Download Practice Test, Module 1, Topic C1 1. Solve each equation or

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Practice Test, Module 1, Topic C1
1. Solve each equation or inequality. Then circle all of the problems where
the solution set.
DO NOT MULTIPLY
Give each parentheses a zero:
is included in
divide by -1
to get:
inequality flips
Then solve each one separately:
Make into 16
Multiply each side by
Left side is just 100
You get:
Solve as usual
Answer:
distribute the 2
add the 14 to the -9
divide by 2
you get:
this DOES include the value
of
since -2 is less than 2.5
Multiply each side by 5
To get:
Solve for x
You get:
subtract 3 from both the 0 and 9
you get:
this DOES include the value
of
since -2 is between
-3 and 6
The problems with solutions that include -2 are circled in green
2. Circle and describe the mistake(s) in the following steps used to solve:
.
Describe the mistake(s):
This is the typo-fixed version. The only mistake is flipping
the inequality when it shouldn’t be flipped.
Graph the correct solution on a number line:
This is the typo-fixed version. This version has an answer
of
so its graph would have a dot at -6 with
shading to the right.
3. Fill in the chart.
Write an equation
or inequality
Describe solution
set in words
example:
all real numbers
except 2
Write the solution in
set notation
Show on Number Line
all real numbers
less than 3
all real #’s greater
or equal to -1
all real #’s less than
or = to 4, or greater
than or = to 6
4
6
all real numbers
between 0 and 3
all real numbers
equal to -2 and 2
-2
0
2
all real numbers
equal to 5
The first column can repeat the solution from the set notation as its equation, or you can make it more
complex by adding 1 or subtracting 2 or multiplying by 3 or whatever to both sides of the solution
4. Using the phrases from the left, fill in the blanks with the property used to convert the equation
from one line to the next. Some may not be used; others may be used more than once.
Associative Property
Commutative Property
commutative (changed order)
Distributive Property
distributive (got rid of parentheses)
Combine like terms
additive prop of equality
Additive Property of Equality
additive prop of equality
(“additive” includes subtracting
something from both sides)
We often end a problem by dividing on both sides; this would be called the multiplicative prop of equality because
dividing can also be done by multiplying by the reciprocal
Multiplicative Prop. of Equality
5. A car salesman earns a percentage of the value of the cars he sells. He also earns $200 per month
to cover expenses. Last month, the value of cars sold was $60,000 and he earned a total of $1700.
a. Write an equation to find the percentage, , that he earns on the cars sold.
(because the value is the only one multiplied by the percent)
b. Find the percentage he earns.
subtract 200 from 1700; divide that by 60,000
but the answer is interpreted as: 2.5%
6. Tax is added to some purchases in Washington. At the grocery store, I bought some items that
were not taxed for $18. The rest of the items cost $25 before tax was added. I paid a total of $45.
a. Write an equation to find the tax percentage, , paid on the second part of my purchase.
(the 25 is the only one multiplied by the percent; the 18 stays 18)
b. What is the tax percentage?
subtract 18 from 45; divide by 25. You get
But that is interpreted as a tax percentage of 8% for the final answer
7. Given this situation:
To get a discounted movie ticket, movie goers must be either
under the age of 10 (not including 10) or aged 65 and older.
Complete the table:
define the variable
write a compound inequality
show on a number line
age in years
Sorry, I can’t draw the graph with this program. But you’d have an open circle on 10, with shading to the left;
then you’d have a dot on 65, with shading to the right. And the # line would probably count by 10’s.
8. Given this situation:
To be considered a miniature poodle, a poodle’s height at its
shoulders must be more than 28 cm but less than 38 cm.
Complete the table:
define the variable
write a compound inequality
show on a number line
graph has open circles on 28 and 38 (# line probably counting by 2’s from mid-20’s) with shading in between.
9. A farmer needs to move some bales of hay between two barns. Right now, the larger barn has
400 bales and the smaller barn has 150 bales. How much hay does he need to move in order for
the larger barn to have four times as much hay as the smaller barn? Support your answer..
group
split
(the split is your x’s, the group is your total)
BUT you then compare: the small group started with 150
now they’re at 110, so they must have moved 40, so the answer is 40
10. A packaging company makes large and small bags of candy. Right now, the machines put 75
candies in the large bag and 45 candies in the small bag. But they want the small bag to have
one third as much candy as the large bag. How many candies do they need to move from the
small bag to the large bag in order to make that happen? Support your answer.
one third is another way of saying “three times as many”,
just from the large bag’s perspective
solve and you get that x is 40, but remember, you need to compare:
small bag started with 45, ended with 40
the answer is: 5 moved
11. A rectangular sandbox measuring 4 feet by 5 feet will have a shredded bark walkway around it.
The walkway is of uniform width, but the width has not been chosen.
There is only enough bark to cover 46 square feet of walkway.
This started as 26, but that was a typo.
a) Write an inequality that represents the total area of the walkway, based on the width
the walkway, given that the total cannot exceed 46 square feet.
of
The
represents the 4 corners. The 18w represents the rectangular
edge pieces, which lie against the inner rectangle’s 4-by-5 perimeter. The 46 is the upper limit.
b) Select all the possible values for the width of the walkway from the chart that could satisfy
the square footage requirement.
1.5 foot
2 feet
2.5 feet
3 feet
Test the given numbers in
Start with something in the middle. Here I’d start
with 2:
and I would get 52. Since that’s too big, 1.5 must be the answer.
12. A small rectangular pool is going to have a concrete edge of uniform width around all of its sides.
The pool is 10 feet by 20 feet, but the width of the concrete edge has not
yet been chosen.
To keep expenses low, the total area of the concrete cannot exceed 220
square feet.
a) Write an inequality that represents the total area of the walkway, based on the width
the walkway, given that the total cannot exceed 220 square feet.
of
again, 4 corners for the first term; perimeter times w for the second term.
b) Select all the possible values for the width of the walkway that could satisfy the square
footage constraint.
1.5 foot
2 feet
2.5 feet
3 feet
Test the given numbers in
Start with something in the middle. Here I’d start with 2:
and I would get 136. So I go bigger & try either 2.5 or 3. (Actually, all of these work.)
13. Solve each equation or inequality:
distribute the 3
divide by -50
combine like terms on the left
it won’t go evenly, so leave it as a fraction
subtract 7 from the 12
remember to flip the inequality
divide by 3 (won’t go evenly --- use a fraction)
distribute the -3 (watch your signs!)
distribute the 2
combine like terms on the left
put all the letters on one side,
subtract the 6 from the 12
numbers on the other
divide
divide (won’t go evenly)
14. Match the solutions in the box to the equations shown below. Not all solutions will be used;
some solutions may be used more than once.
a)
Different x’s --- not a trick problem
#’s will cancel to zero --- answer will be zero
a)
b)
Same x’s, same numbers on each side, so everything cancels
That means “infinite solutions”
b)
c)
c)
the terms cancel; you have different x’s, no numbers
Not a trick problem, but the answer is zero
15. Solve the following equation for x.
Left side:
Distribute the -1
Combine the 2 and -2
(they cancel to 0)
Right side:
Distribute the 2
Combine the 7 and 8
Subtract the 2x from both sides
You should end with
Divide to get
16. Consider the inequality:
.
Decide whether or not each value in the table is a solution.
Solution
Not a solution
-15
8
10
15
Two choices --Option 1: you can solve the inequality (subtract 7 from both sides, divide by -1, flip the inequality).
Consider how you would graph the result. Then look at the #’s in each row of the table. Decide if
the number would be part of the shaded section of the number line graph that would result. If so,
mark it as a solution. If not, mark it as not a solution. Remember, an open circle would not be part
of the shaded solution.
Option 2: take the number from column 1 and plug it in for x in the inequality. Multiply it by -1, add
7, and see if it does result in something larger than -3. If it does, then it’s a solution. If not, then not.