the first digit
cannot be zero?
__________ 2. Simplify: 180  45  20
__________ 3. Find the product  loga b logb a  .
__________ 4. Find the solution for 2 x  5  0 .
__________ 5. Find the area of a regular hexagon with
sides of length 3.
__________ 6. A teacher said that his class had 100
students, 24 were boys and 32 were
girls. What number base did the
teacher use in counting the students?
__________ 16. If 2a  5,2b  3 , express log3 10 in terms
of a and b ,expressed as a single
fraction.
__________ 17. Evaluate log16 8 .
__________ 18. How many right triangles with integer
sides have perimeters less than 50?
__________ 19. Find the product of the solutions of
 2 x  1 3x  4 
2
  2 x  1  3x  4   0 .
2
__________ 7. The interior angles of a quadrilateral
are in an arithmetic progression.
If the measure of the largest angle is
five times the measure of the
smallest, find the measure of the
smallest angle in degrees.
__________ 20. If the three-digit number 56x is divisible
by 6, what is the value of x?
A B

__________ 8. Simplify: B A where no denominator
1 1

A B
__________ 22. Find the conjugate of the complex
number 3i14  5i 23 .
__________ 21. Factor completely: x 3  27 y 3  x  3 y .
Give the sum of the coefficient of the
xy term and the constant.
is equal to zero.
__________ 9. Simplify x
2
x
1
 1 using only positive
1
__________ 23. If 2 x  4 y and 3y  81 , what is the value
of x  y ?
exponents.
__________ 10. The interior angle of a regular n  gon is
170 . n 
__________ 11. Find the number of terms in the
sequence : 6, 12, 18, …, 162
__________ 12. Given the parabola y  x 2  4 x  12 . Find
the area of the triangle with vertices at
the vertex, the y-intercept, and the
positive x-intercept of the parabola.
__________ 13. What is the units digit of 712 ?
__________ 24. By how much does the sum of the two
largest two-digit primes exceed the sum
of the two smallest two-digit primes?
__________ 25. Find the simplified fraction equivalent
6 24 3 48 3
   3
to : 10 18 36 24 4
1
4
3
3
2
5