math basic algebra work sheets 12 work sheets

Math 090 Wk 8 TU Individual Worksheet

1. Are the following factored correctly or incorrectly? If they are correct, mark ”correct”, and if they are
incorrect, factor it correctly.

a. x2 − 5x − 6 b. 4m2 + 20m + 25 c. −x2 + 16x − 60
= (x − 2)(x − 3) = (2m + 5)2 = (−x − 10)(x + 6)

2. Factor the following fully. Remember, it is possible that they may not be able to be factored, in which case
they are called prime.

z2 + 2z − 24 a2 − 9ab + 18b2

12p3 − 12p2 + 3p − 6a3 − 12a2 + 90a

x2 − 25 2×3 − x2 − 8x + 4

50x2y3 − 18y 9w2 − 42w + 49

x4 − 64 x4yz − x2yz

x2 + 16 x3 + 27

64m3 − 125n3 x2 + x + 5

Math 090 Wk 7 TR GW

1. Factor out the greatest common factor.

(a) −3z5w2 − 18z3w4 check:

(b) 15a2c3 − 25ac2 + 5ac check:

(c) 14a3b2 + 7a2b − 21a5b3 + 42ab4 check:

2. Factor each of the following by grouping. You might have to reorder the terms before you can factor by
grouping. Check your answers by multiplying all the factors back together.

(a) 2k + 2h + jk + jh check:

(b) 2xy + 3y + 2x + 3 check:

(c) 2a3 + a2 − 14a − 7 check:

(d) 10ab − 21 − 6b + 35a check:

(e) 5×3 + 15x2y2 − 5xy − 15y3 check:

(f) 2x3y2 + x2y2 − 14xy2 − 7y2 check:

3. Factor the following by grouping, without simplifying first.

a. 8×2 + 10x − 12x − 15

b. Now, looking back at the original equation, simplify it (combine like terms).

c. Check your answer from part a, and see if it matches your answer from part b.

Math 090 Wk 7 TU Individual Sheet

1. Multiply.

14x2y3(−2x5y) 5r3(2r2 + 3r + 4) (2y − 5)(3y + 4)

m3(3m + 7)(3m − 7) (2x + 5)2

2. Divide.

64×3 − 72×2 + 12x
8×3

p3 + 3p2 − 4
p + 2

3. Divide. If there is a remainder, write your solution in the form
P (x)

D(x)

= Q(x) +

R(x)

D(x)
where P (x) is the

dividend; D(x) is the divisor; Q(x) is the quotient; and R(x) is the remainder.

(3k3 + 9k − 14) ÷ (k − 2)

4. Given f(x) = x2 − 2x, g(x) = x − 3, and h(x) = x3 − 2×2 − 9, find the following.
(fg)(x) = f(x) · g(x) (fg)(−1)

(f ◦ g)(x) = f(g(x)) f(g(−1))

(
h

g

)
(x) =

h(x)

g(x)

(
h
g

)
(−1)

5. For P (x) = x3 − 4×2 + 3x − 5 and D(x) = x + 1, find the following.
P (x)

D(x)

P (−1) note this is x = −1, which comes from setting x + 1 = 0 and solving for x. Compare this with your
remainder above. What does this suggest?

Wk 6 Tuesday Exponents and Scientific Notation

1. Determine whether the following have been worked out correctly or not. If they are correct, simply state,
”correct”; if they are incorrect, please find the correct solution.

(ab)2 = ab2

(
2

a

)3
=

8

a3
(a 6= 0) y2 ·y6 = y12

xy0 = 0 45 · 42 = 167 26 = (22)3 = 43 = 64

2. Assume the variables represent nonzero real numbers. Simplify the following.

30 + (−3)0 − 20 + a0 − 2×0

3. Simplify and write each expression with only positive exponents. Assume all variables represent nonzero real
numbers.

7−2 − b−4 2−1 + 8−

1

23×12

2−2×4

4. Simplify and write each expression with only positive exponents. Assume all variables represent nonzero real
numbers.(

1

5

)−2
(5a−1)4(a2)−3 − 4r−2(r4)2

(z−4×3)−2
(p−2)0

5p−4
m2n−8

m−6n3

(
2p

q2

)3 (
3p4

q−4

)−1 (
− 3x4y6

15x−6y7

)−3

5. Write each number in scientific notation.

−976, 000, 000 0.0072 0.000000589

6. Write each number in standard notation.

7.2 × 104 5.42 × 10−6 − 8.91 × 102

Review for Exam 1 Wk 5 TU

1. Find the x-intercept and y-intercept for the following, and then use them to graph the functions.

2x + 4y = −8 y = −1
4
x + 2

2. Find the slope and y-intercept, then graph.

−3x− 5y = −15 − 3x + 4y = −20

3. Find an equation for the line described. You can leave your answer in point-slope form or slope-intercept
form.

Line passing through the points (−9,−6) and (−4, 5).
Line passing through (−8, 2) with a slope of −5

4
.

Line passing through (9, 6) and parallel to the line y = 3
2
x.

Line passing through the origin and perpendicular to the line y = 3
2
.

4. Owners of a recreation area are filling a small pond with water at a rate of 35 liters per minute. There are
700 liters in the pond when they begin.

Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes the
water has been added.

Write an equation relating W to T , and the graph your equation.

5. An internet provider charges an $80 activation fee plus $45 per month. Let m represent the number of
months you have internet from them, and C represent the total cost for that time period. Write an equation
showing the total cost C in terms of the number of months used m. How much does it cost to use their
internet service for one year? If you have $395 budgeted for internet use, how many months can you use this
company’s internet service?

6. In 1980, there were 119,000 farms in Iowa. As of 2012, there were 92,200. Find and interpret the average
rate of change in the number of farms per year.

7. The entire graph of the function h is shown in the figure below. Write the domain and range of h using
interval notation.

8. The graph of a function f is shown below. State the domain and range of the function.

Find f(2) and find one value of x for which f(x) = −3.

9. Given f(x) = 3 − 2x, g(x) = 3x−x2, and h(x) = 10 −|2 −x|, find the following.
f(0) g(3) h(0) g(−x) f(2 + x) h(x + 2)

10. Solve the following system of equations using substitution or elimination.

y = 3x− 4 6x + 9y = −3 7x− 2y = −9 4y + 3x = 20 x−y = 3
4x + 3y = 27 6x + 5y = 9 4x− 5y = −9 8y = 16 − 6x 4x = 4y + 12

11. A jet travels 1464 miles against the wind in 2 hours, and it travels 1704 miles with the wind in the same
amount of time. What is the rate of the jet in still air, and what is the rate of the wind?

12. Hong bought a desktop computer and a laptop. Before financing charges, the laptop cost $400 less than the
desktop. He paid for the computers using two different financing plans. For the desktop, the interest rate
was 7.5% per year, and for the laptop, it was 8% per year. The total finance charge for one year was $371.
How much did each computer cost before finance charges?

13. Tickets to a production of Midsummer Night’s Dream at Broward College cost $5 for general admission or
$4 with a student id. If 184 people paid to see a performance and $812 was collected, how many of each
type of ticket were sold?

Math 090 Week 4 Thursday Worksheet

1. Determine whether the relation defines a function, and give the domain and range.

a. {(9,−2), (−3, 5), (9, 2)} b. c.

d. e. f.

2. Look back at problem 1, and answer the following.

a. For parts d-f, find f(0) for each.

b. Look back at parts d and e, and find for what value of x is f(x) = 1 for each?

3. Given the functions below, find the following.

f(x) = −5x + 7 g(x) = x2 − 2x

f(0) g(0) f(−2)

g(−2) f

(
2

5

)
f(−x)

g(−x) f(x− 2) g(x + 1)

4. Rental on a car is $70 plus $0.25 per mile. Let x represent the number of miles driven, and f(x) represent the total
cost to rent the car.

Write a linear function that models this situation.

Find f(200) and interpret your answer in the context of the problem.

Math 090 Week 4 Tuesday Worksheet

1. Can the slope of two perpendicular lines be positive? Why or why not?

2. Suppose a line is defined by the equation x = 2. What is the slope of a line that is perpendicular to this line? Hint:
Sketch the lines.

3. The U.S. population (in millions) has grown approximately linearly since the year 2000. See the graph below.

a. Find the slope of the line defined by the two given points.

b. Interpret the meaning of the slope in the context of this problem.

4. Determine the slope and y-intercept of the given equations below, and use these to sketch a graph of each line.

y = 2
5
x − 1 − 7x − y = −5

5. Two lines L1 and L2 are defined below either by points or equations. Determine whether the two lines are parallel,
perpendicular, or neither.

a. L1 : (−3, −5), (−1, 2) L2 : (0, 4), (7, 2) b. L1 : 3x − 4y = 12 L2 : 12x −
2
3
y = 1

c. L1 : −y = 3x − 2 L2 : −6x + 2y = 6

6. Write the equation of the line satisfying the given conditions.

a. Line passes through the point (1, 1) and (3, 7).

b. Line passes through the point (4, −2) and is perpendicular to the line 4x + 3y = −6.

7. A health club membership costs $99, plus $30 per month. Let x represent the number of months you have a membership,
and y represents your total cost.

a. Write an equation of the form y = mx + b representing the total cost.

b. Find and interpret the ordered pair associated with the equation for x = 5.

c. How much does the first year’s membership cost?

Math 090 W3 TU Individual Sheet

1. How many solutions will |ax + b| = k have for each situation? Assume a 6= 0.

a. k = 0

b. k > 0

c. k < 0

2. Solve each equation.

|4x| = 20 |2x + 3| = 19 |12 −
1

2
x| = 6

2|4x− 3| + 5 = 17 |8x + 4| = −4 |7x + 12| = |x− 8|

3. Solve each inequality. Graph the solution set, and write answers in interval notation.

|4x + 1| ≥ 21 |− 6x− 6| < 1

|2x + 1| + 3 > 8 |4x + 1|− 2 ≤−5

4. The chart below lists the 10 tallest buildings in Houston, Texas, along with their height.

a. Find the average height of these 10 buildings.

b. Let k be the average height you found in part (a). Then if x is the height of a given building, and x
satisfies the inequality |x−k| < t, then that building is said to be within t within t feet of the average. Let’s use t = 50. Use the inequality |x − k| < t and your answer from part (a), to find the buildings that are within 50 feet of the average. To do this, set up and solve the inequality (plugging in t = 50 and k as your answer from part (a). Then list the buildings that fall into this range.

c. Now write an inequality for the buildings that are NOT within 95 feet of the average. Solve that
inequality, and state the buildings that are not within 95 feet of the average.

Math 090 W2 TR Individual Sheet

1. Let A = {1, 2, 3, 4, 5, 6} and B = {1, 3, 5, 7}. Find the following sets.
A∪B A∩B

2. Solve each compound inequality. Give the solution set in both interval and graph forms.

x + 2 > 7 or 1 −x > 6

4x + 1 ≥−7 or −2x + 3 ≥ 5

x + 1 ≥ 5 and x− 2 ≤ 10

3x− 4 ≤ 8 and −4x + 1 ≥−15

x + 3 ≤ 2 and −2x ≤−6

3. The figures represent the backyards of neighbors Luigi, Maria, Than, and Joe. Find the area and perimeter
of each yard. Suppose each resident has 150 ft of fencing, and enough sod to cover 1400 ft2 of lawn. Give
the names of those whose yards satisfy the conditions below.

a. The yard be fenced and the yard can be sodded.

b. The yard can be fenced and the yard can not be sodded.

c. The yard can not be fenced and the yard can be sodded.

d. The yard can not be fenced and the yard can not be sodded.

e. The yard can be fenced or the yard can be sodded.

f. The yard can not be fenced or the yard can be sodded.

Math 090 Week 2 Tuesday Group Work

1. In 2014, general admission to the Art Institute of Chicago cost $23 for adults and $17 for children and
seniors. If $30,052 was collected from the sale of 1460 general admission tickets, How many adult tickets
were sold?

2. Find the measure of all angles in the given diagrams.

3. A high level of LDL cholesterol in the blood increases a person’s risk of heart disease. The table shows how
LDL levels affect risk.

If x represents the LDL cholesterol number, write an inequality for each category. For example, in the
Optimal category, x < 100.

4. Solve each inequality. Give the solution set in both interval and graph forms.

4x + 1 ≤ −31
2x − 5
−4

> 5

−
1

4
(p + 6) +

3

2
(2p − 5) < 10 − 6 ≤ 2x + 4 ≤ 16

4 ≤ −9x + 5 < 8 − 1 ≤ 2x − 5

6
≤ 5

5. Faith earned scores of 90 and 82 on her first two English tests. What score must she make on her third test
to keep an average of 84 or greater?

Math 090 Wk 1 Thursday Individual Sheet

1. When a formula is solved for a particular variable, several different equivalent forms may be possible. If we

solve

A =

1

2
bh for h, one possible correct answer is h =

2A

b

.

Which of the following are NOT equivalent to this?

A. h = 2

(
A

b

)
B. h = 2A

(
1

b

)
C. h =

A
1
2
b

D. h =
1
2
A

b

2. F =
9

5
C + 32 is an equation used to convert temperature in Celsius to Fahrenheit.

a. Use this to convert 30◦C into Fahrenheit.

b. Solve F =
9

5
C + 32 for C.

c. Use your equation from part (b.) to convert 68◦F into Celsius.

3. Solve the following for the indicated variable.

A =
1

2
h(b + B) for b V =

1

3
πr2h for h −5x + 3y = 12 for y

4. An average middle-income family will spend $241,080 to raise a child born in 2013 from birth through age
17. Below shows percents spent for various categories. Use it to answer the following questions.

a. To the nearest dollar, how much will be spent to provide housing for the child?

b. To the nearest dollar, how much will be spent for child care and education?

c. Use your answer from part (b.) to find how much will be spent on clothing.

d. If the true cost for raising a child as described for a particular family is $252,000, what percent increase
is this over the average?

e. If this average, $241,080, is a 12% increase from the average for a child born in 2005, What was the
average cost to raise a child born in 2005?

Math 090
Wk 1 TU GW: Linear Equations in one

variable
Fall

2

01

6

1. What is the difference between an equation and an expression? Give examples of each.

Solve the following equations.

2. 4x − 17 = 3

5

3. 13y + 4 = 5(y − 4)

4.

2

3

x −

1

6
= −

5

12
x +

3

2
−

1

2

x

5.
2y − 4

5
=

5y + 13

4
+

y

2

Below are sample directions and worked out problems. Determine if the problems are
worked out correctly, or if they contain error(s). If they contain errors, mark where the
error occurred, and correct the work.

6. Solve the following equations.

3x + 2

7
−

x + 4

5
= 2

x − 10
5

+
2

5
= −

x
3

35

1
·

3x + 2
7
−
35

1
·
x + 4

5
= 35 · 2

15

1
·
x − 10

5
+

15
1
·
2
5
= −
15

1
·
x

3
15x + 10 − 7x + 28 = 70 3x − 30 + 6 = −5x

8x + 38 = 70 3x − 24 = −5x
8x = 42 − 24 = −8x

x =
21

4
3 = x

7. Simplify the following expressions.

5 + 2(6 − x) − 22
1

3
x +

1

2
x −

1
6

= 7(6 − x) + 4 =
6

1
·
1
3
x +
6
1
·
1
2
x −
6
1
·
1

6
= 42 − 7x + 4 = 2x + 3x − 1
= 46 − 7x = 5x − 1