Download 07-08 Match 3 Questions

Match 3 Round 1 – Arithmetic: Bases & Scientific Notation
Please note: The symbol 12 B represents a 2-digit number in base B
1.) What number does 412345 represent in base 10?
 7.5 10  4.5 10 
1.5 10 
4
8
2.) Calculate
3.) Find the quotient
Write your answer in scientific notation.
7
353527
5017
Write the answer in base 7.
Match 3 Round 2 –Algebra 1: Word Problems
1.) Jennifer walks from P to Q at an average rate of 3 miles per hour. She then walks from Q to R at
an average rate of 4 miles per hour. The total time for the journey is 2 hours. The distance from Q to
R is twice the distance from P to Q. What is the distance from P to Q?
2.) An alloy consisting of 90% gold and 10% silver is to be mixed with a second alloy consisting of
70% gold and 30% silver to make 40 grams of an alloy consisting of 84% gold and 16% silver. How
many grams of the first alloy are needed?
3.) The sum of David’s and Jim’s ages now is 65. When David is as old as Jim is now, twice Jim’s
age minus David’s age at that time will be 110. How old is David now?
Match 3 Round 3 – Geometry: Polygons
1.) Find the number of diagonals in this nonagon:
2.) A regular hendecagon (11-gon) with one of its long diagonals is shown. Find EFA .
3.) Given a polygon P, define a “super-polygon” S as the polygon that results when all of P’s sides are
dented out into halves of regular hexagons. Fins the area of a super-super-square of side length 1
(shown at right).
Match 3 Round 4 – Algebra 2: Functions & Inverses
1.) Let f ( x) 
ax  b
ax
and g ( x) 
.
a b
b
Find f  g (a  b)  , where a and b are real numbers, a  b .
2.) If f (1)  5 , f (2)  0 , and f (n)  f (n  1)  f (n  2) , where n is a natural number, what is the
smallest value of n such that f (n)  5n ?
3.) If h( x  2)  4 x  3 , find h1 (4 x  5) .
Match 3 Round 5 – Trig and Adv. Topics: Exponential & Logarithmic Expressions & Equations
1.) Solve for x: x log 2 4  log3 81
2.) Solve for y:
 log3 x  log x 2x  log2 x y   log x x2
3.) Solve for x: 3x  3x2  24 3
Match 3 Round 6 – Coordinate Geometry & Discrete Mathematics: Matrices
 2 x 2  1 4 6 6
1.) Find the values of x, y, and z if 



 1 z   2 y 3 5 0 
5 2
 2 4
2.) If A  
and B  

 , find the determinant of the matrix 2 A  3B  AB
 1 3
 1 3 
1 5 
2
3.) If matrix B  
 , find all possible matrices A such that A  B
0
9


Match 3 Team Round
1.) A convex P-gon has Q diagonals, a convex Q-gon has R diagonals, and a convex R-gon has 2849
diagonals. Find P.
2.) Multiply 13678 by 428 and write the answer in base 6.
3.) When Allen and Ben work together, they take 2.4 hours (2 hours 24 minutes) to do a job. When
Ben and Charlie work together, they take 4 hours to do the same job. When Allen and Charlie work
together, they take 3 hours to do the same job. If Allen were to do the job alone, how long would he
take?
 x
4.) Given the function f ( x)  log 2   and a function g ( x)  f 1  f 1 ( x)  , for what value(s) of x
4
does g ( x)  1024 ?
5.) Solve for all real ( x, y ) :
log x 4  log y 3  5
log x 8  log y 9  13
6.) For any matrix A , the matrix At denotes the transpose of matrix A . At is the matrix having the rows of
A as its corresponding columns and the columns of A as its rows.
 2 1
 2 3
For example, if A  
, then At  

.
3 4 
 1 4
Here is your problem:
 x 1
 1 2 0 
1 0 1 




If A  1 0 , B  
, and C  1 1 0 , find the non-zero values of x and y





1 1 0 
 0 y 
 0 2 1 


such that det  AB  C   4 and det ( AB)t  C  0