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Algebra Ready & 7th Grade Math Benchmark Practice Test 09-10 Version B
1. Simplify
3 1 1
    . (Standard NS 1.2*)
4 3 2
First make common denominators for the fractions in parenthesis.
1 1 2 1 3 1 2 3 5
 

  
3 2 23 3 2 6 6 6
Next make common denominators out of the first fraction and the 5 .
3 5 3  3 2  5 9 10
1
 

  
4 6 3  4 2  6 12 12
12
2. Simplify
6
3
 9 .(Standard NS 1.2*)
4
Put a 1 under the 9 as a fraction. Multiply across numerators and denominators.
3 9 27
 
Divide 4 into 27
4 1 4
27
3 (Remainder)
 6 Remainder 3 written as 6
4
4 (Divisor)
3. Simplify
3 11
 . (Standard NS 2.2*)
4 12
First make common denominators.
3 11 3  3 11 9 11
2
1
 
    
4 12 3  4 12 12 12
12
6
3
3
4. Simplify   . (Standard NS 2.3*)
4
First distribute the exponent to both the numerator and denominator.
3
3
3  3  3 27
3 3



 
3
 4  4 4  4  4 64
5. How many centimeters are in 4000 millimeters? (Standard MG 1.1)
There are 100 millimeters in one centimeter (centi means 100). Divide millimeters by 100.
4000
 40 centimeters
100
6. Which property is used in each example? (Standard AF1.3*)
a. 3  4  5  4  3  5 commutative property of addition (3 and 4 are moved)
b. (3  4)  5  3  (4  5) associative property of addition (parenthesis are moves)
c. 5(3  4)  (5  3)  (5  4) distributive property of multiplication over addition ( 5 distributes
everything inside parenthesis)
to
7. Melinda Melody bought a MP3 player on sale for 40% off the original price. If the MP3 player originally
cost $99.00, what is the amount of discount and the sale price? (Standard NS 1.7*)
a. Discount $39.60
b. Sale price $59.40
Formula: Original cost-Amount of discount = Sale Price
Multiply 40% (as a decimal) times original cost to get the
amount of the discount. Then subtract the amount of the
discount from the original price to get sale price.
99  .40  39.60 Amount of discount (Change 40% to .40)
99.00  39.60  $59.40 Sale price
8. Showmey Damoney put $1000 in the credit union and left it there for 1 year. If he earned 5% interest on his
money, how much interest will he earn, and how much will be in his account at the end of 1 year?
(Standard NS 1.7*)
Formula: Interest = Principal * Rate * Time
Principal=amount of money put in
a. Interest earned Interest = $50.00
Rate=interest rate as a decimal
Time=1 year normally
b. Amount in account $1000 + $50 = $1050
I  P • R • T Substitute the values
I  1000 • .05 •1 Simplify
I  50
9.
Ima Houseseller earns a 3% commission for selling a house. If he sells a house for $120,000, what is his
commission? (Standard NS1.7*)
Formula: Commission = Principal * Rate
C  P•R
Substitute the values Change % to decimal
C  120,000 • .03 Simplify
C  $3,600
10.
Simplify
74
. (Standard NS2.1)
73
When dividing powers with the same base, subtract the exponents.
74
 743  71  7
3
7
11.
Write the equation below that represents 8 less than a number n is 14. (standard AF1.1*)
Put 8 less than after the variable, because you want 8 less than the number n.
n  8  14
12.
Simplify the following expression using the correct Order of Operations (PEMDAS).
(Standard AF1.2*)
(7  3)2  6  5
(7  3) 2  6  5 PEMDAS says parenthesis first
(4)2  6  5 PEMDAS says Exponents next
16  6  5 PEMDAS says Multiplication pr Division next
96+5 PEMDAS says Addition or Subtraction next
101
13.
Simplify - |-8|. (Standard NS 2.5*)
Do the absolute value first.
|-8| = 8 Absolute value sign removes positive and negative signs from inside | |
-8 = -8
14.
Write the number 670,000 in scientific notation. (Standard NS1.1)
Put a decimal point between the 2 numbers on the left
670,000  6.70000 Count how many decimal points to the end of the number
6.70000 Has 5 numbers to the end. This becomes the exponent with a base of 10
6.7  105
15.
Put these values in order from least to greatest. |13|
(Standard NS2.5*)
-|5|
-|-8|
|9|
|-12|.
Find the real values of all the numbers first. |13| = 13, -|5|= -5, -|-8|= -8, |9| = 9, |-12| = 12
Put in order from least (smallest) to greatest (biggest) -8, -5, 9, 12, 13
16.
What is the mean, median, mode, maximum, and minimum of the following values?
56 34 45 56 23 8 (Standard SDAP1.1)
First, put the numbers in order from least (smallest) to greatest (biggest)
8, 23, 34, 45, 56, 56
Mean is the average. Add all the numbers and divide by the number of entries.
8  23  34  45  56  56  222
222  6  37
Median is the number in the middle. If there are 2 numbers in the middle, add then and divide by 2.
8  23  34  45  56  56
8  23  34  45  56  56 34  45  79 79  2  39.5
Mode is the number that appears most often.
8  23  34  45  56  56
Minimum is the smallest number,8
Maximum is the biggest number, 56
17.
Write an example of the properties below. (Standard AF1.3*)
a. Associative Property of Addition (1 + 2) + 3 = 1 + (2 + 3) (Parenthesis move)
b. Commutative Property of Multiplication 3 * 4 = 4 * 3 (Numbers move)
c. Distributive Property of Multiplication over Subtraction 2(3 + 4) = (2 * 3) + (2 * 4)
d. Inverse Property of Multiplication 2  5  10  1 (A number times its inverse = 1)
5 2 10
e. Identity Property of Multiplication 6 * 1 = 6 (A number times 1 = the number)
18.
Harry Leggs rides his scooter at a steady speed of 10 miles per hour. Record his progress for the first 5
hours of his ride on the line graph below. (Standard AF1.5*)
50
(5 ,50)
40
Miles
1) Plot the points
2)Draw a line with a ruler
through the points.
3) Label the points
(4 , 40)
30
(3 , 30)
20
(2, 20)
10
(1 , 10)
1
2
3
4
5
Hours
19.
Sheeza Beyer bought a new pair of shoes on sale. The regular price was $35.00, but she had a coupon
for 35% off. Write an equation first, then solve for the amount she paid.
(Standard NS1.3)
Cost of items – (Cost of items * Percent of discount as a decimal) = Price Paid
P is the amount paid
a. Equation 35  (35  .35)  P
b. Amount of Discount 35  .35=12.25
Amount of discount
c. Amount Paid 35.00 -12.25  22.75 Price Paid
20.
Give an example of the Associative Property of Multiplication. (Standard AF1.3*)
(3  4)  5  3  (4  5)
Parenthesis move
21.
If k = 4, what is k  k  k ? (Standard AF2.0*)
2
3
4  42  43  4123  46
(4  4)  (4  4)  (4  4)  (16  16)  16  256  16  4,096
22.
3
What are the prime factors of 6z ? (Standard AF2.1*)
6 z3
2 3 z z z
23 z  z  z
23.
Prime factors
If m  13  27 , what does m equal? Show all work in steps. (Standard AF4.1*)
m  13  27
-13 -13
Subtract 13
Simplify
m  -40
24.
Winnifred Watchmee made $108 babysitting for her neighbor last month. If she earned $9.00 an hour,
how many hours did she work? Write an equation and solve in steps. (Standard AF4.2*)
9h  108
9 dollars  hours = total
9h  108 Divide by 9
9h 108

Simplify
9
9
h  12
25.
What is the area and perimeter of the side of the stairs in the figure below? (Standard MG2.2)
a.
Area 6 square feet
b. Perimeter 12 feet
12 inches
12 inches
12 inches 12 inches
For the Area: Every 4 boxes equals 1 square
foot, or 12” by 12”. There are 3 square feet in
the last step, 2 in the middle step, and 1 in the
first step. 3 + 2 + 1 = 6 square feet.
For the Perimeter: Remember the perimeter is
the measurement if you had to walk around the
entire box. Every 2 squares has a length of 1
foot. The last step has 6 feet, the middle step
has 3 feet, and the first step has 3 feet.
6 + 3 + 3 = 12 feet.
26.
What is the area of the trapezoid below? Use the formula A  12 h(b1  b2 ) or A 
(Standard MG2.1*)
1
 9  11  13 Simplify
2
1
1
A  •1287 Multiply by (or divide by 2)
2
2
A  643.5 square feet (or ft 2 )
A
11 in
9 in
h(b1  b2 )
2
9 in
13 in
27.
What is the area of the shaded part of the rectangle below? (Standard MG2.1*)
First, find the area of the rectangle, then divide it
by 2. The area of a rectangle is length times
width.
14 in
20 in
28.
A  l  w Substitute the values
A  20 •12 Simplify
A  240 square inches Divide by 2
240
A
 120 square inches, or 120 in 2
2
The class needs $75.00 for a class celebration. Students have already brought in $20. If 11 more
students pay their share, how much does each student need to bring in? (Standard AF4.1*)
Use the equation 11d  20  75 to help you solve the problem.
11d  20  75 Subtract 20
-20 -20 Simplify
11d  55 Divide by 11
11d 55

Simplify
11 11
d 5
29.
What is the value of w if 7 w  14  35 . (Standard AF4.1*)
7 w  14  35 Add 14 to each side
+14 +14 Simplify
7 w  -21 Divide by 7
7 w -21

Simplify
7
7
w  -3
30.
Evaluate (4  3  8) . (Standard 7AF1.2)
3
2
(4  33  8) 2 Use PEMDAS Solve exponents in the parenthesis
(4  27  8) 2 Use PEMDAS Solve adding
(31-8) 2
2
23
Use PEMDAS Solve subtracting
Square 23
23 • 23  529
31.
The H1N1 virus count is increasing at a steady rate each hour. How fast are the viruses increasing?
(Standard PS1.2*)
Every hour the number of
viruses increases by 5. Add
5 viruses each hour.
5
4
Hours
3
2
1
5
10
15
20
25
Number of Viruses Present
32.
Jack and Jill ran up the hill at 6 miles per hour for 4 hours. They ran back down the hill at 8 miles per
hour for 3 hours. How far did they run in all? (Standard AF4.1*)
Uphill: 6 miles  4 hours = 24 miles
hour
Downhill: 8 miles  3 hours = 24 miles
hour
Total: 24 + 24 = 48 miles
33.
Cameron wants to open a business selling MyFace and Spacebook web pages. If he borrows $3200 and
sells his pages for $60 each, how many pages does he need to sell to pay back the money he owed,
assuming he doesn’t have to pay any interest? (Standard AF4.2*)
Divide the amount of money $3200 by $60 to find out how many pages he needs o sell.
3200  60  53.33 You can't sell part of a web page, round up to 54.
34.
Jeannie can skate 1 mile in 4 minutes for the first mile, then can only skate 1 mile in 10 minutes. How
long would it take for her to skate 16 miles? (Standard MG1.3*)
Time for 1 mile + time for (16-1) miles = total time
4 minutes + 15*10 minutes = 154 minutes
Change to hours by dividing by 60 minutes
154  60  2 hours 34 minutes
35.
Gravity exerts a force of about 15 pounds of pressure per square inch of surface area at sea level. How
much pressure is exerted on a hand that is approximately 4 by 6 inches?
(Standard MG1.3*)
First, find the area of the hand, then multiply by 15.
4  6  24
24  15  360
36.
The value of the
88 is between what 2 integers? (Standard NS2.4)
12  1, 22  4, 32  9, 42  16, 52  25, 62  36, 7 2  49, 82  64, 92  81, 102  100
88 is between 9 and 10
37.
Wally is 5 years more than 3 times Talley’s age. If Talley is 8, how old is Wally?
(Standard 7AF1.1)
Put the 5 years more (+5) after the 3 times t (3*Talley’s age)
3t  5  w 3 times Talley's age = Walley's age
(3 • 8)  5  w Substitute the 8 for Talley's age
24  5  29  w Walley is 29
38.
Write 3.34 as an improper fraction. (Standard NS1.5*)
34
17
and reduced to 3
100
50
17
Make 3 an improper fraction by multiplying the 50 times the 3, then adding 17 to it to
3.34 can be written as 3
50
make 150 + 17 = 167. Put this number over the denominator.
39.
167
50
If it takes 99 person-hours to paint the house, and the foreman assigns 6 workers to do the painting, how
many hours will it take to finish the job? (Standard MG1.3*)
99 total hours divided by 6 workers gives the number of hours to finish.
99
 16.5 hours
6
40.
The $150 snow skiis were reduced to $105. What is the percentage of discount?
(Standard NS1.6)
Divide the reduced price by the original price to get the percentage of the reduced
price. Then subtract the percentage of the reduced price from 100 to get the percentage
of discount.
105
 .7 or 70% Percent of reduced price
150
100% - 70%  30% Percent of discount
41.
What is
32
written as a decimal? (Standard NS1.3)
1000
You can read this fraction as 32 thousandths. As a decimal, it is written as .032, with the
2 in the thousandths place, and the 3 in the hundredths place.
42.
What is the length of side c, the longest side of a right triangle? (Standard MG3.3*)
Use the Pythagorean Theorem.
a 2  b 2  c 2 c is the diagonal or longest side. Substitute
62  82  c 2 Simplify
6
36  64  c 2 Simplify
100  c 2 Take the square root of both sides
8
100  c 2
Simplify
10  c
43.
What is the slope of the line in the graph below? (Standard AF3.3*)
y
Find where the line drawn crosses exactly
where the gridlines cross, as shown below.
Make 2 points where gridlines cross the
line. Make a right triangle with legs going
horizontal and vertical.
The slope is measured as
6
1
4
3
2
x
0
-6
-4
-2
0
2
4
6
y  value 3
  3 slope
x  value 1
-2
-4
-6
Line must
cross on
gridline to
count as a
point
44.
Find the length of the rectangle below if the width is 7 feet and the diagonal is 25 feet.
(Standard MG3.3*)
First make a quick drawing.
Use the Pythagorean Theorem like #42
a 2  b 2  c 2 c is the diagonal or longest side. Substitute
25
7
7 2  b 2  252 Simplify
49  b 2  625 Subtract 49 from each side
-49
-49
b 2  576 Take the square root of both sides
b 2  576
b  24
45.
Simplify
What is the minimum, mode, and maximum of the set of numbers below? (Standard PS1.3*)
{23, 125, 65, 77, 23, 14}
Put the numbers in increasing order first. {14, 23, 23, 65, 77, 125}
Minimum is the smallest number, 14.
Maximum is the largest number, 127.
The mode is the number that appears most often, which is 23.
46.
What is the median price of homes in Colton, according to the table below? (Standard PS1.3*)
Home #
1
2
3
4
5
47.
m2 24


8 m5
Price
$144,000
$250,000
$300,000
$186,000
$100,000
Median is the number in the middle. Put the numbers in
increasing order first.
100,000 144,000 186,000 250,000 300,000
The number in the middle is $186,000
(Standard AF2.2)
Remember that you don’t divide by a fraction, you multiply by the inverse (reciprocal) of the
fraction.
m2 24

Change to multiply by the inverse
8 m5
m 2 m5

Multiply the numerators together and the denominators together
8 24
m 2+5
m7

8  24 192
48.
Simplify 8  8
3
5
(Standard NS2.3*)
If powers with the same bases are multiplied, add the exponents.
83  85  835  82 This may be one answer, but usually negative exponents are not left in an
answer. Remember, a negative exponent DOES NOT make a negative number, it makes a fraction
with a positive exponent.
82 
1
1

82 64
The base number goes in the denominator with a positive exponent, and 1 becomes the numerator.
49.
On the map, the distance from Colton to Yucaipa is 2.5 inches. If each inch in the map equals 3 miles,
how far is the real distance form Colton to Yucaipa? (Standard MG1.2)
If each inch on the map equals 3 miles, multiply the number of inches times 3.
3  2.5  7.5 miles
50.
What is the equation of the graph below in slope-intercept form? (Standard AF3.1)
y
See #43 above first.
6
4
2
x
0
-6
-4
-2
0
-2
-4
-6
2
4
6