MAT1033 – Intermediate Algebra – Final Exam Review

MAT1033 - Intermediate Algebra - Final Exam Review

Intermediate Algebra Final Exam Review for MAT1033 focuses on essential algebraic concepts and problem-solving techniques. This review includes equations, inequalities, and systems of equations, providing practice problems and solutions to prepare students for their final exam. Key topics cover linear equations, factoring, and functions, making it ideal for students seeking to reinforce their understanding of algebra. The review also features graphical representations and real-world applications of algebraic principles, ensuring comprehensive exam preparation.

Key Points

  • Covers solving linear equations and inequalities in one variable.
  • Includes practice problems on quadratic equations and factoring techniques.
  • Explains the concepts of functions and their graphical representations.
  • Provides real-world applications of algebraic principles for better understanding.
  • newtopiccyclegrowin
225
/ 6
MAT1033
-
Intermediate Algebra
-
Final Exam Review
Textbook: Beginning & Intermediate Algebra, 5th Ed., by Martin
-
Gay
Section 2.3
Solve the equation.
1)
9
x
-
3
x
-
1)
=
2
2)
1
3
x
+
2
=
1
6
x
+
4
3
3)
-
0.07
y
+
0.12
(
6000
-
y)
=
0.06
y
Section 2.4
Solve.
4)
Four
times the sum of some number plus
2
is
equal to 8 times the number minus 20. Find
the number.
5)
The length of a rectangular room is
9
feet
longer than twice the width. If the room's
perimeter is 210 feet, what are the room's
dimensions?
Section 2.5
Solve the formula for the specified variable.
6)
P
=
2L
+
2W
for
L
7)
V
=
1
3
Ah for A
Section 2.6
Solve. If needed, round to two decimal places.
8)
Robin got a
4
% raise in her salary from last
year. This year she is earning $37,440. How
much did she make last year?
9)
How much pure acid should be mixed with
6
gallons of a 50% acid solution in order to get
an 80% acid solution?
Section 2.7
Solve.
10)
If
$2000
is invested at 10% simple annual
interest, how much should be invested at 12%
annual simple interest so that the total yearly
income from both investments is $5000?
Section 2.8
Solve the inequality. Graph the solution set and write it in
interval notation.
11)
-
21
x
-
9
≤
-
3
(
6
x
-
5
)
12)
3
≤
3
x
-
3
≤
18
Section 3.1
Complete the ordered pair so that it is a solution of the
given linear equation.
13)
6
x
+
y
=
-
22
;
(
-
5
, ), (0, ), (1, )
Section 3.2
Find three ordered pair solutions by completing the table.
Then use the ordered pairs to graph the equation.
14)
y
=
-
3
x
+
2
x y
0
1
-
1
Section 3.3
Graph the linear equation by finding and plotting its
intercepts.
15)
-
6
x
-
12
y
=
12
Graph the linear equation.
16)
x
=
-
2
17)
y
=
-
2
Section 3.4
Find the slope of the line that passes through the given
points.
18)
(
9
, 0) and (0,
-
1
)
19)
(
-
8
,
10
) and (
-
8
,
4
)
1
Determine whether the pair of lines is parallel,
perpendicular, or neither.
20)
3
x
-
4
y
=
16
8x
+
6y
=
1
Find the slope of the line and write the slope as a rate of
change with proper units.
21)
The graph shows the total cost y (in dollars) of
owning and operating a mini
-
van where x is
the number of miles driven.
x
5000 10000 15000 20000
y
4000
3000
2000
1000
(4000, 1090.9)
(8000, 2181.8)
x
5000 10000 15000 20000
y
4000
3000
2000
1000
(4000, 1090.9)
(8000, 2181.8)
Section 3.5
Use the slope
-
intercept form to graph the equation.
22)
y
=
1
2
x
+
5
Find an equation of the line with the given slope that
passes through the given point. Write the equation in the
form Ax
+
By
=
C.
23)
m
=
4
; (
9
,
7
)
24)
m
=
-
2
3
; (5, 2)
Find an equation of the line described. Write the equation
in slope
-
intercept form if possible.
25)
Slope
2
, through (
-
6
,
-
3
)
26)
Through (
2
,
-
26
) and (
-
7
,
46
)
Find an equation of the line.
27)
Perpendicular to y
=
10
, through (
-
3
,
-
1
)
Section 3.6
Find the domain and the range of the relation.
28)
{(
9
,
2
), (
-
7
,
2
), (
-
5
,
2
)}
Determine whether the relation is also a function.
29)
{(
-
2
,
2
), (
2
,
-
2
), (
4
,
-
9
), (
8
,
-
5
), (
10
,
-
2
)}
Determine whether the graph is the graph of a function.
30)
x
-5 5
y
5
-5
x
-5 5
y
5
-5
Evaluate the function.
31)
Find f(
-
2) when f(x)
=
3x
2
+
2x
+
2.
Section 4.1
Solve the system of equations by graphing.
32)
y
=
-
x
+
2
y
=
2x
+
8
33)
x
+
y
=
-
6
x
+
y
= -
4
Sections 4.2
-
4.3
Solve the system of equations by the substitution or
addition method.
34)
-
2
x
+
y
=
-
1
-
3x
-
2y
=
-
19
35)
2
x
+
y
=
10
8x
+
4y
=
40
36)
8
x
+
5
y
=
60
-
2x
-
5y
= -
90
37)
-
3
x
+
5
y
=
-
7
-
5x
+
3y
= -
1
2
Section 4.5
Solve.
38)
One number is
10
less than a second number.
Twice the second number is 59 more than 5
times the first. Find the two numbers.
39)
Devon purchased tickets to an air show for
8
adults and 2 children. The total cost was $140.
The cost of a child's ticket was $5 less than the
cost of an adult's ticket. Find the price of an
adult's ticket and a child's ticket.
Section 9.4
Graph the inequality.
40)
5
x
+
y
>
-
10
41)
-
3
x
-
5
y
≤
15
Graph the solution of the system of linear inequalities.
42)
y
≥
x
+
3
y
≥
5
-
x
43)
y
+
2
x
≥
-
7
3x
-
4y
≤
8
Section 5.1
Simplify the expression.
44)
3x
2
y
2
z
3
2
45)
15m
13
n
13
3m
12
n
10
46)
-
4y
0
Section 5.2
Perform the indicated operation.
47)
(
-
6y
+
9)
+
(
-
4y
2
+
3y
-
4)
48)
(5n
6
-
19n
5
+
13)
-
(2n
6
-
7n
5
+
9)
Section 5.3
Multiply.
49)
(
3
x
-
12
)(x
+
6
)
50)
(a
-
6)(a
2
+
6a
-
9)
Section 5.4
Multiply.
51)
(9a
-
7)
2
52)
(
5
p
+
12
)(
5
p
-
12
)
Section 5.5
Simplify the expression. Write the result using positive
exponents only.
53)
4
-
3
54)
(x
-
5
y
6
)
-
3
55)
2
-
9
x
-
5
y
4
2
-
6
x
-
8
y
8
Evaluate the expression using exponential rules. Write the
result in standard notation.
56)
5.6
×
10
2
0.8
×
10
-
4
Section 5.6
Perform the division.
57)
-
40x
4
+
56x
3
-
40x
2
-
8x
3
Find the quotient using long division.
58)
x
2
+
12x
+
23
x
+
9
Section 6.1
Factor completely. If the polynomial cannot be factored,
write "prime."
59)
32x
9
y
8
-
16x
7
y
5
-
24x
4
y
3
60)
s(t
2
+
6)
-
7(t
2
+
6)
61)
xy
-
2
yz
+
9
x
-
18
z
3
/ 6
End of Document
225
You May Also Like

FAQs of MAT1033 – Intermediate Algebra – Final Exam Review

What types of equations are included in the MAT1033 review?
The MAT1033 Intermediate Algebra Final Exam Review includes various types of equations such as linear equations, quadratic equations, and systems of equations. Each section provides step-by-step solutions to help students understand the solving process. Additionally, the review emphasizes the importance of graphing these equations to visualize their solutions and relationships. Practice problems are included to reinforce these concepts, ensuring students are well-prepared for their final exam.
How does the review help with understanding inequalities?
The review addresses inequalities by providing clear explanations and examples of how to solve and graph them. It covers both linear and compound inequalities, teaching students how to interpret and represent solutions on a number line. The document also includes practice problems that challenge students to apply their knowledge in various contexts. This comprehensive approach ensures that students gain a solid understanding of inequalities, which is crucial for success in algebra.
What real-world applications of algebra are discussed?
Real-world applications of algebra in the MAT1033 review include scenarios such as budgeting, calculating distances, and analyzing data trends. These examples illustrate how algebraic concepts can be applied to solve practical problems. By connecting algebra to everyday situations, the review helps students appreciate the relevance of their studies. This approach not only enhances understanding but also motivates students to engage with the material more deeply.
Are there graphical representations included in the review?
Yes, the MAT1033 Intermediate Algebra Final Exam Review includes graphical representations of functions and equations. These visuals help students understand the relationship between algebraic expressions and their graphs. By studying these graphs, students can better grasp concepts such as slope, intercepts, and the behavior of functions. The inclusion of graphs enhances the learning experience by providing a visual context for the algebraic concepts covered in the review.

Related of MAT1033 – Intermediate Algebra – Final Exam Review