This study aimed to determine the difficulties inIntermediate Algebra of Second Year students in publicsecondary schools in Bongabong.

Specifically, it sought to answer the followingquestions:

1.What is the index of difficulty of the students inradical expressions in terms of the following:

1.1 roots of real numbers

1.2 expressions with rational exponents1.3 simplifying radical expressions1.4 addition and subtraction of radicalsmultiplication of radicals

1.6 division of radicals?

2. What is the index of difficulty of the students invariation in terms of the following:

2.1 direct variation2.2 direct square variation

2.3 inverse variation2.4 joint variation?

3. Is there a significant difference in the index ofdifficulty in radical expressions of the students interms of roots of real numbers, expressions withrational exponents, simplifying radical expressions,addition and subtraction of radicals, multiplication ofradicals and division of radicals?

4. Is there a significant difference in the index ofdifficulty in variation of the students in terms of thefollowing: direct variation, direct square variation,inverse variation and joint variation?

1. There is no significant difference in the index ofdifficulty in radical expressions of the students interms of roots of real numbers, expressions withrational exponents, simplifying radicalexpressions, addition and subtraction of radicals,multiplication of radicals and division of radicals.

2. There is no significant difference in the index ofdifficulty in variation of the students in terms ofthe following: direct variation, direct squarevariation, inverse variation and joint variation.

The diagram shows the variables in the studywhich include the index of difficulty of Second YearStudents in Public Secondary Schools in BongabongDistricts in terms of: radicals –roots of realnumbers, expressions with rational numbers,simplifying radical expressions, addition andsubtraction of radicals, multiplication of radicalsand division of radicals; and variation– directvariation, direct square variation, inverse variationand joint variation.

The two-headed arrow signifies thehypothesized differences among the index ofdifficulty in the indicators of radical expressionsand variations.

To determine the index of difficulty ofeach item, the majority criterion (50 percentplus one) was used as basis to describe theMeans.

Range Description

51% - 100% Easy (E)

50% Neither Easy nor Difficult (N)

1% - 49% Difficult (D)

1. What is the index of difficulty of the studentsin radical expressions in terms of the following:

1.1 roots of real numbers

1.2 expressions with rational exponents

1.3 simplifying radical expressions

1.4 addition and subtraction of radicals

1.5 multiplication of radicals

1.6 division of radicals

2. What is the index of difficulty of the students in variation in terms of the following:

2.1 direct variation

2.2 direct square variation

2.3 inverse variation

2.4 inverse variation

3. Is there a significant difference in the index ofdifficulty in radical expressions of the students interms of roots of real numbers, expressions withrational exponents, simplifying radical expressions,addition and subtraction of radicals, multiplication ofradicals and division of radicals?

4. Is there a significant difference in the index ofdifficulty in variation of the students in terms of thefollowing: direct variation, direct square variation,inverse variation and joint variation?

This chapter presents the summary of thefindings, conclusions and recommendations.

1. What is the index of difficulty of the students in radicalexpressions terms of the following:

1.1 Roots of real numbers. This topic has a mean index ofdifficulty of 66.6, described as easy.1.2 Expressions with rational exponents. The items underthis topic have a mean index of difficulty of 63.4 describedas easy.1.3 Simplifying radical expressions. Items under this topichave a mean difficulty index of 48.8 described as difficult.1.4 Addition and subtraction of radicals. This topic has anoverall mean index of difficulty 61.4 described as easy.1.5 Multiplication of radicals. All items on multiplication ofradicals has a mean index of difficulty 64.4 described aseasy.1.6 Division of radicals. This topic has an overall meanindex of difficulty 61.8 described as easy.

2. What is the index of difficulty of thestudents in variation terms of the following:

2.1 Direct variation. The mean index ofdifficulty of these items is 49.2 described asdifficult.

2.2 Direct square variation. The items have amean difficulty index of 51 described as easy.

2.3 Inverse variation. The mean index ofdifficulty for inverse variation is 49.4described as difficult.

2.4 Joint variation. The mean difficulty indexof the items is 44 described as difficult.

3. Is there a significant difference in the index of difficulty ofthe students in terms of radical expressions?

The computed F-value of 4.98 was greater than thecritical f-value of 2.62 using 5 and 24 degrees of freedomat 5% level of significance. Therefore, the null hypothesiswas rejected. This means pupil respondents havevaried index of difficulty in learning radical expressions.

4. Is there a significant difference in the index of difficulty ofthe students in terms of variation?

The computed value of 2.89 was lower than the criticalvalue of 3.24 using 3 and 16 degrees of freedom at 5%level of significance. Thus, the null hypothesis wasaccepted. There is no significant difference in the index ofdifficulty of the students in terms of variation. This meansthey encountered similar difficulties in answering theitems on variations.

Based on the findings of the study, the study concluded the following:1. The study revealed that the students found roots of real numbers easy.2. The results also showed that expressions with rational exponents were easy for the students.3. Simplifying radical expressions is difficult for the students.4. The results suggested that addition and subtraction of radicals is easy for the students.5. Multiplication of radicals was found out easy by the students.6. Division of radicals was easy for the students.7. Direct variation is difficult for the students.8. The items for direct square variation were easy for the students.9. Inverse variation was difficult for the students.10. Solving joint variation was difficult for the student-respondents.11. The index of difficulty of the students in radical expressions varies significantly.12. The index of difficulty of the students in variation does not vary.

Based on the findings and conclusions, the researcher arrived atthe following recommendations:1. Mathematics teacher should continue using their strategies inteaching roots of real numbers.2. The teacher should continuously give emphasis on exponentswhen teaching radical expressions with radical exponents.3. Factoring should be given attention when teaching simplifyingradical expressions.4. Constant drills and exercises in addition, subtraction,multiplication and division should be done to further enhancethese skills; thus, making solving easy for the students.5. Comprehension skills, clear understanding of directrelationship between quantities, skills to represent and operatethe unknown, analysis and problem solving skills should bedeveloped to make problem-solving easy for the students.6. Future research related to this study should be conducted togeneralize the findings of this study.

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