College Math Unit 2 Lesson 1 Classwork
Solve each equation. Check your solution.
1.
7𝑥 − 5𝑥 + 15 = 𝑥 + 8
2.
12𝑤 + 15𝑤 − 9 + 5 = −3𝑤 + 5 − 9
3.
3(2𝑡 − 4) = 20 − 2𝑡
4.
−2𝑥 + 5𝑥 − 9 = 3(𝑥 − 4) − 5
5.
−2(𝑡 + 3) − 𝑡 − 4 = −3(𝑡 + 4) + 2
6.
2[𝑤 − (2𝑤 + 4) + 3] = 2(𝑤 + 1)
7.
−3𝑚 + 6 − 5(𝑚 − 1) = −5𝑚 − (2𝑚 − 4) + 5
8.
−[3𝑥 − (2𝑥 + 5)] = −4 − [3(2𝑥 − 4) − 3𝑥]
9.
10.
11.
5
− 𝑘=2
9
𝑚
+
2
3𝑥−1
4
𝑚
3
+
=5
𝑥+3
6
=3
12.
0.05𝑥 + 0.12(𝑥 + 5000) = 940
13.
0.2(50) + 0.8𝑟 = 0.4(50 + 𝑟)
College Math Unit 2 Lesson 1 Homework
Solve each equation. Check your solution.
1.
2𝑥 + 4 − 𝑥 = 4𝑥 + 5
2.
−4𝑡 + 5𝑡 − 8 + 4 = 6𝑡 − 4
3.
2(3 − 2𝑥) = 𝑥 − 4
4.
−6𝑥 + 2𝑥 − 11 = −2(2𝑥 − 3) + 4
5.
4(2𝑑 + 7) = 2𝑑 + 25 + 3(2𝑑 + 1)
6.
2[𝑤 − (2𝑤 + 4) + 3] = 2(𝑤 + 1)
7.
8.
9.
10.
11.
−[2𝑧 − (5𝑧 + 2)] = 2 + (2𝑧 + 7)
7[2 − (3 + 4𝑥)] − 2𝑥 = −9 + 2(1 − 15𝑥)
3
11
𝑥
5
𝑧 = −5
𝑥
− =1
4
3𝑥+2
7
−
𝑥+4
5
=2
12.
0.09𝑘 + 0.13(𝑘 + 300) = 61
13.
0.8𝑥 + 1.2(260 − 𝑥) = 4.8𝑥
College Math Unit 2 Lesson 2 Classwork
Solve the formula or equation for the specified variable.
1.
𝑃 = 2𝐿 + 2𝑊 𝑓𝑜𝑟 𝐿
2.
𝑉 = 𝐿𝑊𝐻 𝑓𝑜𝑟 𝑊
3.
𝐴 = 2 ℎ(𝑏 + 𝐵) 𝑓𝑜𝑟 𝐵 (area of a trapezoid)
4.
𝐹 = 5 𝐶 + 32
5.
2𝑘 + 𝑎𝑟 = 𝑟 − 3𝑦
6.
(perimeter of a rectangle)
(volume of a rectangular prism)
1
9
𝑤=
3𝑦−𝑥
𝑦
𝑓𝑜𝑟 𝐶 (Celsius to Fahrenheit)
𝑓𝑜𝑟 𝑟
𝑓𝑜𝑟 𝑦
Solve each problem
7. Faye Korn traveled from Kansas City to Louisville, a distance of 520 mi. in 10 hr. Find her rate in
miles per hour. (d=rt)
8.
As of 2009, the highest temperature ever recorded in Chicago was 40°C. Find the
9
corresponding Fahrenheit temperature. (𝐹 = 5 𝐶 + 32 )
9.
The circumference of a circle is 480π in. What is the radius of the circle? (C= 2πr)
10.
A mixture of alcohol and water contains a total of 36 oz. of liquid. There are 9 oz. of pure
alcohol in the mixture. What percent of the mixture is water? What percent is alcohol? (percent =
part/whole)
11. A real estate agent earned $6300 commission on a property sale of $210,000. What is her rate
of commission?
College Math Unit 2 Lesson 2 Homework
Solve the formula or equation for the specified variable.
1.
𝑃 =𝑎+𝑏+𝑐
2.
𝐴 = 2 𝑏ℎ 𝑓𝑜𝑟 ℎ
3.
𝑆 = 2𝜋𝑟ℎ + 2𝜋𝑟 2 𝑓𝑜𝑟 ℎ
4.
𝐶 = 9 (𝐹 − 32 ) 𝑓𝑜𝑟 𝐹 (Fahrenheit to Celsius)
5.
4𝑠 + 7𝑝 = 𝑡𝑝 = 7 𝑓𝑜𝑟 𝑝
6.
1
𝑓𝑜𝑟 𝑏
(perimeter of a triangle)
(area of a triangle)
(surface area of a right circular cylinder)
5
𝑐=
−2𝑡+4
𝑡
𝑓𝑜𝑟 𝑡
Solve each problem
7. The distance from Melbourne to London is 10,500 mi. If a jet averages 500 mph between the
two cities, what is its travel time in hours? (d=rt)
8.
As of 2009, the lowest temperature ever recorded in Memphis was -13°F. Find the
5
corresponding Celsius temperature. (𝐶 = 9 (𝐹 − 32 ) )
9.
The radius of a circle is 2.5 in. What is the circumference of the circle? (C= 2πr)
10.
A mixture of acid and water contains is 35% acid. If the mixture contains a total of 40 L, how
many liters of pure acid are in the mixture? (percent = part/whole)
11. A certificate of deposit for 1 yr pays $221 simple interest on a principal of $3400. What is the
interest rate being paid on this deposit? (I = Prt)
College Math Unit 2 Lesson 3 Classwork
Use x to represent the number and translate each expression, equation or inequality into algebraic
terms.
1.
2.
3.
4.
a. 12 more than a number
a. 4 is less than a number
Twice a number decreased by 13.
The product of 8 and 12 less than a number.
b. 12 is more than a number
b. 4 less than a number
Write an equation or inequality and solve.
5.
If the product of a number and -4 is subtracted from the number, the result is 9 more than the
number. Find the number.
6.
When 2/3 of a number is subtracted from 12, the result is 10. Find the number.
7.
The Bermuda triangle supposedly causes trouble for aircraft pilots. It has a perimeter of 3075
mi. The shortest side measures 75 mi. less than the middle side, and the longest side measures 375
mi. more than the middle side. Find the lengths of the 3 sides.
8
Two of the longest running Broadway shows were Cats, which played from 1982 through 2000,
and Les Miserables, which played from 1987 through 2005. Together there were 14,165
performances of these two shows during their Broadway runs. There were 805 fewer performances of
Les Miserables than of Cats. How many performances were there of each show?
9.
Composite scores on the ACT exam fell from 21.0 in 2001 to 20.8 in 2002. What percent
decrease was the drop?
10.
At the end of a day, Jeff Hornsby found that the total cash register receipts at the motel where
he works amounted to $2,725. This included the 9% sales tax charged. Find the amount of the tax.
11.
Carter Fenton earned $12,000 last year by giving tennis lessons. He invested part of the
money at 3% simple interest and rest at 4%. I one year, he earned a total of $440 in interest. How
much did he invest at each rate?
College Math Unit 2 Lesson 3 Homework
Use x to represent the number and translate each expression, equation or inequality into algebraic
terms.
1.
2.
3.
4.
a. 3 less than a number
b. 3 is less than a number
a. 6 greater than a number
b. 6 is greater than a number
The product of 6 and a number, decreased by 12.
The product of 9 more than a number and 6 less than the number.
Write an equation or inequality and solve.
5.
If the quotient of a number and 6 is added to twice the number, the result is 8 less than the
number. Find the number.
6.
When 75% of a number is added to 6, the result is 3 more than the number. Find the number.
7.
The perimeter of a certain rectangle is 16 times the width. The length is 12 cm more than the
width. Find the length and width of the rectangle.
8
Galileo Galilei conducted experiments involving Italy’s famous Leaning Tower of Pisa to
investigate the relationship between an object’s speed of fall and its weight. The Leaning Tower is
804 ft. shorter than the Eiffel Tower in Paris, France. The two towers have a total height of 1,164 ft.
How tall is each tower?
9.
In 1995 the average cost of tuition and fees at public four-year universities in the United States
was $12, 216 for full-time students. By 2005 it had risen approximately 95%. To the nearest dollar,
what was the approximate cost in 2005?
10.
Fino Roverato sold his house for $159,000. He got this amount knowing that he would have to
pay a 6% commission to his agent. What amount did he have after the agent was paid?
11.
Courtney Slade won $60,000 on a slot machine in Las Vegas. She invested part of the money
at 2% simple interest and the rest at 3%. In one year she earned a total of $1,600 in interest. How
much was invested at each rate?
College Math Unit 2 Lesson 4 Classwork
Solve each inequality. Give the solution set in both interval and graph form.
1.
𝑥 − 4 ≥ 12
2.
−1.3𝑚 ≥ −5.2
3.
2𝑘−5
−4
>5
4.
6𝑥 − 4 ≥ −2𝑥
5.
−(4 + 𝑟) + 2 − 3𝑟 < −14
6.
1
3
4
2
− (𝑝 + 6) + (2𝑝 − 5) < 10
2𝑥−5
7.
−1 ≤
8.
4 ≤ −9𝑥 + 5 < 8
6
≤5
Write and solve an inequality to find the unknown numbers.
9.
Half a number is between –3 and 2.
10.
One third of a number is added to 6, giving a result of at least 3.
Solve the problem.
11.
Finley Westmoreland earned scores of 90 and 82 on his first two tests in English literature.
What score must he make on his third test to keep an average of 84 or greater?
College Math Unit 2 Lesson 4 Homework
Solve each inequality. Give the solution set in both interval and graph form.
1.
5𝑧 + 6 < 76
2.
−2.5𝑦 ≤ −1.25
3.
3𝑧−2
−5
<6
4.
−2𝑚 + 8 ≤ 2𝑚
5.
−(9 + 𝑘) − 5 + 4𝑘 ≥ 4
6.
7.
3
5
1
(𝑘 − 2) − (2𝑘 − 7) ≤ 3
4
4 ≤ −2𝑥 + 3 < 8
8.
−16 < 3𝑡 + 2 < −10
Write and solve an inequality to find the unknown numbers.
9.
Six times a number is between –12 and 12.
10.
Three times a number, minus 5, is no more than 7.
Solve the problem.
11.
Jack Hornsby scored 92 and 96 on his first two tests in Calculus. What score must he make on
his third test to keep an average of 90 or greater?
College Math Unit 2 Lesson 5 Classwork
Let 𝐴 = {1,2,3,4,5,6}, 𝐵 = {1,3,5}, 𝐶 = {1,6} 𝑎𝑛𝑑 𝐷 = {4}
Specify each set
1.
𝐵∩𝐴
2.
𝐵∪𝐷
Two sets are specified by graphs. Graph the intersection of the two sets.
3.
4.
For each compound inequality, give the solution set in both interval and graph form.
5.
6.
𝑥 ≤ 3 𝑎𝑛𝑑 𝑥 ≥ 6
𝑥 − 3 ≤ 6 𝑎𝑛𝑑 𝑥 + 2 ≥ 7
7.
3𝑥 − 4 ≤ 8 𝑎𝑛𝑑 − 4𝑥 + 1 ≥ −15
8.
𝑥 ≤ 1 𝑜𝑟 𝑥 ≤ 8
9.
𝑥 + 2 > 7 𝑜𝑟 1 − 𝑥 > 6
10.
4𝑥 + 1 ≥ −7 𝑜𝑟 − 2𝑥 + 3 ≥ 5
Express each set in the simplest interval form
11. (−∞, −1] ∩ [−4, +∞)
12.
[3, 6] ∪ (4,9)
College Math Unit 2 Lesson 5 Homework
Let 𝐴 = {1,2,3,4,5,6}, 𝐵 = {1,3,5}, 𝐶 = {1,6} 𝑎𝑛𝑑 𝐷 = {4}
Specify each set
1.
𝐴∩𝐷
2.
𝐵∪𝐶
Two sets are specified by graphs. Graph the intersection of the two sets.
3.
4.
For each compound inequality, give the solution set in both interval and graph form.
5.
𝑥 ≤ −1 𝑎𝑛𝑑 𝑥 ≥ 3
6.
𝑥 + 5 ≤ 11 𝑎𝑛𝑑 𝑥 − 3 ≥ −1
7.
7𝑥 + 6 ≤ 48 𝑎𝑛𝑑 − 4𝑥 ≥ −24
8.
𝑥 ≥ −2 𝑜𝑟 𝑥 ≤ 4
9.
𝑥 + 1 > 3 𝑜𝑟 𝑥 + 4 < 2
10.
3𝑥 + 2 ≤ −7 𝑜𝑟 − 2𝑥 + 1 ≤ 9
Express each set in the simplest interval form
11. [−1, +∞) ∩ (−∞, 9]
12.
[−1, 2] ∪ (0,5)
College Math Unit 2 Lesson 6 Classwork
Solve and graph the solution set.
1.
|2𝑥 − 1| = 11
2.
|2 𝑥 + 3| = 2
3.
|𝑟 + 5| ≥ 20
4.
|3𝑥 − 1| < 8
5.
|−6𝑥 − 6| ≤ 1
6.
1
|𝑥 + 4| + 1 = 2
7.
|𝑥| ≥ −10
8.
|2𝑡 − 3| = −8
9.
|7𝑥 + 3| ≤ 0
10.
|10𝑧 + 7| + 3 < 1
11. The 2005 recommended daily intake (RDI) of calcium for females aged 19-50 is 1000 mg.
Actual mineral needs vary from person to person. Write an absolute value inequality with x
representing the RDI, expressing the RDI plus or minus 100 mg., and solve the inequality.
College Math Unit 2 Lesson 6 Homework
Solve and graph the solution set.
1.
|2𝑦 + 3| = 13
2.
|3 𝑞 − 1| = 5
3.
|3𝑥 − 1| ≥ 8
4.
|𝑡 + 2| ≤ 10
5.
|2𝑠 − 6| ≤ 6
6.
2
|𝑟 − 2| − 3 ≤ 4
7.
|4𝑥 + 1| = 0
8.
|8𝑛 + 4| = −4
9.
|7𝑥 + 3| ≤ 0
10.
|4𝑥 − 1| ≥ 0
11.
The average clotting time of blood is 7.45 sec., with a variation of plus or minus 3.6 sec. Write
this statement as an absolute value inequality with t representing the time, and solve the inequality.