FINAL EXAM
MISCELLANEOUS REVIEW
PERIMETER, AREA, SURFACE AREA,
AND VOLUME
QUESTION #1
FIND THE PERIMETER FIGURE BELOW.
ANSWER #1
FIND THE PERIMETER FIGURE BELOW.
P = 8x + 12
QUESTION #2
FIND THE PERIMETER FIGURE BELOW.
ANSWER #2
FIND THE PERIMETER FIGURE BELOW.
P = 11x + 4
QUESTION #3
FIND THE AREA OF THE FIGURE BELOW.
ANSWER #3
FIND THE AREA OF THE FIGURE BELOW.
A = 1.1 in2
QUESTION #4
FIND THE AREA OF THE ORANGE SECTION IN THE
FIGURE BELOW.
QUESTION #4
FIND THE AREA OF THE ORANGE SECTION IN THE
FIGURE BELOW.
A = 201.0 in2
QUESTION #5
THE LENGTH OF A RECTANGLE IS 3 MORE THAN
THE WIDTH. IF THE DIMENSIONS OF THIS
RECTANGLE ARE INCREASED BY 300%.
A)WHAT IS THE AREA OF THE ORIGINAL FIGURE?
B)WHAT IS THE NEW TOTAL AREA?
C)WHAT IS THE AREA OF THE EXPANDED
REGION?
ANSWER #5
THE LENGTH OF A RECTANGLE IS 3 MORE THAN
THE WIDTH. IF THE DIMENSIONS OF THIS
RECTANGLE ARE INCREASED BY 300%.
A)WHAT IS THE AREA OF THE ORIGINAL FIGURE?
A = x2 + 3x
B)WHAT IS THE NEW TOTAL AREA?
A = 9x2 + 27x
C)WHAT IS THE AREA OF THE EXPANDED
REGION?
A = 8x2 + 24x
QUESTION #6
FIND THE VOLUME OF A
RECTANGULAR PRISM IF THE
LENGTH OF THE BASE IS (3X+2),
THE WIDTH OF THE BASE IS (X-1),
AND THE HEIGHT OF THE PRISM
IS (X+4).
ANSWER #6
FIND THE VOLUME OF A
RECTANGULAR PRISM IF THE
LENGTH OF THE BASE IS (3X+2),
THE WIDTH OF THE BASE IS (X-1),
AND THE HEIGHT OF THE PRISM
IS (X+4).
V = 3x3 + 11x2 – 6x - 8
QUESTION #7
USE THE SOLID FROM THE
PREVIOUS PROBLEM AND
DOUBLE THE DIMENSIONS! FIND
THE VOLUME.
QUESTION #7
USE THE SOLID FROM THE
PREVIOUS PROBLEM AND
DOUBLE THE DIMENSIONS! FIND
THE VOLUME.
V = (6x+4)(2x-2)(2x+8)
V = 24x3+88x2-48x-64
(Volume triples when dimensions double)
PROBABILITY
QUESTION #8
A DIE IS ROLLED.
FIND THE PROBABILITY OF EACH OUTCOME.
P(LESS THAN 3)
ANSWER #8
A DIE IS ROLLED.
FIND THE PROBABILITY OF EACH OUTCOME.
P(LESS THAN 3) = 2/6 = 1/3
QUESTION #9
A DIE IS ROLLED.
FIND THE PROBABILITY OF EACH OUTCOME.
P(INTEGER)
ANSWER #9
A DIE IS ROLLED.
FIND THE PROBABILITY OF EACH OUTCOME.
P(INTEGER) = 6/6 = 1
QUESTION #10
A JAR CONTAINS 65
PENNIES, 27 NICKELS, 30
DIMES, AND 18 QUARTERS.
A COIN IS RANDOMLY SELECTED FROM THE JAR.
FIND EACH PROBABILITY.
P(NOT DIME)
ANSWER #10
A JAR CONTAINS 65
PENNIES, 27 NICKELS, 30
DIMES, AND 18 QUARTERS.
A COIN IS RANDOMLY SELECTED FROM THE JAR.
FIND EACH PROBABILITY.
P(NOT DIME) = 110/140
QUESTION #11
A JAR CONTAINS 65
PENNIES, 27 NICKELS, 30
DIMES, AND 18 QUARTERS.
A COIN IS RANDOMLY SELECTED FROM THE JAR.
FIND EACH PROBABILITY.
P(NICKEL OR QUARTER)
QUESTION #11
A JAR CONTAINS 65
PENNIES, 27 NICKELS, 30
DIMES, AND 18 QUARTERS.
A COIN IS RANDOMLY SELECTED FROM THE JAR.
FIND EACH PROBABILITY.
P(NICKEL OR QUARTER)
27/140 + 18/140 = 40/140 = 2/7
QUESTION #12
THE STUDENTS IN A CLASS ARE
RANDOMLY DRAWING CARDS
NUMBERED 1 THROUGH 28 FROM
A HAT TO DETERMINE THE
ORDER IN WHICH THEY WILL
GIVE THEIR PRESENTATIONS.
FIND EACH PROBABILITY.
P(LESS THAN 14)
ANSWER #12
THE STUDENTS IN A CLASS ARE
RANDOMLY DRAWING CARDS
NUMBERED 1 THROUGH 28 FROM
A HAT TO DETERMINE THE
ORDER IN WHICH THEY WILL
GIVE THEIR PRESENTATIONS.
FIND EACH PROBABILITY.
P(LESS THAN 14) = 13/28
QUESTION #13
THE STUDENTS IN A CLASS ARE
RANDOMLY DRAWING CARDS
NUMBERED 1 THROUGH 28 FROM
A HAT TO DETERMINE THE
ORDER IN WHICH THEY WILL
GIVE THEIR PRESENTATIONS.
FIND EACH PROBABILITY.
P(NOT 2 OR 17)
ANSWER #13
THE STUDENTS IN A CLASS ARE
RANDOMLY DRAWING CARDS
NUMBERED 1 THROUGH 28 FROM
A HAT TO DETERMINE THE
ORDER IN WHICH THEY WILL
GIVE THEIR PRESENTATIONS.
FIND EACH PROBABILITY.
P(NOT 2 OR 17)
= 1/28 + 1/28 = 2/28 = 1/14
QUESTION #14
THE STUDENTS IN A CLASS ARE
RANDOMLY DRAWING CARDS
NUMBERED 1 THROUGH 28 FROM
A HAT TO DETERMINE THE
ORDER IN WHICH THEY WILL
GIVE THEIR PRESENTATIONS.
FIND EACH PROBABILITY.
P(13)
QUESTION #14
THE STUDENTS IN A CLASS ARE
RANDOMLY DRAWING CARDS
NUMBERED 1 THROUGH 28 FROM
A HAT TO DETERMINE THE
ORDER IN WHICH THEY WILL
GIVE THEIR PRESENTATIONS.
FIND EACH PROBABILITY.
P(13) = 1/28
QUESTION #15
BRENDAN SPINS A SPINNER
EQUALLY COLORED IN RED,
BLUE, GREEN, AND WHITE AND
ROLLS A FAIR DIE.
WHAT IS THE PROBABILITY THAT
THE SPINNER WITH LAND ON
WHITE SECTION AND DIE WILL
LAND ON 6?
QUESTION #15
BRENDAN SPINS A SPINNER
EQUALLY COLORED IN RED,
BLUE, GREEN, AND WHITE AND
ROLLS A FAIR DIE.
WHAT IS THE PROBABILITY THAT
THE SPINNER WITH LAND ON
WHITE SECTION AND DIE WILL
LAND ON 6?
P(W, 6) = 1/4*1/6=1/24
QUESTION #16
IN A BAG, THERE ARE 3 BLUE, 2
GREEN, AND 5 BLACK MARBLES.
FIND THE PROBABILITY OF
PICKING A BLACK THEN ANOTHER
BLACK, WITHOUT REPLACEMENT.
ANSWER #16
IN A BAG, THERE ARE 3 BLUE, 2
GREEN, AND 5 BLACK MARBLES.
FIND THE PROBABILITY OF
PICKING A BLACK THEN ANOTHER
BLACK, WITHOUT REPLACEMENT.
P(B, B)=5/10*4/9=2/9
QUESTION #17
ANNALISE WENT SHOPPING AND
BOUGHT 4 T-SHIRTS, 3 SKIRTS,
AND 2 SHOES.
HOW MANY DIFFERENT OUTFITS
CAN SHE MAKE?
QUESTION #17
ANNALISE WENT SHOPPING AND
BOUGHT 4 T-SHIRTS, 3 SKIRTS,
AND 2 SHOES.
HOW MANY DIFFERENT OUTFITS
CAN SHE MAKE?
4*3*2=24
QUESTION #18
THE VENN DIAGRAM BELOW SHOWS THE TYPES
OF NOVELS THE LITERATURE CLUB MEMBERS
READ DURING THEIR SUMMER BREAK.
IF 133 STUDENTS ARE IN THE
LITERATURE CLUB MEMBERS AND ALL
STUDENTS READ AT LEAST ONE BOOK,
HOW MANY STUDENTS READ ADVENTURE
AND MYSTERY?
QUESTION #18
THE VENN DIAGRAM BELOW SHOWS THE TYPES
OF NOVELS THE LITERATURE CLUB MEMBERS
READ DURING THEIR SUMMER BREAK.
IF 133 STUDENTS ARE IN THE
LITERATURE CLUB MEMBERS AND ALL
STUDENTS READ AT LEAST ONE BOOK,
HOW MANY STUDENTS READ ADVENTURE
AND MYSTERY?
133-(36+14+7+43+3+28)=2
PYTHAGOREAN THEOREM
QUESTION #19
FIND THE MISSING LENGTH.
ANSWER #19
FIND THE MISSING LENGTH.
b = 112.5 units
QUESTION #20
FIND THE MISSING LENGTH.
QUESTION #20
FIND THE MISSING LENGTH.
b = 7.2 units
QUESTION #21
DETERMINE WHETHER EACH SET OF MEASURES
CAN BE THE LENGTHS OF THE SIDES OF A RIGHT
TRIANGLE.
QUESTION #21
DETERMINE WHETHER EACH SET OF MEASURES
CAN BE THE LENGTHS OF THE SIDES OF A RIGHT
TRIANGLE.
92+402=412 is true, so it is a right triangle
QUESTION #22
DETERMINE WHETHER EACH SET OF MEASURES
CAN BE THE LENGTHS OF THE SIDES OF A RIGHT
TRIANGLE.
ANSWER #22
DETERMINE WHETHER EACH SET OF MEASURES
CAN BE THE LENGTHS OF THE SIDES OF A RIGHT
TRIANGLE.
42+√262=122 is NOT true, so it is NOT a
right triangle
QUESTION #23
DETERMINE WHETHER EACH SET OF MEASURES
CAN BE THE LENGTHS OF THE SIDES OF A RIGHT
TRIANGLE.
QUESTION #23
DETERMINE WHETHER EACH SET OF MEASURES
CAN BE THE LENGTHS OF THE SIDES OF A RIGHT
TRIANGLE.
(√65)2+(6√2)2=(√97)2 is NOT true, so it
is NOT a right triangle
QUESTION #24
FIND THE DISTANCE BETWEEN A AND B. ROUND
TO THE NEAREST HUNDREDTH.
QUESTION #24
FIND THE DISTANCE BETWEEN A AND B. ROUND
TO THE NEAREST HUNDREDTH.
102+72=c2, so AB=11.7 units
QUESTION #25
EACH SIDE OF A CUBE IS 7
INCHES LONG. FIND THE
LENGTH OF THE DIAGONAL
OF THE SOLID.
ANSWER #25
EACH SIDE OF A CUBE IS 7
INCHES LONG. FIND THE
LENGTH OF THE DIAGONAL
OF THE SOLID.
7
d
c
72+72=c2, so c=√98 72+(√98)2=d2,
so d=12.1 units
THE END
GOOD LUCK