Download 04-05 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 4321five represent in base 10?
2.) Find the product of 1.5 104  2.5 105  4 106  in scientific notation.
3.) What base is B if 132B equals 812 in base 10 ?
Match 3 Round 2 –Algebra 1: Word Problems
1.) Elaine and Fred both leave school at 3 p.m. and bicycle in opposite directions. Elaine travels at 10
mph and Fred travels at 8 mph. At what time will they be 6 miles apart?
2.) You need to have 30 ml of a 40% alcohol solution for an experiment. You have a 20% solution
and pure alcohol. How much of each should you mix?
3.) Emily hikes up a mountain at a rate of 1¼ miles per hour, then comes down the same mountain at a
rate of 3 mph. If her total time was 5 hours, how long is the trail (one-way)?
Match 3 Round 3 – Geometry: Polygons
1.) The figure shows kite ABCE and regular hexagon ABCDEF. Find the measure of AEC .
2.) The total number of interior angles in two regular polygons is 17, and the total number of
diagonals is 53. How many sides does each regular polygon have?
3.) Find the perimeter of a regular polygon if each exterior angle is 10 degrees less than
angle and each side has length 8 cm.
1
an interior
6
Match 3 Round 4 – Algebra 2: Functions & Inverses
1.) f ( x)  3x 2  7 and g ( x)  4  x . Find f ( g ( x)) .
2.) f ( x)  2 x 2  5 x  3 . Find the domain of f 1 ( x) .
3.) The function f ( x) is a linear function which satisfies the equation f (1  x)  3 f ( x)  2 x . Find
f ( x) .
Match 3 Round 5 – Trig and Adv. Topics: Exponential & Logarithmic Expressions & Equations
1.) What is the value of log 7  log
1
?
49
2.) Solve for x: log10  200  log x 32   3
3.) Solve for x: 9 x  2  9 x  2214
Match 3 Round 6 – Coordinate Geometry & Discrete Mathematics: Matrices
 2 p 5  1 4 0   3 1 5
1.) Find the values of p, q, and r if 



 q 8 3  p 2  q   1 6 r 
 4 5 
0 2 
2.) Find the determinant of AB if A  
and B  


 3 1
 4 1
3.) In a point matrix, row 1 represents the x-values and row 2 represents the y-values of points in the
a c e 
coordinate plane. For example, the matrix 
 represents a triangle with vertices (a, b) ,
b d f 
(c, d ) , and (e, f ) . Matrix operations can perform transformations on figures in the coordinate plane.
0 1  0 2 4 
If the matrix multiplication 

 is performed, identify the type of transformation
1 0 3 1 2
(reflection, rotation, or translation) that took place on the figure represented by the second matrix, and
also identify the line of reflection or the angle and center of rotation or the distance and direction of the
translation.
Match 3 Team Round
1.) Write 1623seven in base four.
2.) A train leaves Union Station for Suburban Station, 351 miles away, at 9 a.m. One hour later, a
second train leaves Suburban Station for Union Station. They pass on the tracks at 1 p.m. If the
second train had started at 9 a.m., and the first train at 9:50 a.m., they would still have passed each
other at 1 p.m. Find the speed of each train.
3.) The interior angles of two regular polygons are in the ration 3:2. One of the polygons has 15 more
sides than the other. How many sides does each polygon have?
4.) If f ( x)  3 x and g ( x)  ln( x  2) , find the domain of f ( g ( x)) .
5.) If log10 2  a and log10 3  b , find an expression for log5 12 in terms of a and b .
 0 1 2 
6.) Find the inverse of the matrix  1 5 4


 3 0 6 