Readiness in college algebra

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READINESS OF STUDENTS IN COLLEGE ALGEBRA
An Institutional Research
Presented to
the Research Management Office
Saint Louis College
City of San Fernando, La Union
by:
Ragma, Feljone G.
Manalang, Edwina M.
Rodriguez, Mary Joy J.
Hoggang, Gerardo
Fernandez, Mark Edison
Oredina, Nora A.
Parayno, Dionisio Jr.
Hailes, Imelda Lyn R.
Coloma, Roghene A.
February 26, 2014

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TABLE OF CONTENTS
Page
TITLE PAGE………………………………………………………………… i
TABLE OF CONTENTS………………………………………………….. ii
LIST OF TABLES…………………………………………………………. v
LIST OF FIGURES……………………………………………………….. vi
CHAPTER
I INTRODUCTION……………………………………………… 1
Background of the Study.……......………….......... 1
Theoretical Framework……………………………..... 4
Conceptual Framework……………………………….. 6
Statement of the Problem…………........................ 9
Hypotheses……………………………………........... 9
Importance of the Study……………...................... 9
Definition of Terms…………………………………..... 11
II METHOD AND PROCEDURES…………………………… 14
Research Design……………………………………… 14
Sources of Data………………………………………. 14
Locale and Population of the Study……………... 14
Instrumentation and Data Collection ..……….... 16
Validity and Reliability of the
Questionnaire…………………………………….. 16

iii
Page
Data Analysis ………………………………………….
Data Categorization……………………………….....
16
19
Parts of the Learning Activity
Sheets..….………………………………………………. 21
Ethical Considerations…………………………...... 22
III RESULTS AND DISCUSSION…………………………….. 23
Profile of the College Students……………………..
Level of Readiness of Students in College
Algebra……………………………………………..
23
25
Correlation between Profile and Level of
Readiness………………………………………….. 27
Comparison on the Level of Readiness of the
three respondent groups………………………..
29
Strengths and Weaknesses of Students in
College Algebra………………………………….. 31
Learning Activity Sheets………..…………………… 33
IV SUMMARY, CONCLUSIONS AND RECOMMEN-
DATIONS……………………………………………….. 96
Summary………………………………………………. 96
Findings………………………………………………… 96
Conclusions…………………………………………… 98
Recommendations…………………………………… 99
BIBLIOGRAPHY……………………………………………… 101

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APPENDICES………………………………………………… 95

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LIST OF TABLES
Table Page
1 Distribution of Respondents………………………….
2 Profile of Respondents ………………………………. 24
3 Level of Readiness of Students in College
Algebra …………………………………………………. 26
4 Correlation between Profile and Level of
Readiness………………………………………………. 28
5 Difference in the Level of Readiness among the
respondent groups………………………………. 30
6 Strengths and Weaknesses of Students in
College Algebra …………………………………… 32
7 Level of Validity of the Learning Activity
Sheets…………………………………………………

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LIST OF FIGURES
Figure Page
1 The Research Paradigm ……………………………………….. 8

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CHAPTER I
INTRODUCTION
Background of the Study
Quantitative Literacy, as defined by the Mathematical Association
of America (MAA), is the ability to apply the minimum computational
competency or fluency to solve problems in the real world
(http://www.maa.org/college-algebra). It is implicit that when a person
is quantitatively literate, he is able to use his mathematical skills in
dealing with situations in his life, whether it is in the complex line of
business, economics, and politics or in the simple context of time
reading, scheduling, and many others. Indeed, Mathematics is
necessary.
One mathematics subject that is necessary to person’s life is
College Algebra. Packer (2004) explains that College Algebra is the
introductory mathematics subject to any university or community
college. He added that College Algebra is the starting course for students
to be trained logically as they would deal with algebraic expressions,
axioms of equations, functions and the like. Furher, Leeyn (2009)
exemplifies that College Algebra is a critical element to 21st century jobs
and citizenship. Gateschools staff (2013) also asserts that it is the
gatekeeper subject. It is so because it is used by professionals ranging
from electricians to architects to computer scientists. Robert Moses

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(2009), founder of the Algebra Project, says that learning College Algebra
is no less than a civil right. As such, College Algebra is really very
important.
However, no matter how important College Algebra is, it is still
considered by most students as a non-helpful subject. According to a
paper presented in the Mathematics Association of America (MAA)
conference in the year 2009 which revealed that College Algebra is the
last mathematics course many students take. A majority entered the
classroom having already decided that it would be their final
mathematics course. Data, contained in the same conference report,
indicated that only one in ten College Algebra students go on to take
other higher math subjects. Many would skip College Algebra if they did
not have to pass it to get the degree they need to enter their chosen
career field. In addition, enrollment in this subject tends to fall
dramatically when colleges make quantitative reasoning or intermediate
algebra the requirement. It was also reported that, a few years after
finishing the course, the students cannot recall anything they learned.
All of these pinpoint to the fact that college algebra seemed hard for most
students (http://www.maa.org/college-algebra). As a result, readiness,
evident in their performances, declines. According to the New York
Times, in the last fall of 2013, results from national math exams stirred

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up a tempest in a standardized test. It turned out that math scores
declined more quickly. It was also mentioned that math scores haven’t
improved since 2007 (http://www.nytimes.com/). In addition, Shepherd
(2005) revealed that most students do not excel in their Algebra course.
Most of them cannot perform indicated operations, especially when
fronted with word problems. Students find it hard to solve problems in
Algebra. Some just do not answer at all. These situations reflect poor
understanding of and performance in the course (The Journal of
Language, Technology & Entrepreneurship in Africa, Vol. 2, No.1,
2010).Moreover, Kuiyuan (2009) also mentioned that in University of
Florida, the student’s success rate in College Algebra is more than the
desired level. Kuiyan (2009) stressed that with this trend in dismal
performance, the readiness of students in such subject is very low.
In the Philippines, College Algebra is a pre-requisite subject in all
course curricula. CHED Memorandum Order 59 series of 1996 mandates
the inclusion of College Algebra as a basic subject in all courses. The
country is not exempted from the predicaments on College Algebra
performance. A recent study of on the readiness graduating high school
students of Marian Schools in College Algebra revealed that their
readiness is only at the moderate level. This means that the students did

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not yet fully attain the desired competence to be able to hurdle the
demands of College Algebra.
In the provincial scene, the recent study of Ragma (2014) revealed
that the students have only poor performance in College Algebra. In
Saint Louis College, the study of Oredina (2009) revealed that the
students had only moderate performances. Additionally, the mathematics
instructors, the researchers of the study, observed that most students
enrolled in College Algebra are not yet ready for the subject. This is
shown in their quizzes, exams and grades. In fact, in a class of 50, more
than 40% have failing grades in their prelim grades. The state of dismal
performances in this subject point out to the fact that the students are
not ready to take up College Algebra.
The foregoing situations encouraged the math instructors to
embark on assessing the level of readiness of SLC students in College
Algebra for school year 2013-2014 as basis for formulating learning
activity sheets.
Theoretical Framework
E. Thorndike (1978) proposed the law of readiness. The readiness
theory states that a learner’s satisfaction is determined by the extent of

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his preparatory set. It implies the need of acquisition of necessary pre-
requisite skills so that learners will be ready to tackle the succeeding
lessons and at the same time, they can anchor the new lessons to the
previous ones. This theory serves as the main foundation of the proposed
study since it looked into the level of readiness of students in College
Algebra.
Central to the theory of readiness are the concepts where the
theory is founded. According to the theory, there are several factors
affecting readiness. These include maturation, experience, relevance of
materials and methods of instruction, emotional attitude and personal
adjustment. In addition, the same theory proposes several strategies in
building readiness skills. These strategies include the analysis of skills
using diagnosis or pre-assessment and the design of an instructional
intervention programmed to match the individual’s level of readiness.
This central concept of the readiness theory provided the justification of
formulating a College Algebra readiness test as a form of diagnostic
assessment among students.
Moreover, Jeane Piaget (1964), a Swiss psychologist and biologist
formulated one of the most widely used theories of cognitive
development. Piaget’s theory stresses that the potentials of formal
operational thought develop during the middle school years. These

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potentials can be actualized by ages 14, 15, or 16 years. Apparently,
learning mathematics involves formal operational thought. The research
of Piaget shows that individuals are formal operational thinkers by ages
15 or 16, the usual ages of college freshmen in the Philippines. In this
connection, this study utilizes this Piaget’s theory to investigate whether
a group of college freshmen performs at the expected level of formal
thought, in other words, if they are ready to take up collegiate courses in
Mathematics.
The law of readiness and its central concept laid the concepts in
structuring the research. The cognitive development theory, on the other
hand, gave additional foundations in formulating the learning activity
sheets.
The learning activity sheets are worksheets that contain the topic,
its objectives, activities with the teacher and activities for group and
independent learning.
Conceptual Framework
Teaching and learning mathematics becomes more meaningful and
directed when the teachers know the level of the learners’ preparation
and when the learners are ready to grasp concepts presented in the
teaching-learning process. In this manner, the teachers know where to

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start, how to start and what concepts need to be more emphasized;
students, on the other hand, know when to study more and where to
focus on.
As part and parcel of improving performance, instructional
materials such as worktext, activity books and activity sheets are
inevitable. The learning activity sheets are instructional support
materials that provide supplements to classroom instruction and give
opportunities for students to study on their own and deal with some
more additional exercises. These materials provide avenue for the
students to enhance more their competencies required in each topic by
providing relevant activities pertinent to the full understanding of the
topic. Students can even have advanced studies and make study work
using the learning activity sheets.
It is in this light that this study is formulated and thought of. The
research paradigm in figure 1 highlights the relationship of the indicated
variables. The input incorporates the profile of the respondents along
sex, high school graduated from and the mathematics high school final
grade. It also includes the level of readiness of the students along
elementary topics, special products, factoring, rational expressions,
linear equations, systems of linear eqautions and radicals and
exponents.

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The process includes the interpretation and analysis of the profile,
the level of readiness of the students, the strengths and weaknesses
based on the level of readiness, the correlation between the profile
variables and the level of readiness, and the difference among the level of
readiness among the three colleges: ASTE-IT-CRIM, CCSA, CEA.
The output, therefore, are validated learning activity sheets in
College Agebra.

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Process OutputInput
Validated
Learning
Activity Sheets
in College
Algebra for
Saint Louis
College
I. Analysis and
Interpretation of:
a. Profile
b. Level of Readiness
II. Correlational
Analysis of Profile and
Level of Readiness
III. Difference on the
level of readiness
among ASTE-IT-
CRIM, CCSA, CEA
IV. Analysis and
Interpretation of the
Strengths and
Weaknesses of the
Students in College
Algebra
III.
I. Profile of the Students
in College Algebra
along:
a. gender
b. type of high school
graduated from
c. HS Math IV grade
II. Level of Readiness of
the students in
College Algebra along:
a. Elementary Topics
b. Special Products
and Patterns
c. Factoring
d. Rational
Expressions
e. Linear Equations
in One Variable
f. Systems of Linear
Equations in Two
Variables
g. Exponents and
Radicals
Figure 1. The Research Paradigm

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Statement of the Problem
This study aimed primarily to determine the level of readiness of
frsehmen in College Algebra in Saint Louis College for the first semester,
school year 2013-2014. Specifically, it aimed to answer the following
questions:
1. What is the profile of the students in College Algebra along:
a. Gender;
b. High School Math IV Final Grade; and
c. Type of High School Graduated from?
2. What is the level of readiness of the students along the following
topics in College Algebra:
a. Elementary Topics;
b. Special Products and Patterns;
c. Factoring;
d. Rational Expressions;
e. Linera Equations in One Variable;
f. Systems of Linear Equations in Two Variables; and
g. Exponents and Radicals?
3. Is there a significant relationship between profile and the level of
readiness of the students?

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4. Is there a significant difference between the level of readiness of
a. ASTE-IT-CRIM and CCSA;
b. ASTE-IT-CRIM and CEA; and
c. CCSA and CEA?
5. What are the major strengths and weakness of the students along
the specified topics in College Algebra?
6. Based on the results, what learning activity sheets can be
proposed?
Hypotheses
The researchers were guided with the following hypothesis:
1. There is no significant relaionship between profile and the level of
readiness of the students in College Algebra
2. There is no significant difference among the level of readiness
among ASTE-IT-CRIM, CCSA, CEA.
Importance of the Study
The researchers considered this endeavor vital not only to them as
mathematics instructors, but also to the school community specifically
the administrators, students as well as future researchers.
The SLC Administrators. The results of this study can serve as
one of the bases for curricular evaluation and planning. It will also guide

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the administrators in their conscious effort to undergo planned changes
in drawing up systematic scheme of evaluating students’ performance.
The Mathematics Instructors. The knowledge of the level of
readiness including the specific areas of deficiencies of their students will
lead them to a conscientious and periodic evaluation of the courses of
study. They will be led in formulating instructional strategies and
interventions that suit their students’ level of readiness.
The students. The output of this study can enhance the students’
readiness level; thus, increasing their competence level in College
Algebra.
The future researchers. The future researchers can make use of
this study in formulating researches in other disciplines.
Definition of Terms
The following terms are operationally defined to further understand
this study:
College Algebra. This is a requisite subject in college. The topics in
this subject include elementary topics, special product patterns,
factoring patterns, rational expressions, linear equations in one
unknown, systems of linear equations in two unknowns and exponents
and radicals.

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Elementary Topics. These topics include concepts on sets,
real number system and operations, and polynomials.
Factoring patterns. These include the topics in factoring
given a polynomial. These include common monomial factor, perfect
square trinomial, general trinomial, factoring by grouping and factoring
completely.
Linear Equations in One Unkown. This includes topics on
equations with one variable such as 2x- 4 = 10 and 5x - 2x=36. The main
thrust of this topic is for an unkown variable to be solved in an equation.
Rational Expressions. These are expressions involving two
algebraic expressions, whose denominator must not be equal to zero.
This includes topics on simplifying and operating on rational
expressions.
Special Product Patterns. These topics include the patterns
in multiplying polynomials easily. These patterns include sum and
difference of two identical terms, square of a binomial, product of two
binomials, cube of a binomial and square of a trinomial.
Systems of Linear Equations in Two Unknowns. This topic
discusses how the solution set of a given system is solved. The methods
that are used in this certain topics include graphical, substitution and
elimination methods.

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Readiness Level. This is the degree of preparation of the students
along the specified topics in College Algebra. This is categorized into:
highly ready, ready, slightly ready and not ready.
Strengths. An area under readiness level is considered strength
when it has a decriptive equivalent of highly ready and above.
Validated Learning Activity Sheets. This is the output of the
study. It consists of the rationale, the learning objectives and the varied
activities that address the needs of the students based on the identified
level of readiness.
Weaknesses. An area under readiness level is considered a
weakness when it has a decriptive equivalent of ready and below.

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CHAPTER II
METHOD AND PROCEDURES
This chapter presents the research design, the sources of data,
data analysis and ethical considerations.
Research Design
The descriptive method of investigation was used in the study.
Calmorin (2005) describes descriptive design as a method that involves
the collection of data to test hypothesis or to answer questions regarding
the present status of a certain study. This design is apt for the study
since the study is aimed at describing the level of readiness of students
in College Algebra.
Further, since the comparisons on the level of readiness among the
three departments and the relationship of profile and the level of
readiness were established, the descriptive-comparative and the
descriptive-correlational methods were employed, respectively.
Sources of Data
Locale and Population of the Study

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The total population of 1,349 students enrolled in College Algebra
for the first semester, school year 2013-2014 was surveyed. Since the
population reached 500, random sampling was conducted. The sample
population of the study was computed using the Slovin’s Formula. The
formula is: n =
where:
n = the sample population
N = the population
1 = constant
e = level of significance @ 0.05
Thus, the sample population is 309 students distributed according
to the three departments: 72 for CASTE-IT-CRIM, 155 for CCSA and 82
for CEA.
Table 1 shows the distribution of the number of specified
respondents.
Table 1. Distribution of Respondents
Department N n
CASTE-IT-CRIM 316 72
CCSA 675 155

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CEA 358 82
Total 1349 309
Instrumentation
Documentary analysis was used to get the needed data for profile,
specifically for gender, high school Math IV final grade and type of
high school graduated from.
To gather the data pertinent to the level of readiness, a researcher-
made test was made. The researcher-made test is 50-point item test
covering all the topics in College Algebra. (Please see appended table of
specifications)
The readiness test was administered by all the Mathematics
instructors during the 2nd week of June in their respective classes. A
one-hour period was allotted to each student. The instructors
guaranteed that calculators were not utilized in taking the readiness
test.
Data Analysis

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The data which were gathered, collated and tabulated were
subjected for analysis and interpretation using the appropriate statistical
tools. The raw data were tallied and presented in tables for easier
understanding.
For problem 1, frequency counts and rates were used to determine
the status of the profile of the respondents along gender, high school
Math IV final grade and the type of high school graduated from. The
rates were obtained by using the formula below:
R = n x 100
N
where: R - rate
n - number of frequencies gathered in each item
N - the total number of cases
100 – constant
For problem 2, mean and rates were utilized to determine the level
of readiness in College Algebra. The formula for mean is as follows
(Ybanez, 2002):
M = ∑x
N
Where: M – mean
x – sum of all the score of the students

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N – number of students
For problem 3, the Pearson-r moment of correlation was used to
determine the significance of relationship between profile and the level of
readiness in College Algebra. The formula according to Ybanez (2002) is:
where: X – observed data for the independent variable
Y – observed data for the dependent variable
N – size of sample
r – degree of relationship between X and Y
The computed correlation coefficients were subjected to
significance; thus the formula used
(http://faculty.vassar.edu/lowry/ch4apx.html) was:
where: r – computed correlation coefficient
n-2 – degree of freedom
t – degree of significance for r
For problem 4, t-test independent (t-test between means), taken
two at a time was used to determine the difference in the perceptions of

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the respondents. The formula for t-test for means
(http://en.wikipedia.org/wiki/Student%27s_t-test) is:
where:
= estimator of the common standard deviation of the two
samples
n = number of participants, 1 = group one, 2 = group two.
n – 1 = number of degrees of freedom for either group
n1 + n2 – 2 = the total number of degrees of freedom, which is used
in significance testing.
t = degree of difference
For problem 5, the major strengths and weaknesses were deduced
based on the findings, particularly on the level of readiness in College
Algebra through statistical ranking. An area was considered strength
when it received a descriptive rating of highly ready; otherwise, the area
was considered a weakness.

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The MS Excel Data Analysis Tool was employed in treating the
data.
Data Categorization
For the profile of the students along high school grade in Math IV,
the scale system was used:
Grade range Descriptive Equivalent
92.6-97.00 Outstanding Performance
88.2-91.59 Very Satisfactory Performance
83.8-88.19 Satisfactory Performance
79.4-83.79 Fair Performance
75-79.39 Poor Performance
For the level of readiness in each topic in College Algebra, the Scale
System was utilized.
Elementary Topics/ Factoring
Score Range Level of Readiness/ DER
7.20-9.00 very highly ready
5.40-7.19 highly ready
3.60-5.39 fairly ready
1.8-3.59 slightly ready
0.00-1.79 not ready

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Special Products and Patterns/ Systems of Linear Equations
0.00-1.39 not ready
Rational Expressions/ Linear Equations in One Variable
0.00-1.59 not ready
Exponents and Radicals
0.80-1.19 ready
0.00-0.39 not ready

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For the general level of readiness, the scale below was used:
40.00-50.00 80%-100% very highly ready
30.00-39.99 60%-79.99% highly ready
20.00-29.99 40-59.99% fairly ready
10.00-19.99 20-39.99% slightly ready
0.00-9.99 0-19.99% not ready
For the strengths and weaknesses, an area was considered
strength if it got descriptive equivalent rating of highly ready and above;
otherwise, it was considered a weakness.
Parts of the Learning Activity Sheets
The learning activity sheets comprise of the rationale, the learning
objectives, the subject matter, the learning activities and sheets.
The learning activities are either with the help of the teacher or are
designed for independent learning.
Ethical Considerations
To establish and safeguard ethics in conducting this research, the
researchers strictly followed and obeyed the following:
The respondents’ names were not mentioned in any part of this
research. The respondents were not coerced just to answer the test.

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Proper document sourcing or referencing of materials was done to
ensure copyright.
A communication letter was presented to the registrar’s office to
ask authority to get the needed data on profile.

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CHAPTER III
RESULTS AND DISCUSSION
This chapter presents the data analysis and interpretation of the
gathered data.
Profile of the Students
The first problem of the study is on the profile of the students in
College Algebra.
Table 2 presents the profile of the students along sex, type of high
school graduated from and their high school final math grade. It shows
that out of 309 students, 161 or 52.10% are males while 148 or 47.90%
are females. This means that there are more male respondents than the
females. This is easy to understand since the courses which include
college algebra in their curriculum for the first semester are along
engineering, architecture, business administration and criminology.
Massey (2011) highlights that male students are more inclined to
enrolling to a course aligned to mathematics, engineering, architecture,
business management and criminal education. Registrar records as of
July 2013 also indicated that there were really more males than females.

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Further, out of 309 students, 125 or 40.45% graduated from
public schools while 184 or 59.55% graduated from private schools. This
means that majority of the students came from private schools in and
Table 2. Profile of Students
Profile variables Frequency Rate
A. Sex
Male
Female
161
148
52.10%
47.90%
B. Type of High School Graduated from
309 100%
Public
Private
125
184
40.45%
59.55%
C. HS Final Math Grade
309 100%
75-78
79-84
39
106
12.62%
34.30%

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85-88
89-93
94-97
92
64
8
309
29.77%
20.71
2.59%
100%
outside of La Union. This is because majority of the students came from
families that can afford education offered in the private schools. A
testament to this is their enrolment in SLC, a private HEI.
Lastly, it also shows the grade range of the students in their high
school mathematics subject. It reveals that 39 or 12.62% have grades
ranging from 75-78%, interpreted as poor performance, 106 or 34.30%
have grades ranging from 79-84%, interpreted as fair performance, 92 or
29.77% have grades ranging from 85-88%, interpreted as satisfactory
performance, 64 or 20.71% have grades ranging from 89-93%,
interpreted as very satisfactory performance and only 8 or 2. 59% have
grades ranging from 94-97, interpreted as outstanding performance. It
means that majority of the students had fair-satisfactory performance in
their high school mathematics. This points out to the fact that the
students had not fully mastered the desired learning competencies of

28
Mathematics IV. The finding of the study jibes with Oredina (2011)
stating that students in College Algebra had not fully mastered the
competencies.
Level of Readiness in College Algebra
The second problem of the study is on the level of readiness of the
students in College Algebra.
Table 3 shows the level of readiness of students in College Algebra.
It is shown that the students have a mean score of 2.87 or 31.88% in
elementary topics, 3.70 or 52. 86% in special product patterns, 3.6 or
40% in factoring, 3.84 or 48% in rational expressions, 3.36 or 42% in
linear equations in one variable, 2.8 or 40% in systems of linear
Table 3. Readiness in College Algebra
TOPIC Mean Score Rate Descriptive
Equivalent
Elementary Concepts 2.87 31.88% Slightly ready
Special Product Patterns 3.70 52.86% Fairly Ready
Factoring 3.6 40% Fairly Ready

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Rational Expressions 3.84 48% Fairly Ready
Linear Equation in One
Variable
3.36 42% Fairly Ready
Systems of Linear Equations in
Two Variables
2.8 40% Fairly Ready
Exponents and Radicals
1.13 56.50% Fairly Ready
TOTAL 21.3 42.60% Fairly Ready
equations and 1.13 or 56.50% in exponents and radicals. Thus, the
students were slightly ready in elementary concepts while ready in the
other remaining topics which include special products and factoring,
rational expressions, linear equations, systems of linear equations and
exponents and radicals. This means that the students were not so much
prepared to hurdle topics on sets, number line, operations on integers,
algebraic expressions and polynomials. Further, this means that the
students were prepared to apply special product and factoring patterns,
manipulate rational expressions, solve linear equations and systems and
deal with expressions involving exponents and radicals. However, since

30
the rates of the mean scores are only between 30-57%, the students still
lack the necessary mastery to be able to hurdle the challenges of the
specified topics in College Algebra.
Generally, the students’ mean score is 21.3, equivalent to 42.60%,
interpreted as ready. Thus, students are generally ready for the course
content of College Algebra. They are familiar with the course contents
since majority of the contents of the course are just a review of high
school mathematics. However, it can be construed that students have
not really mastered well the competencies required in each topic.
Testament to this is the fair-poor performance of the students based on
their high school math grades.
This finding of the study corroborate with Kuiyuan (2009) stating
that the level of readiness of the students in College Algebra is at the
moderate level only. It was mentioned that students did not possess the
needed pre-requisite skills.
Correlation between Profile and Level of Readiness
The third problem of the study is on the significant relationship
between the profile and the level of readiness of the students.
Table 4 shows the relationship between profile and the level of
readiness of the students. It shows that the correlation coefficient
between sex and the level of readiness is 0.18, interpreted as negligible

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Table 4. Correlation between profile and level of readiness
Profile Variables Level of
Readiness
t-
critical
@ 0.05
Interpretation
Sex 0.18
Negligible
0.112 Significant
Type of HS graduated
from
0.12
Negligible
0.112 Significant
HS math final grade 0.63
marked
0.112 Significant
correlation. This negligible correlation is significant at 0.05 level of
significance. This signifies that sex does not significantly affect the level
of readiness and vice versa. Thus, sex does not determine the level of
readiness in college algebra.
Further, it also shows that the correlation coefficient between type
of high school graduated from and the level of readiness is 0.05. This
negligible correlation is significant at 0.05 level of significance. This
denotes that the type of high school graduated from does not
significantly affect the level of readiness and vice versa. Thus, the type of

32
high school graduated from does not necessarily determine the level of
readiness. This is true since schools, regardless of type, offer the same
curriculum provided by the Department of Education, hence, the
students still learned the same content in their secondary schools.
Moreover, it also divulges that the correlation coefficient between
high school math grade and level of readiness in College Algebra is 0.63.
This marked correlation is significant at 0.05 level of significance. This
means that high school math grades significantly affect the level of
readiness. This means that the high school mathematics performance of
students affect their level of readiness in College. This is easy to
understand since the high school mathematics subjects provide solid
foundation for students to hurdle the course contents of College Algebra,
especially so that the contents of the course are review of the high school
topics. This finding of the study corroborates with the study of Kuiyuan
(2009) stating that high school GPA strongly correlates to college
readiness.
This finding run parallel to the study of Kuiyuan (2009) revealing
that high school and college GPA had strong correlation with the
students’ level of readiness in College Algebra, while the other factors
such as national exam scores, type of school graduated from had weak
correlations.

33
Comparison on the Level of Readiness of the Students in the
Three Colleges
The fourth problem of the study is the significant difference
between the level of readiness of the students in the three colleges,
CASTE-IT-CRIM, CCSA, and CEA.
Table 5. Comparison on the Level of Readiness
Departments Mean
Difference
Computed t-
value
p-value Interpretation
ASTE-IT-
CRIM and
CCSA
2.173 1.80 0.0729 Not
Significant
ASTE-IT-
CRIM and
CEA
3.82 3.09 0.0023 Significant
CCSA and
CEA
1.64 1.43 0.1531 Not
Significant
Table 5 reveals the comparison of the level of readiness of students
in the three (3) departments of SLC, the CASTE-IT-CRIM, the CCSA, and

34
the CEA. It shows that the comparison on the level of readiness of
students from CASTE-IT-CRIM and CCSA has a computed t-value of
1.80. This is not significant at 0.05 level of significance since the p-value
is larger than 0.05. Thus, it can be inferred that the mean difference of
2.173 is not significant. This denotes that there is no significant
difference in the performance of the students in the CASTE-IT-CRIM and
the CCSA. Thus, it is safe to construe that students in CASTE-IT-CRIM
are not better than CCSA students, and vice versa. This finding runs
parallel to the hypothesis of the study that there is no significant
difference in the performance of the students in the two identified
departments.
Further, it shows that the comparison on the level of readiness of
students from CASTE-IT-CRIM and CEA has a computed t-value of 3.09.
This is significant at 0.05 level of significance since the p-value is smaller
than 0.05. Thus, it can be inferred that the mean difference of 3.82 is
significant. This denotes that there is a significant difference in the
performance of the students in the CASTE-IT-CRIM and the CEA. This
finding does not run parallel to the hypothesis of the study that there is
no significant difference in the performance of the students in the two
identified departments. Thus, students in CEA are better in College
Algebra than the students in CASTE-IT-CRIM. This is easy to understand

35
since students enrolled in engineering and architecture courses are
inclined to mathematics.
It also shows that the comparison on the level of readiness of
students from CCSA and CEA has a computed t-value of 1.43. This is not
significant at 0.05 level of significance since the p-value is larger than
0.05. Thus, it can be inferred that the mean difference of 1.64 is not
significant. This denotes that there is no significant difference in the
performance of the students in the CCSA and the CEA. This means that
students CSA are not better in College Algebra than students in the CEA,
and vice versa. This finding runs parallel to the hypothesis of the study
that there is no significant difference in the performance of the students
in the two identified departments.
Strengths and Weaknesses in the Level of Readiness in College
Algebra
The fifth problem of the study is the strengths and weaknesses in
the level of readiness of the college students.
Table 6 shows the strengths and weaknesses of the students in
College Algebra as culled out from their level of readiness. It can be seen
from the table that all the content areas under College Algebra are
considered as weaknesses of the students. This means that the students
are not that prepared in taking the subject. This implies that they did not

36
possess yet the needed skills needed to hurdle the demands of the
course.
This finding of the study harmonizes with the study of Leongson
(2001) that students’ performance in College Algebra is alarming. It was
mentioned that the students were at the poor-fair levels only.
This finding also corroborates with the study of Ragma (2014)
revealing that all content areas in College Algebra are found to be
constraints. He explained that the students were not able to successfully
imbibe the skills in algebraic concepts and manipulations.
Table 6. Strengths and Weaknesses in College Algebra
TOPIC Mean Score Rate Classification
Elementary Concepts 2.87 31.88% Weakness
Special Product Patterns 3.70 52.86% Weakness
Factoring 3.6 40% Weakness
Rational Expressions 3.84 48% Weakness
Linear Equation in One
Variable
3.36 42% Weakness
Systems of Linear Equations
in Two Variables
2.8 40% Weakness
Exponents and Radicals 1.13 56.50% Weakness

37
CHAPTER IV
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
This chapter incorporates the summary, findings, conclusions and
recommendations of the study.
Summary
The study aimed to determine the level of readiness of frsehmen in
College Algebra in Saint Louis College for the first semester, school year
2013-2014. It specifically looked into the profile of the students, their
level of readiness along the specified topics, the significant relationship
between profile and the level of readiness, the significant difference
betweeen the level of readiness of the students in the three departments
of the college, the strengths and weaknesses based on the level of
readiness and the proposed learning activity package.
The study is descriptive with a validated researcher-made
readiness test as the main data-gathering tool.
Findings
The findings of the study are:
1. a. There were 161 males and 148 females;
b. Out of 309 students, 125 came from public schools while 184 came
from private schools.

38
c. 237 students had a high school math grade ranging from 75-88%;
while 72 had grades ranging from 89-97%.
2. The students were slightly ready in elementary topics while fairly
ready in the remaining topics which include special product and
factoring patterns, rational expressions, linear equations, systems of
linear equations and exponents and radicals. Generally, they were failry
ready in College Algebra.
3. a. There was a negligible correlation between sex and level of
readiness.
b. There was a negligible correlation coefficient between type of high
school graduated from and level of readiness.
c. There was a marked correlation between high school final math
grade and level of readiness.
4. a. There was no significant difference between the level of readiness of
students from the CASTE-IT-CRIM and CCSA.
b. There was a significant difference between the level of readiness of
students from the CASTE-IT-CRIM and CEA.
c. There was no significant difference between the level of readiness of
students from the CCSA and CEA.
5. All the topics were found to be weaknesses.

39
Conclusions
In the light of the above-cited findings, the following conclusions
are drawn:
1. a. Majority of the students were males.
b. Majority of the students were graduates of private high schools.
c. Majority of the students had fair-poor performance in their high
school mathematics.
2. The students were not able to acquire sufficient pre-requisite skills to
be able to hurdle the demands of College Algebra.
3. a. Sex did not significantly affect level of readiness and vice versa.
b. Type of high school graduated from did not significantly affect the
level of readiness.
c. High school final math grades significantly affected the level of
readiness.
4. a. The level of readiness of students from the CASTE-IT-CRIM and
CCSA was the same. CASTE-IT- CRIM students were not better than
CCSA students and vice versa.
b. The level of readiness of students from the CASTE-IT-CRIM and
CEA was not the same. CEA students were better than CASTE-IT-CRIM
students.

40
c. The level of readiness of students from the CCSA and CEA was the
same. CCSA students were not better than CEA students and vice versa.
5. Students were really not that ready to take College Algebra course.
Recommendations
Based on the conclusions of the study, the researcher recommends
the following:
1. The learning activity sheets should be adopted by mathematics
instructors.
2. The readiness test used in this research should be utilized as a
diagnostic tool by all College Algebra instructors before starting the
formal lessons every start of the school year.
3. Students who wish to enroll in mathematically-inclined subjects
should be really good in mathematics.
4. A future study looking into the effectiveness of the learning activity
should should be conducted.

41
BIBLIOGRAPHY
A. Books
Becker, Jon (2004). Flash review for college algebra. U.S.A.: Pearson
Education, Inc.
Barnett, Raymond (2008). College algebra with trigonometry. Boston:
McGraw Hill.
Bautista, Leodegario, et al. (2007). College algebra. Quezon City: C & E
Publishing, Inc.
Calmorin, L. (2005). Methods of research and thesis writing. Manila: Rex
Bookstore, Inc.
Cayabyab, Sheila P., et al. (2009). College algebra for filipino students.
Quezon City: C & E Publishing, Inc.
Covar, Melanie M., and Rita May L. Fetalvero (2010). Real world
mathematics, intermediate algebra. Quezon City: C & E Publishing
Inc.
Ee, Teck. (2011). Maths gym. Singapore: SAP Group Pte Ltd.
Huettenmueller, Rhonda (2003), Algebra demystified. New York:
McGraw-Hill Companies Inc.
Lial, Margaret (2001). College algebra. Boston: Addison-Weley, Inc.
Oredina, Nora (2011). College algebra. Manila: Mindshapers Co., Inc.
Parreno, Elizabeth (2001). College Algebra. Mandaluyong City: Books
atbp.
Petilos, Gabion (2004). Simplified college algebra. Quezon City: Trinitas
Publishing, Inc.
Rider, Paul (2009). College algebra. New York: Macmillan Co. Inc.

42
Sta. Maria, Antonia C. et al, (2008). College mathematics: modern
approach. Mandaluyong City: National Bookstore.
B. E-journals and Online Sources
http://www.emergo.ca/RecentCourses-Disorder_201111-
Celebrating_Women,_Understanding_Men_Introduction.htm
(retrieved July 23, 2013)
http://www.maa.org/college-algebra (retrieved February 21, 2014)
Leeyn, Shiela
http://www.enablemathcollege.com/enablemath/algebra.jsp
(retrieved February 21, 2014)
http://www.greatschools.org/students/academic-skills/354-why-
algebra.gs (retrieved January 20, 2013)
Moses, Robert (2009). The Algebra Project; http://answers. ask. com/
science/ mathematics/ why_is_algebra_important (retrieved
February 20, 2014)
http://www.nytimes.com/ (retrieved February 10, 2014)
The Journal of Language, Technology & Entrepreneurship in Africa, Vol.
2, No.1, 2010
Kuiyuan, L. P. (2007). “A study of college readiness in college algebra.”
The e-Journal of Mathematical Sciences and Mathematics Education
Retrieved July 29, 2013 from http://www.uwf.
edu/mathstat/Technical%20Reports/Assestment2%202010-1-
6.pdf
Leongson, J. A. (2001). Assessing the mathematics achievement of college
freshmen using Piaget’s logical operations. Bataan, Philippines.
Retrived August 11, 2013 from www.cimt. plymouth.ac.uk/
journal/limjap.pdf

43
http://www.mariancatholichs.org/download.axd?file=ba3db97c-eee0-
475b-a77b-7182c50b7ad9&dnldType=Resource (retrieved
February 21, 2014)
http://www.google.com.ph/url?sa=t&rct=j&q=worskheets%20in%20sign
ed%20numbers%20.doc&source=web&cd=1&cad=rja&ved=0CCcQ
FjAA&url=http%3A%2F%2Fwww.yti.edu%2Flrc%2Fimages%2FMat
h_Integers.doc&ei=kqkJU8qRLaidiAfEmYHYBw&usg=AFQjCNFJPdi
Bq4UQGqn-1fLtkbypEI9_gQ (retrieved February 21, 2014)
http://www.google.com.ph/url?sa=t&rct=j&q=activities%20in%20polyno
mials.doc&source=web&cd=2&cad=rja&ved=0CCwQFjAB&url=http
%3A%2F%2Fwww.wsfcs.k12.nc.us%2Fcms%2Flib%2FNC0100139
5%2FCentricity%2FDomain%2F822%2FPolynomials%2520Handou
t.doc&ei=TawJU730IISZiQevhoCYBw&usg=AFQjCNE0gj5KIHWOqs
oUHmeEQAqWGJfN0A (retrieved January 15, 2014)
http://www.google.com.ph/url?sa=t&rct=j&q=worksheets%20in%20facto
ring%20patterns.doc&source=web&cd=10&cad=rja&ved=0CFYQFj
AJ&url=https%3A%2F%2Fwww.santarosa.k12.fl.us%2Flessonplan
s%2FHigh%2FPreviousYear%2FWorrell%2520Lesson%2520Plan.do
c&ei=2LQJU6WcJunkiAf6jYHwBw&usg=AFQjCNFp4nwVpTc9VIyfR
5L7fkSPuF0W_g&bvm=bv.61725948,d.aGc (retrieved February 21,
2014)
C. Unpublished Researches
Oredina, Nora A. (2010). “A validated worktext in college algebra.”
Institutional Research. Saint Louis College, City of San Fernando,
La Union.
Ragma, Feljone G. (2014). “Error Analysis in College Algebra in the Higher
Education Institutions of La Union.” Unpublished Dissertation. Saint
Louis College, City of San Fernando, La Union.

44
APPENDIX
Saint Louis College
City of San Fernando, La Union
READINESS TEST IN COLLEGE ALGEBRA
Name:_________________________________Yr & Course:________________Score:______
I. MULTIPLE-CHOICE TYPE: Write the letter of the correct/best answer on the answer matrix given. WRITE
CAPITAL LETTERS ONLY. (50 pts.)
1. If U is the set of integers and set A is the set of counting numbers, what is A’?
a. 0 c. the union of whole and negative numbers
b. whole numbers d. 0 and the negative numbers
2. In a survey of a group of college freshmen, it was found out that 800 love Mathematics, 750 love English
and 450 love both subjects. How many students were surveyed?
a. 1,100 b. 1,250 c. 1,550 d. 2,000
3. Which of the following statements is always true?
a. Decimals are rational numbers. c. Integers are fractions.
b. Zero is counting. D. Zero is whole.
4. Which property is being illustrated by (2x+y) + 4 = 4 + (2x + y)?
a. distributive b. associative c. commutative d. identity
5. What is the answer in 22+3•4-12+8-(2-4)3+8÷(-2+4)?
a. 0 b. 12 c. 24 d. -1
6. Which has a degree of 15?
a. 2x9y5z b. 12x13y2 c. 15x15 d. all of the options
7. What is the result when –{-[-4(-x)-(3x-(x+2))]} is simplified?
a. 7x-2 b. -2x +2 c. -2 d. 2x+2
8. What is the simplified form of [(4x3y5)/ (2x4y3)]2 ?
a. 4x2y4 b. (4y4)/x2 c. 2y2/x4 d. 22x4y2
9. Which is equal to {12,500 x3]0 – (5x/5)?
a. 1-x b. -1 c. 5-x d. 1+x
10. What is the product of (2x-y)(x-y+z)?
a. 2x +y-z b. 2x2-3xy+2xz+y2-yz c. 2x2-y2-yz d. 2x2+x-y+2z
11. The volume of a rectangular solid is expressed as 4x3+6x2+4x+2. If its base area is expressed as
4x2+2x+2, what is the solid’s
height? a. 4x + 4 b. 4x2 + 4 c. x+1 d. x-1
12. Which is the product of (2x-4)(2x+4)? a. (2x-4)2 b. 4x2-16 c.4x2+8 d.
4x2+16
13. Which is the square of the binomial (2x+3y)? a. 4x+9y b. 4x2+9y2 c. 4x2+6xy+9y2
d. 4x2+12xy+9y2
14. Which is the expanded form of (x+2)3? a. x3+23 b. x3+6x2+12x+8 c. x3-6x2-12x+8
d. x3+6x2+12x+6

45
15. Which is the expanded form of (x+y+3)2?
a. x2+y2+9+2xy+6x+6y c. x2-y2+6+2xy+6x+6y
b. x2-y2+9+2xy-6x+6y d. x2+y2+6+2xy+6x+6y
16. What is the area of a square if its side measures (2x-12) cm?
a. 4x- 48 cm2 b. 4x2-24x+144 cm2 c. 4x2-48x+144 cm2 d. 4x2 +144 cm2
17. Which is the common monomial factor of the expression 2x5y + 10x3y7 – 6x4y3?
a. 2xy b. 2x5y7 c. x3y d. 2x3y
18. Which is the factored form of x2n + x n+2?
a. xn (xn+x2) b. x2 (xn+x2) c. x2 (xn+x) d. cannot be factored
19. Which is the factored form of 16x2-36y4?
a. (4x+6y2) (4x-6y2) c. (4x-6y2) (4x-6y2)
b. (8x+18y2) (8x-18y2) d. (4x+6y) (4x-6y)
20. Which of the following is a perfect square trinomial?
a. 4x2-20xy+25y2 b. x2+2xy + y2 c. x2-10x+25 d. all options
21. Which is the factored form of x2-6x+8?
a. (x-8)(x+1) b. (x-4)(x+2) c. (x-8)(x-1) d. (x-4)(x-2)
22. Which is not factorable?
a. x2+1 b. x2-1 c. 2x+4xy d. 100-x2
23. Which is the factored form of x2-2xy+y2-x+y?
a. (x+y)(x-y-1) b. (x-y)(2y) c. (x-y)(y-1) d. unfactorable
24. Which must be placed on the blank (m8-n8) = (m4+n4)(m2+n2) (____) (m-n) to make a correct factoring
process?
a. m-n b. m2-n2 c. m+n d. n2
25. The area of a square is expressed as 16x2+24xy+9y2, what is the measure of a side of the square?
a. 4x-3y b. 4x +3y c. 16x + 9y d. 16x- 9y
26. Which is the simplified form of 6x8/8x6?
a. ¾ b. 3x/4 c. 3x2/4 d. 3/4x
27. Which is the answer when (5t/8) is multiplied to (4/3t2)?
a. 5/6t b. 5/6 c. 5/t d. 6t
28. Which is the quotient of (2x/3) and (x/9)?
a. 2 b. 3x c. 6x d. 6
29. Which is the sum of (5/4x2) and (7/6x)?
a. 19x/12x2 b. 19/12x2 c. (15+14x)/12x2 d. (15+4x)/12
30. Which is not a rational expression?
a. 5x/x b. (2x-1)/(x-1) c. 2x/ x d. none
31.Which is the simplest form of (2x-4)/ (x2-4)?
a. ½ b. 2/(x+2) c. 2/(x-2) d. 2x-4
32. Which is the sum of 1/3 and 1/5?
a. 2/8 b. ¼ c.8/15 d. cannot be added

46
33. Which is the simplified form of the complex fraction, ?
a. ½ b. 7/10 c. ¼ d. 1/5
34. Which is the value of x in 2x+5x+3 = -11?
a. 2 b. 14 c. -2 d. -14
35. One number is greater than the other by 13. If their sum is 41, what are the 2 numbers?
a. 12, 29 b. 40, 1 c. 27, 14 d. 16, 25
36. If a rectangle has a length of 3 cm less than four times its width and its perimeter is 19 cm, what are the
dimensions of the rectangle? a. 3 and 7 b. 5.25 and 10 c. 2.5 and 7 d. 8 and
11
37. Lorna is 20 years older than her daughter, Rudylyn. In ten years, she will be twice as old as her
daughter, how old are they now?
a. 25, 35 b. 10, 20 c. 15, 25 d. 20,30
38. Two buses leave the station at the same time but in different directions. Bus A drives at a distance of 24
km while Bus B at a distance of 28 km. If they arrive at their destinations at the same time, what are their
average rates if Bus A’s average rate is 12 km/hr less than Bus B’s? a.72 kph, 84 kph b. 7 kph,
12 kph c. 2 kph, 8 kph d. 70 kph, 80 kph
39. An encoder can finish a file of documents in 4 hours. Another encode can do the same job in 3 hours.
How long will it take for the job to be done if the 2 encoders help each other?
a. 1 hr 13 mins and 13.21 secs c. 1hr 42 mins and 51.43 secs
b. 2 hr 12mins and 12.23 secs d. 2 hr 2mins and 12.23 secs
40. Feljone has 56 bills consisting of 10-peso and 5-peso bills, If he has a total of 440 pesos, how many 10-
peso bills does he have?
a. 32 b. 18 c. 24 d. 48
41. Three consecutive even integers have a sum of 138. What is the largest among the three numbers?
a. 40 b. 42 c. 44 d. 48
42. In what quadrant can (-2, 4) be located? a. QI b. QII c. QIII
d. QIV
43. What is the slope of 2x- 3y = 4? a. 2/3 b. -4/3 c. -2/3
d. 4/3
44. Which has an undefined slope? a. diagonal line b. horizontal line c. vertical line
d. all lines
45. Which equation has an x- intercept of 8 and y-intercept of -16?
a. y = 2x-16 b. y = -2x -16 c. y = -2x +16 d. y = 2x +16
46. Which is the solution of the system x- y =5 ?
X+2y=2
a. (0,-5) b. (4,-1) c. (3,1) d. (1,1)
47. Which of the following have infinitely many solutions?
a. parallel lines b. skew lines c. intersecting lines d. perpendicular lines

47
48. The sum of two numbers is 315. Their difference is 119. What are the two numbers?
a. 115, 200 b. 15, 300 c. 150, 165 d. 98, 217
49. Which is equal to (81)-3/4?
a. ½ b. 1/36 c. 1/27 d. 2/5
50. Which will make the equation correct?
a. 12 b. 16 c. 18 d. 24

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