Algebra Ready Benchmark Test Form C Practice Test Solutions
Show ALL work or you will receive no credit. Solve all equations in steps showing ALL steps.
Circle your answers.
1.
3 1 1
   
12  2 3 
Before you add or subtract fractions, you need common denominators. The denominators 12, 2, and 3 will
all divide into 12, so 12 will be the common denominator.
3 6 1 4 1
      Make common denominators
12  6 2 4 3 
3 6 4
    Simplify
12  12 12 
3  10 
   Simplify
12  12 
7
12
2.
When do you need a common denominator?
You need a common denominator when adding or subtracting fractions
3.
11 3
 
12 8
Before you add or subtract fractions, you need common denominators. The denominators 12 and 8 will
both divide into 24, so 24 is your common denominator.
11 3
 Make common denominators
12 8
2 11 3 3
  
Simplify
2 12 3 8
22 9 13


24 24 24
3
4.
2
  
3
First, distribute the exponent to the numerator and denominator. Then, to make the exponents positive,
change the position of the number from numerator to denominator, or denominator to numerator.
3
2
Distribute the exponent
 
3
2-3
Change position to make exponent positive
33
33 3  3  3
=
Find the values
23 2  2  2
27
8
5.
Shaquita rides her bike at 15 miles per hour. If 1 mile equals 5,280 feet, how many feet per minute can she
ride?
First, find how many feet she rides in 15 miles, then divide that number by 60 to find out feet per
minute.
15  5280
Reduce the fraction first
60
1  5280
Divide
4
feet
1,320
minute
6.
Write an example of the additive inverse property of addition.
Additive Inverse Property: Any number added to its opposite equals 0.
7.
7 + -7 = 0
Ricardo wanted to buy a new computer for $700. He found one online at a 33% discount. How much did he
have to pay for the computer?
Multiply the amount of the computer times the discount written as a decimal.
$700  .33  $231 Original  % of Discount = Discount
$700-$231=$469 Original - Discount = Sale Price
8.
Alyssa received $2000 for babysitting all summer. She put it in the credit union at 4% interest for a year. How
much money did she make in interest, and how much money does she have in the bank at the end of the year?
For interest problems, use the formula
i  prt , where I is the amount of interest, p is the principal, or
amount of money invested or lent, r is the interest rate written as a decimal, and t is the amount of time,
which is usually 1 year. In this problem, p= 3000, I = 4% which is .04, and t is 1 for 1 year.
i  prt Substitute in the values
i  2000 • .04 •1 Simplify
i  80 Interest is $80.
2000+80 Simplify
$2080 Amount in the account after 1 year
9.
Vincent sold $3000 worth of phones and accessories today at Ontario Mills. If he receives a 15% commission,
how much money does he make?
To find the amount of commission, multiply how much sold times the % commission written as a
decimal.
3000  .15 Amount sold times % as a decimal
$450 Commission
10.
4 3

48
There are several ways to solve this problem. The easiest way is to subtract the smallest exponent form
the largest exponent. Where the smallest exponent was becomes a 1.
43
1
1


48 48( 3) 411
11.
Make a math sentence out of the following: twice the difference of a number and 12 is 11.
Start with the difference of a number and 12, which means (n - 12). Twice that means multiply that
difference by 2, which is 2(n – 12). Is 11 means = 11. Putting it all together, the sentence is 2(n – 12)= 11.
12.
Simplify
3(7  12) 2
Use the Order of Operations to tell you what order to solve the expression with. Remember, PEMDAS
means solve parenthesis first, then exponents, then multiplication OR division from left to right, then
addition OR subtraction from left to right.
3(7  12) 2
2
Parenthesis first
3(-5) Exponents next
3(25) Multiplication or Division
75
13.
| 234 | 2 
The absolute value of -234 is 234. Multiply 234 times 2.
| 234 | 2 Take the absolute value, remove the sign
234  2 Simplify
468
14.
Write the number 54,378,210 in scientific notation.
Remember, scientific notation has one number to the left of the decimal point, and usually 2 numbers to
the right. Remember to round the last number to the right. Next, count how far from the new decimal
point to the old one, usually at the end of the number, and this becomes the exponent to the base 10.
54,379,210 Move the decimal point between the first 2 numbers
5.4379210 Round to the 2nd number after the decimal point
5.44 Count how far the decimal point moved, 7 places
5.44  107
15.
Why can’t an absolute value be negative?
An absolute value can’t be negative, because absolute value measures distance, and distance can’t be 0.
The direction of travel may change, but it is always a positive distance.
16.
a.
What is the mean of the set of numbers 2, 4, 8, 12, 20?
The mean of a set of numbers is the average. Add all the numbers together and divide by the
number of entries.
2  4  8  12  20  46 Add the numbers
46  5  9.2 Divide by the number of entries
b.
What is the median of the set of numbers 2, 4, 8, 12, 20?
The median is the number in the middle when the numbers are in order from least to greatest.
The number in the middle of 2, 4, 8, 12, 20 is 8. If there is no middle number because there is an
even number of entries, add the 2 middle numbers and divide by 2.
17.
Give an example of the distributive property of multiplication over addition.
Distribute what is outside to everything inside parenthesis.
Example
3(4  5)  3  4  3  5
18.
Chunky Cheezy software company recorded sales for the first 16 weeks of the year. Make a line graph showing
the sales figures using the table below.
Week #
2
4
6
8
10
12
14
16
Sales (in
millions)
3
3.5
2
3
5
5.5
6
7
14
12
Dollars
10
(in millions)
8
6
4
2
2
4
6
8
10
12
14
Week Number
19.
Mr. Aday worksfor 14 hours out of each 24 hours in the day. What percentage of the day does he work, and
what percentage does he not work?
Make a fraction, with the part you want over the total number of parts. Divide denominator into the
numerator to get the decimal number, then change the decimal into a percent.
14 hours 7
  .583  58.3%
24 hours 12
20.
Write an example of the associative property of multiplication.
In the associative property, just the parenthesis moves.
(3  4)5  3(4  5)
21.
Evaluate
c3  c 2  c if c = 2.
Substitute and solve.
c3  c 2
Substitute the 2
2  2 Simplify
2  2  2  2  2 Simplify
32
3
22.
Expand
2
5c 2 k 3
5c 2k 3  5  c  c  k  k  k
23.
What is the value of x if
x  11  3 .
Show all work in steps going down the paper.
x  11  3 Subtract 11
-11 -11 Simplify
x  -14
24.
Bettikina watched her neighbor’s cats while they were on vacation. She earned $15 a day and made $105. How
many days did she pet sit?
Divide how much she make by how much she earned per day.
105  15  7 days
25.
Find the area and perimeter of the figure below.
6
3
2
5
1
6*5=30
4
3*4=12
5*5=25
14
Perimeter is the distance around an object. First,
find the missing lengths.
4  3  1  5  2  6  5  14  40 units
5
Find the area of each of the 3 boxes, and add
them together to get the area. A = l * w
12  25  30  67 square units
26.
A rectangular garden pictured below has a 3 foot wide sidewalk going all around it. What is the area of the
garden, and what is the area of the sidewalk?
3’ Sidewalk
The easiest way is to find the area of the
inside garden and subtract it from the area
16’
of the outside box.
Garden area = 16  4  64
4’
Outside area
(16  3  3)  (4  3  3) Simplify
22  10 Simplify
220 Subtract Garden Area
-64 Simplify
156 Square Feet for the sidewalk
27.
The rectangle below is cut in half. What is the area of half of the rectangle?
7
12
First, find the area of the rectangle using the formula
A  length  width , then divide the product by 2.
A  length  width Substitute in the values
A  12 • 7 Simplify
A  84 Divide by 2
84
A
 42 Square Units
2
28.
Solve
3x  16  11
Show All steps going down the page.
3 x  16  11 Add 16
+16 +16 Simplify
3 x  27 Divide by 3
3 x 27

Simplify
3
3
x9
29.
Find the solution set of the inequality
3x  13  11.
Show ALL steps going down the page.
3 x  13  11 Subtract 13
-13 -13 Simplify
3 x  -24 Divide by 3
3x
24

Simplify
3
3
x  -8
30.
Find the value of
(7  32  4)2 .
Use PEMDAS to solve in the proper order.
(7  32  4) 2 Inside parenthesis, use PEMDAS Exponents first
(7-9+4) 2 Inside parenthesis, Add or Subtract left to right
(-2+4) 2 Inside parenthesis, Add or Subtract left to right
31.
22 Simplify
4
Bacteria
are increasing at the same rate each hour. What is that rate? Use the table to record your findings.
16
14
Number of
Bacteria
Present
12
Hours
# Bacteria
1
1
2
2
*2
3
4
*2
4
8
*2
5
16
*2
10
8
6
4
2
2
4
6
8
Hours
10
12
14
Bacteria are increasing times 2
each hour.
32.
Mutt drove his Mustang for 3 hours at 65 miles per hour. Jeff drove his Camaro for 4 hours at 50 miles per hour.
How far did they both drive, and what was the average speed for both cars?
Find out how far each person drove, then add together. Divide by the total number number of miles to get
the average speed.
3  65  195 miles Mutt
4 • 50  200 miles Jeff
395 miles in 7 hours Divide
395
miles
 56.43
average
7
hour
33.
Jabari wants to pay $2800 for professional wrestling lessons. If his summer job pays $8.00 an hour, how many
hours will he have to work to pay for the lessons?
Divide the amount of money by how much he earns per hour.
2800
 350 hours
8
34.
Ashley runs the 1st mile in 6 minutes, then can only run the rest of the miles in 8 minutes each. How long would
it take her to run 10 miles?
1st mile = 6 minutes
10-1=9 miles left at 8 minutes = 72 minutes
Total 6 + 72 = 78 minutes
35.
Jack can dye 4 eggs in 2 hours, and Jill can dye 6 eggs in 4 hours. How many eggs can they both dye in 8 hours?
Set up 2 proportions, one for Jack and one for Jill.
4 eggs x eggs

Cross multiply
2 hours 8 hours
4 • 8  2 x Simplify
32  2 x Divide by 2
32 2 x

Simplify
2
2
16  x 16 eggs for Jack
36.
What is the coefficient of
6 eggs
x eggs

Cross multiply
4 hours 8 hours
6 • 8  4 x Simplify
48  4 x Divide by 4
48 4 x

Simplify
4
4
12  x eggs for Jill
4 x2  9 ?
The coefficient is the number in front of the x-value, which is 4.
37.
Write a math sentence showing that Buela is 7 years younger than Leland.
Leland – 7 = Buelah L – 7 = B
Buelah + 7 = Leland B + 7 = L
38.
Change the decimal .8 into a fraction.
.8=
39.
8 4
=
10 5
If it takes 2 gallons of soda to serve 6 students, how many gallons of soda would be needed for 9 students?
Set up a proportion
2 gallons x gallons
=
cross multiply
6 students 9 students
2 • 9  6 x Simplify
18  6 x Divide by 6
18 6 x

Simplify
6
6
6  x 6 gallons of soda
40.
A $70 cell phone is marked down to $40. What is the percent of savings?
Subtract the sale price from the original price to find the amount of savings. Divide the amount of savings
by the original price of the cell phone, and change the decimal into a percent.
70  40  30 Amount of savings
30
 .428 Change to a percent
70
42.8%
41.
Change
2
to a decimal.
3
Divide the denominator into the numerator.
2
means 2 divided by 3
3
.666 round to .667
42.
Find the length of the hypotenuse, or longest side, of the triangle using the Pythagorean Theorem.
8
The Pythagorean Theorem is a  b  c . Where a and b are the
sides and c is the hypotenuse, or longest side. Substitute the numbers
into the equation to solve.
2
6
?
2
2
a 2  b 2  c 2 Substitute the numbers
82  62  c 2 Simplify
64  36  c 2 Simplify
100  c 2 Square root both sides
100  c 2 Simplify
10  c
43.
Find the slope and y-intercept of the line below.
y
Find the slope by locating 2 points on the line
that also cross where gridlines meet. The
points to use are (0, -1) and (4, 2).
4
4
2
3
-6
-4
x
0
-2
The y-intercept is where the line meets the yaxis, which is -1.
0
2
4
6
The slope is the distance up over the distance
to the right between the points.
-2
-4
44.
The slope is
3
.
4
Find the length of the rectangle below.
On any right triangle, use the Pythagorean Theorem
to find the missing length.
The Pythagorean Theorem is a  b  c . Where a
and b are the sides and c is the hypotenuse, or
longest side. Substitute the numbers into the
equation to solve.
2
10
6
2
a 2  b 2  c 2 Substitute the numbers
?
62  b 2  102 Simplify
36  b 2  100 Subtract 36
-36
-36 Simplify
b  64 Square root both sides
2
b 2  64 Simplify
b8
2
45.
Find the minimum, maximum, median, mode, and mean of the following set of numbers.
{2, 5, 6, 6, 8, 10, 12]
First, put the numbers in order from least to greatest.
Minimum is the smallest number 2
Maximum is the largest number 12
The median is the number in the middle, which is 6
The mode is the number that appears most often, 6.
The mean is the average. Add all the numbers and divide by the number of entries.
2  5  6  6  8  10  12  45 Divide by 7
45
 6.43
7
Minimum 2
46.
Maximum 12 Median 6 Mode 6 Mean 6.43
What is the median price of the swimsuits listed in the table below?
$20
$32
$11
$15
$16
Median is the number in the middle. Put the numbers in order first.
11, 15, 16, 18, 20, 30, 32 The number in the middle is 18.
47.
Simplify
m6 m 2

3
9
When dividing by fractions, multiply by the inverse.
m6 m 2

Multiply the inverse
3
9
m6 9

Gather like terms
3 m2
m6 9

Simplify
m2 3
m62  3 Simplify
3m 4
$18
$30
48.
Simplify
24 3

32 23
When dividing by fractions, multiply by the inverse.
24 3

Invert and multiply
32 23
2 4 23

Gather like terms
32 3
24+3
Simplify
3-2+1
27
Change the negative exponent to positive by moving it to the top
3-1
27  31 Expand and simplify
2 • 2 • 2 • 2 • 2 • 2 • 2 • 3  384
49.
On a map, the distance from Colton to Palm Springs is 7 inches. If the map has a scale of 1 inch = 10 miles, how
far away is Palm Springs?
Solve as a proportion
1 inch
7 inches

Cross multiply
10 miles x miles
7 •10  1x Simplify
70  x
70 miles
50.
In the quadratic equation
y  3x 2  2 x  1 , does the parabola open up or down?
2
Why?
If the number in front of the x value is positive, the parabola opens up. If the number in front of
negative, the parabola opens down. Since the number is -3, the parabola opens down.
x 2 is
51.
Find the prime factors of 144.
Remember, prime numbers are numbers that can only be divided by 1 and itself. The prime numbers we
covered were 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59.
144
2
72
2
36
2
18
2
9
3
The prime factors are
52.
3
2  2  2  2  3  3  24  3
What is the mean of the set of data {3, 6, 9, 12, 4, 2}?
The mean is the average. Add all of the numbers together, and divide by the number of entries.
3  6  9  12  4  2  36 Divide by 6
36
6
6
53.
In the cafeteria, you can order several different combinations of food. You have a choice of 3 main courses, 2
side items, and 3 desserts. How many possible combinations of meals are there?
Main Course
Side Items
Dessert
Pizza
Salad
Ice Cream
Corn Dog
French Fries
Fruit
Vegetable Plate
Granola Bar
The easiest way to find the number of combinations is to multiply the number of entries for each type of food
together. The main course has 3 entries, the side items have 2 entries, and the dessert has 3 entries.
3  2  3  18 possible combinations
54..
On the circle below, make a circle graph showing that 25% of the time is spent being active and 75% of the time
is spent sitting down.
active
Sitting down
55.
If Maritza rolls one six-sided die, what is the probability that she rolls an odd number?
Maritza could roll a 1, 2, 3, 4, 5, or a 6. The odd numbers are 1, 3, and 5. So she has a 3 out of 6 chance
she will roll an odd number. This can also be written as
56.
3 1
 , or 1 out of 2 chances.
6 2
Make a line graph below showing that the cost for each person for admission to Scandia is $10.
Make a table to put points on
the graph.
140
120
People
Cosst
1
10
2
20
40
3
30
20
4
40
5
50
100
Price
80
60
2
4
6
8
Number of People
10
12
14
57.
In the grid below, where would the other 2 points be to make a 20 square unit rectangle?
y
Since there are 4 boxes across,
4
4 x  20 Divide by 4
4 x 20

Simplify
4
4
x  5 There must be 5 boxes high
2
x
0
-6
-4
-2
0
-2
-4
2
4
6
The other 2 points must be at (-1, 2)
and (-5, 2)