1) Triangle ABC is a right triangle

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```					Math 8 Benchmark Review                                                    Name______________________

Triangle ABC is a right triangle. The shortest side is 6 m long and the longest side is 11 m long. What is
the approximate length of the third side?
A. 7 m        B. 8 m         C. 9 m         D. 10 m

Which expression represents the length of leg b?
A.   32 + 52
5 ft
B. 9  25                   3 ft

C. (25  9)                                b

D.   25 -   9

The top of a ladder is placed against the side of a house. The ladder is 15 feet long and the wall is 12
feet high. How far from the wall will the base of the ladder be positioned if the top of the ladder
meets the top of the wall?
a. 9 feet             b. 9.5 feet                c. 10 feet          d. 10.5 feet

The below dimensions represent the side measurements of triangles. Which one is not a right triangle?
a. 12, 16, 20         b. 5, 12, 13               c. 6, 7, 8          d. 3, 4, 5

Graph the ordered pairs (2, –2) and (5, 3). Then find the approximate distance between the points.
y

x

a. 5.8,       b. 6.1       c. 4          d. 3.1

The size of a rectangular television screen is determined by the measurement of its diagonal. What is
the diagonal of a television that has a width of 20 inches and a height of 25 inches? Give your
answer to the nearest inch.

Ricardo wants to build a right triangular shaped pen for his dog as shown in the diagram below. If
fencing cost \$20 per yard, how much will he spend on fencing?
Complete the following statements with one of the given vocabulary words to make a true
statement: enlargement, reduction, image, pre-image, congruent, similar.

           A dilation with a scale factor greater than 1 results in a(n) ___________________ of the original
figure.
           The dilated figure is referred to as the __________________ of the original figure.
           A dilation, with a scale factor other than 1, results in a figure that is ________________ to the
original figure.
           A dilation with a scale factor of 1 results in a figure that is _____________________ to the original
figure.

One of the coordinates, B, of a square is (2, 6). After a dilation with center at the origin, the
coordinates of B’ are (1, 3). The scale factor of the dilation is ________.

Which of the following describes the image of a figure after a dilation that has a scale factor
between 0 and 1?
a. It has a different shape from the original figure and is smaller than the original figure.
b. It has the same shape as the original figure and is larger than the original figure.
c. It has the same shape as the original figure and is smaller than the original figure.
d. It has the same shape and size as the original figure.

Use the diagram below to answer the following questions. (Students should be able to answer similar
questions involving squares and right triangles.)
y

6

5
J                     K
4

3

2

1
M                     L
1     2   3   4   5   6   7   8   9 x

Dilate the figure by a scale factor of 1.5 with the origin as the center of dilation. What are the vertices
of the image?
a. J´(1.5, 6), K´(9, 6), L´(9, 1.5), M´(1.5, 1.5)
b. J´(–1.5, –6), K´(–9, –6), L´(–9, –1.5), M´(–1.5, –1.5)
c. J´(6, 1.5), K´(6, 9), L´(1.5, 9), M´(1.5, 1.5)
d. J´(1.5, 6), K´(9, 6), L´(6, 1), M´(1, 1)

If the rectangle is dilated by a scale factor of 2, what will be the ratio of the lengths of the sides of the
pre-image to the lengths of the sides of the image?
A. 2:1        B. 1:2         C. 1:4        D. 4:1

If the rectangle is dilated by a scale factor of 2, what will be the ratio of the area of the pre-image to
the area of the image?
A. 2:1        B. 1:2         C. 1:4        D. 4:1

Which of the following describes the image of a right triangle after a dilation that has a scale factor
of 2/3?
a. Each angle is 2/3 of the measure of its corresponding angle in the original triangle.
b. Each angle is 3/2 times the measure of its corresponding angle in the original triangle.
c. Each angle is 1/3 larger than the measure of its corresponding angle in the original triangle.
d. Each angle has the same measure as its corresponding angle in the original triangle.

If a right triangle with area 36 sq. units is dilated with a scale factor of ½, what will be the area of the
dilated figure?
A. 72 sq. units B. 36 sq. units. C. 18 sq. units D. 9 sq units

Given the two similar polygons below, use proportional reasoning to find the length of the missing
side.

19.2                                  9.6

k                                                                        3
9.6          4.8

8.6
17.2

a. 18.7                 b. 6                        c. 3                  d. 49.3

A 5 foot tall boy casts a 3 foot shadow at the same time that a flagpole casts an 18 foot shadow.
Find the height of the flagpole.

a. 10.8ft               b. 30 ft             c. 37.9 ft    d. 81 ft

In the figure,   ABC ~         DEC. Write and solve a proportion to find the distance from Middletown to
Maysville.
On the plans for a new house, the house is 18 inches wide by 20 inches long. If the house is actually
going to be 27 feet wide, what will the actual length of the house be?
a. 40.5 ft          b. 25 ft             c. 24.3 ft           d. 30 ft

Which unit would you use to find the most precise measurement?
A. inch             B. centimeter       C. millimeter     D. yard

Which unit of measure is most appropriate for measuring the amount of water in a swimming pool?
a. Fluid ounce      B. Pint      C. Gallon                  D. Pound

James measured the length of a wooden board twice. The first measurement he took was 35 inches.
The second measurement he took was 3 feet. Which of the following is true of his two
measurements?
a. 35 inches is a more precise measurement than 3 feet.
b. 35 inches is a less precise measurement than 3 feet.
c. 35 inches and 3 feet are equally precise measurements.
d. One of his measurements must be incorrect, because 35 inches and 3 feet are not close in length.

Four students measured the width of their classroom.
There results are shown below.
The actual width of the room is exactly 25 feet. Which measurement is most accurate?
3                 11                             1
A. 25 ft. 1 in.    B. 24 ft.     in      C. 25      ft.          D. 24 ft. 11     in.
4                 12                             2

Mr. Jones wants to find the area of his rectangular lawn so he will know how much inexpensive grass
seed to purchase to cover it. To do this he will need to measure the length and width. Using his tape
measure he can either measure in feet or inches. Which would be the most appropriate unit for this
situation?
a. He should measure in inches, because he should use a smaller unit to measure a large space.
b. He should measure in feet, because he should use a larger unit to measure a large space.
c. He should measure in feet, because that would yield the most precise measurement.
d. He should measure in inches, because that would yield the most accurate measurement.

Lean ground beef is on sale for \$3.29 per pound. What is the cost in ¢ per ounce?
Which option shows the unit analysis steps to correctly solve the problem? (Clone of released PASS
item)
\$ 3.29 × \$ 1 × 16 oz                                    \$ 3.29 × \$1 × 1 lb
1 lb 100¢ 1 lb                                          1 lb 100¢ 16 oz

\$ 3.29 × 100 ¢ × 1 lb                                     \$ 3.29 × 100¢ × 16 oz
1 lb    \$1   16 oz                                        1 lb    \$1     1 lb

Cans of juice are sold in cases of 24. If each can holds 12 ounces, about how many liters are in a
case? Which option shows the unit analysis steps to correctly solve the problem?
288 oz × 1 qt × 1 liter                                288 oz × 1 qt × 1.06 liter
1      32 oz 1.06 qt.                                  1       32 oz 1 qt.

24 oz × 1 qt × 1 liter                                    12 oz × 32 qt × 1 liter
1      32 oz 1.06 qt.                                     1      1 oz 1.06 qt.

Joe is driving 45 miles per hour. About how fast is that in feet per second? (Clone of released PASS
item)
A. 660 ft/sec         B. 31 ft/sec        C. 66 ft/sec           D. 310 ft/sec
A road sign indicates that Charleston is about 150 miles away. About how many kilometers is this?
A. 94 km B. 240 km C. 275        D. 125 km

A can of fruit weighs 225 grams. About how many pounds is this?
A .5 pounds          B. 1 pounds        C. 5 pounds        D. 1 pound

3456 milliliters = _________ liters

144 inches = ______________ yds                A. 1.44    B. 4   C. 12     D. 576

7 kg. = ________________ mg

In June of 1965, the record high temperature in South Carolina was 109°F. In January of 1975, the
record low temperature in South Carolina was –15°F. Which integer represents the change from 111°F
to –19°F? (Clone of released PASS Item)         A. 94°F B. –124°F C. 124°F D. –94°F

True or False? If false, give a counter example.

    The sum of two negative integers is always positive.
    The difference to two negative numbers is always negative.
    The quotient of a positive and negative number is always negative.

3 – 4(2 – 7) + 15 ÷ 3 (Clone of released PASS Item) A. 10         B. 28   C. 18     D. 0

( -2) 3 = ______
-2(-4)(-7)(-1) = _________
39
= _______
2                                                           48
=   _______
8
5 – (– 6 ) = _______
-10 – 28 = ______
-8 + -3 + 12 – 15 = _______

The temperature is 26°F outside. Over the next 4 hours the temperature drops 8 degrees per hour.
What is the temperature after 4 hours? _____________

Solve: –2x + 3 = –15

3
Jesse multiplies -     by a number. His answer is less than 0. Jesse multiplies by which number? (Clone of
5
released PASS item)
1
a. -3          b. -              c. 0          d. 3
2
1
Jesse divides a whole number by           . Which statement best describes his answer?
2
1                                C. It is greater than the whole number.
a. It is smaller than        .
2
B. It is a mixed number.                                    D.It is less than the whole number.
During a football game Derek’s team was penalized 5 times and lost 15 yards on each penalty. The
other team was penalized 2 times, and Derek’s team gained 5 yards for each of those penalties. Find
the total net change in yards for Derek’s team because of the penalties.
a. -85 yards        b. -65 yards          c. -325 yards     d. -3 yards

0.6        0.2 =

0.4 x 0.2 =

Use estimation to find the product 12.4 x 0.68
A. 0.8432            B. 8.432             C. 84.32             D. 843.2

Use estimation to find the quotient 12.4  0.4
A. 0.31              B. 3.1              C. 0.031              D. 31

3     4
-     x-    =
5    15

1   3
–1        x2 =
2   5

1                 1
Solve: 1       x        = –4
7                 2

Solve: – 1.2 x + .16 = 1

1
If you multiply –     by a number between 0 and 1, the product will be which of the following?
3
a. A number between – 1 and 0                            c. A number greater than 1
1                     d. A number between 0 and 1
b. A number less than –
3

If you divide 32 by a number greater than 1, the quotient will be which of the following?
a. A number greater than 32                           c. A negative number greater than – 32
b. A positive number less than 32                     d. A negative number less than – 32

2
If you multiply – by a number between – 1 and 0, the product will be which of the following?
3
2                                                               2
a. A number greater than                           c. A negative number greater than –
3                                                               3
2                                                           2
b. A number less than –                            d. A positive number less than
3                                                           3

1        2      3          4       5   6   7
In Which set of numbers is graphed on this number line?
1                                                      1                                    2                                        2
A. 2     , 4.5, 5.2                                    B. 2     , 3.5,    26                C. 1     , 4.5,    39                   D. 1      , 4.5,   33
3                                                      3                                    3                                        3

Draw and label a number line. Locate the following numbers on it.  ,                                                   15 ,   8,   3
9

The square root of a number has been graphed on the number line. The point on the number line
below is the graph of which of the following numbers.
7                8        9             10           11

A.        75                             B.       87                          C.   99                   D.    110

A                              B                       C                             D

0                1         2             3            4         5        6    7           8

Which point above is the graph of                                   3
25 ?

Compare the following numbers by placing the correct symbol ≤, ≥, <, >, or = in the blank.

5                                       2
22 ______ 6.3                                         5.5% ______                          450% ______ 4                           0.457 _______0.8
100                                      5

5                                                                2            1
125% _______                                              49 _______100%                    –     _________–                        3
28 ______ 3.8
4                                                                3            2

5
.55 ______                              0.5% ______
8

The figure below shows the graphs of the points A, B, C, and D on a number line. Match each
number with the appropriate letter.

–0. ,          ,               , – 0.925.

A    B                              C       D

–1                                                    0

a. A =             ; B = –0. ; C =                     ; D = –0.925                         c. A = –0.925; B =             ; C = –0. ; D =

b. A = –0.925; B = –0. ; C =                                  ;D=                           d. A =           ;B=       ; C = –0. ; D = –0.925

A class is selling magazines as a fundraiser. Of the 200 magazines sold, Tracy sold                                                     . Monica sold

0.035 of the magazines. Luke sold                                       of the magazines, and Sandra sold 0.275 of the magazines. Who

sold the most magazines?
a. Monica                     B. Sandra                   C. Tracy

The SDE “stretches” this indicator to include operations with rational numbers.

Compare the following numbers by placing the correct symbol ≤, ≥, <, >, or = in the blank.

1   2                                             5      3              2
–     +   ________ .5 – .21                      –3     – (–1 ) ________ –1
2   3                                             8      4              3
Look at each pair of numbers. If they are the
same distance from 0, write “same”. If they
are not the same distance from 0, circle the
number that is closer to 0.

 3  7 and 10                 25 and       25                 - 3  7 and 10     3  7 and 100

Simplify:

 3 + –6(2 – 5) = _______________

 3  12 – 15 = _______________

–  5  12 = ___________________

Evaluate:
3 a – 2 b if a = -7 and b = 3

Compare the following numbers by placing the correct symbol ≤, ≥, <, >, or = in the blank.
|-5 | ______ -|4 |

What integer is the same distance from 0 as              15  12 ?

150 is between what two whole numbers? Explain how you know.

Which is number is greater?     3
63 or 3.5?

A square bedroom has an area of 180 square feet. Between which two whole numbers is the length
of one side of the bedroom?

In a student body election, Olivia was selected president. The ratio of the number of votes Olivia
received to the number of votes Tom received was 5:4. Using the information in the table below, how
many total votes were cast for both candidates?
Candidate     Number of Votes
Olivia           195
Tom               ?
A factory worker can package 150 games in 15 minutes. How many games can he package in 4
hours at this same rate?
a. 10                b. 400         c 600                d. 2400

A light-year is a unit used to measure large distances in space. One light-year is approximately equal
to 5.88 trillion miles. On a map of the Milky Way Galaxy, the scale is 3 inches represents 50 light-years.
If two stars on the map are 18 inches apart, about how far apart are they in the galaxy?
a. 411 light years            b. 16.67 light years      c. 1.08 light years          d. 300 light years

Sal earns \$480 per week. Lidia earns \$300 per week. Are their salaries proportional if Sal works 40 hours
per week and Lidia works 25 hours per week?

In her catering business, Elena usually estimates that 8 pounds of meat will feed about 36 people.
How many pounds of meat should she prepare if she is expecting 144 people?

The cost of a tent rental is \$160 for 5 days. Which proportion could be used to find the cost of renting
a tent for 8 days at the same rate?
160   x              160   x              160 8                 160 5
A.       =           B.       =           C.      =             D.      =
8    5               5    8               5   x                 8   x

A certain computer can perform a maximum number of operations per second. If this computer is
running at 25% of the maximum and is performing 110 operations per second, what is the maximum
number of operations the computer can perform per second?

A bank offers a savings account that pays a simple interest rate of 3.5%. Umeki opens a savings
account at this bank and deposits \$4000 into the account. How much money will Umeki have in the
account after 7 years?
a. \$13,800.00        b. \$4980.00       c. \$980.00             d. \$4140.00

According to the United States Census Bureau, the United States population was projected to be
about 294,000,000 people on July 1, 2004. The two most populous states were California, with a
population of about 36,000,000, and Texas, with a population of about 23,000,000. About what
percent of the United States population lived in California or Texas? Round your answer to the
nearest percent.

A. 8%                B. 12%               C. 20%                D. 27%

Roberto farms a tract of land that typically yields 69.6 kilograms of peas. A fertilizer manufacturer
claims that its fertilizer will produce a 60% increase in the yield. What total amount of peas should
Roberto expect from this tract of land if he applies the fertilizer?
a. 27.84 kg              b. 41.76kg          c. 111.36 kg          d.4,245.6kg

Mr. Rodriguez sells holiday greeting cards in his gift shop. Before the holidays, he sells the cards at a
200% markup on the price he paid to his supplier. After the holidays, he discounts the cards 55% of
the marked up price. What is the post-holiday price of a card he originally bought from his supplier for
\$2.50?
a. \$2.25     b. \$4.13              \$3.38          d. \$2.75

An employee earned \$56,000.00 in a year and had \$8,680 withheld for federal income tax. What
percent of his salary was withheld for federal income tax? If necessary, round your answer to the
nearest hundredth of a percent.
a. 645.16%                                    b. 15.5%                   c. 17.5%        d. 0.16%

After a nice dinner, Lung decides to leave a 20% tip. The total bill comes to \$21.05. About how much
should he leave for the tip?
a. \$0.42              b. \$25.25          c. \$3.75             d. \$4.20

On a scale drawing,                                in. = 1 ft. A room on the scaled drawing measures 7.5 inches by 6 inches. How
many square yards of carpet are needed for the room?

Thomas has been offered two jobs. The first job pays \$880.00 per week. The second job pays \$790.00
per week plus 12% commission on his sales. How much will he have to sell in order for the second job
to pay as much as the first job?

Mr. Martin repairs refrigerators in people’s homes. He charges \$50 for a house call and \$20 for each
hour he works. If h represents the number of hours he works on a repair job and T represents the total
amount he charges the homeowner, which equation can be used to represent Mr. Martin’s earning
for a repair job?
a. T = 20h – 50              b. T = 20h + 50           c. T = 20(h – 50)          d. T = 20(h + 50)

The table below represents the amount of money Mr. Johnson earns as a function of the number of
hours he works.
h, hours      1     2      3    4    5
E, earnings   45    60     75 90     105

Write an equation that represents Mr. Johnson’s earnings as a function of the number of hours
worked.
Explain the meaning of each number in your equation.

The graph below shows the total cost of renting a bike from Coastal Bike Rentals as a function of the
number of hours rented.

What is the cost of renting a bike for 4 hours?
What is the hourly rate (rate of change) for renting a bike? Include units in your answer.
Write an equation that gives the total cost, T, of renting a bike for h hours.
y

45

40
Total Rental Cost

35

30

25

20

15

10

5

1   2   3   4    5     6   7   8   9   x
Number of Hours
Complete the function table below for y = -3x + 7

x            -1           0              1           2            3            4
y

Jeff works as a carpenter. He earns \$35 per hour and pays his assistant \$55 per day from his earnings.
Jeff wants to make \$225 today. Which equation can you use to find h, the number of hours he must
work today to meet his goal.
35h + 55 = 225
35h – 55 = 225
55h + 35 = 225
55h – 35 = 225

The quotient of a number and 5 is 15 _______

14 increased by the opposite of a number is equal to 35.
A. n – 14 = 35                        C. 14 + (–n) = 35
B. 14 ÷ (–n) =35                      D. 14 + n = 35

16 points is 5 fewer than Michelle scored last game.
A. 16 = p ÷ 5                            C. 16p = 5
B. 16 = p + 5                            D. 16 = p – 5

The daily rental fee a company charges to rent a mid size car includes a \$20 fee for insurance plus
\$.25 a mile.
Which equation below can be used find the cost of renting the car for one day if you drive m miles?
a. C = .25m + 20           b. C = .25m – 20          c. C = .25(m + 20)          d. C = .25(m – 20)

Is the relationship linear? Explain how you know.
Is the relationship proportional? Explain how you know.

An elevator that can hold no more than 2000 pounds contains a 350 pound package. Write an
equation for finding, n, the number of 150-poind people that can safely get into the elevator with the
package. (This could also be phrased so that students could write and inequality instead of an
equation.)

P      1      2      3        4     5
C      11     18     25       32    39

The table above shows the cost of ordering pizzas from the local pizza parlor which charges a fee to
deliver.
Write an equation that relates the number of pizzas ordered (p) to the total cost (C) charged for the
delivered pizzas.
Is the relationship linear? Explain how you know. (also 8-3.5)
If you double the number of pizzas ordered, does the cost also double? What does this indicate
What is an equivalent way of writing 24a -18?
A. 6(4a - 3)       B. 6(4a + 3)         C. 6a(4a – 3)                   D. 18(6a – 1)

True or False?
The multiplication of rational numbers is associative.
The division of rational numbers is commutative.
The distributive property allows you to change the order in which you add two rational numbers

Use the distributive property to find the expression that is equivalent to 6x + 12 y.
A. 6(x + 6y)                B. 6(x + 2y)           C. 18xy              D. 12(2x + y)

Match:
(ab)c = a (bc)                                A. assoc. prop. of add.
(a + b)c = c(a + b)                           B. comm. prop. of add.
(a + b)c = (b + a) c                          C. assoc prop of mult.
(a + b) + c = a + (b + c)                     D. comm. prop of mult

Verify that a(b + c) is equivalent to ab +bc by substituting a = 2 b = -3 and c = 5.

Simplify by using the commutative property, the associative property, and the distributive property.
(This skill will be re-emphasized second semester when solving multistep equations.)
3x + 5y + 7x
5(x – y) + -2x
3x -6 + 5y + 10
3(a + 5) + 2(a – 7)

Use the indicated proportion to fill in the blank with an equivalent expression.
3(2x + 6) = ________________________Distributive property
3(2x + 6) = ________________________Commutative property of addition
3(2x + 6) = ________________________Commutative property of multiplication
(3x + 2) + - 5_______________________Associative property of addition

dollars

60

55

50

45

40

35

30

25

20

15

10

5

1       2   3   4   5   6   7   8    9   10   11   pizzas

3. Seagrove Waverunners rents jet skis for \$60 per hour. In addition to the hourly rental fee,
there is a charge of \$15 for insurance.

Flying Balloon Adventures gives people hot air balloon rides for a fee of \$145 per person.
The cost of renting a bicycle from the Bayside Bike Rental Company is determined by the formula y =
5x + 10 where y represents the total cost for x hours.

The gravitational pull of the moon is less than the earth’s surface because the moon is smaller in size.
An object on the moon weighs about that object’s weight on the earth’s surface. The equation y =
x can be used to approximate the weight y in pounds on the moon based on the number of
pounds x that an object weighs on the earth.

The table shows the tuition for a private school for the number of children from one family.

Tuition for Private School
Number Attending           Tuition Amount
1                        \$2,250
2                        \$4,250
3                        \$6,000
4                        \$7,000

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