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ALGEBRA 2
TEST REVIEW
PERMUTATIONS
COMBINATIONS
AND
PROBABILITY
VHHS
SPRING 2016
1. ROLL TWO STANDARD DICE:
A. MAKE A SAMPLE SPACE FOR THE POSSIBLILTIES
B. FIND THE PROBABILITY OF ROLLING A 10
C. FIND THE PROBABILITY OF NOT ROLLING A 10
D. FIND THE PROBABILITY THAT THE SUM IS
LESS THAN OR EQUAL TO 8
F. DESCRIBE A SITUATION IN RELATION TO THE
SAMPLE SPACE THAT RESULTS IN A
2
PROBABILITY OF
3
2. A SACK CONTAINS THE BALLS FROM A POOL
TABLE, I.E., BALLS MARKED FROM ONE THRU
FIFTEEN. SEVEN ARE STRIPPED AND 8 ARE SOLID.
FIND THE PROBABLITIES.
A. YOU RANDOMLY PULL A BALL FROM THE BAG
AND REPLACE IT. THEN YOU DRAW A SECOND BALL.
1ST EVENT: YOU DRAW A STRIPPED BALL
2ND EVENT: YOU DRAW A SOLID BALL.
B. YOU DON’T REPLACE THE FIRST BALL
1ST EVENT: THE FIRST BALL IS 5
2ND EVENT: THE SECOND BALL IS GREATER THAN 8
3. A BOX CONTAINS 8 CHOCOLATE AND 10 VANILLA
COOKIES. A COOKIE IS TAKEN FROM THE BOX
AT RANDOM AND EATEN. A SECOND COOKIE IS
TAKEN AT RANDOM AND EATEN. WHAT IS THE
PROBABILITY THAT BOTH COOKIES
WERE VANILLA?
4. HOW MANY PERMUTATIONS ARE THERE
FOR THE LETTERS IN THE WORD:
A. BOOKKEEPER
B. ADDRESSEE
C. SLEEPLESSNESS
5. HOW MANY WAYS CAN YOU ARRANGE
8 KNICKKNACKS ON A SHELF?
6. SUPPOSE YOU NEED TO SEND 5 STUDENTS
TO REPRESENT YOUR CLASS AT THE NEXT
ASSEMBLY. HOW MANY WAYS CAN YOU
CHOOSE THE 5 STUDENTS FROM 28 STUDENTS?
7. IF THERE ARE 35 PEOPLE RACING BICYCLES
FROM HERE TO THE TOP OF MOUNT WILSON,
HOW MANY WAYS CAN THEY COME IN
FIRST, SECOND AND THIRD?
8. YOU ARE SENDING IN SAMPLES OF YOUR ART
IN ORDER TO BE CONSIDERED FOR ENTRANCE TO
AN ART SCHOOL. THE SCHOOL WANT TO ONLY
CONSIDER 5 OF YOUR PIECES. HOW MANY WAYS
CAN YOU CHOOSE 5 ART PIECES FROM 18?
9. YOU ARE STACKING BOXES SO THAT EACH
ROW HAS TWO MORE BOXES THAN THE PREVIOUS
ROW. IF THE BOTTOM ROW OF YOUR STACK
HAS 45 BOXES, HOW MANY BOXES CAN YOU
STACK USING THE GIVEN PATTERN.
10. GIVEN THE FOLLOWING FUNCTION:
f ( x)  x  5 x  4 x  20
3
2
a. STATE THE END BEHAVIORS OF THE FUNCTION
b. FACTOR THE FUNCTION COMPLETELY
c. FIND ALL ZEROS OF THE FUNCTION
d. SKETCH THE GRAPH OF THE FUNCTION
11. SIMPLIFY
x
8x
 2
x  5 x  2 x  15
12. KNOW WHAT AN INDEPENDENT AND
DEPENDENT EVENT IS.
13. KNOW THAT A PERMUTATION IS AN
ORDERING AND FOR A COMBINATION
ORDER DOESN’T MATTER.
14. The number of unique orderings of the
Letters {2,4,6,8} is?
15. How many times does the following
Function bounce off the x-axis.
f ( x)   x  4  ( x  3) ( x  5)  x  3
2
6
4
16. SIMPLIFY THE FOLLOWING
a. 3 98
b.
3
128
c. 27  48
d . 64
1
3
e. 122
17. SIMPLIFY THE FOLLOWING
A. 64
1
3
B. 12
2
C.  6 x y
2
4
 4 x y 
28 x 4 y 8
D.
4 2
14 x y
5
7 2
18. USING THE FORMULA, FIND THE SUM OF THE
FIRST 8 TERMS OF THE FOLLOWING SEQUENCE:
{4,8,16,32...}
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