On The Theory Of Perfect Numbers and Primes

This paper explores the properties of the set $\frac{n(n+1)}{2}$ and its implication on the distribution of perfect numbers. A major takeaway is a conjecture that all perfect numbers - even and odd lie on that line. It also describes primes arising from the perfect number line equation and equivalent statements of perfectness.

ANALISIS KESALAHAN FAKTA DAN KESALAHAN KONSEP MAHASISWA DALAM MENYELESAIKAN SOAL GEOMETRI ANALITIK RUANG

This study aims to describe both fact and concept error of students in solving space analytic geometry problems. The subjects of this research are two students of Mathematics Department of Universitas Negeri Makassar. Each of them represents for each error (fact and concept errors). The collecting data were employed by using space analytic geometric tests and depth-interview. Interview guidelines and researcher were as research instruments. Data were qualitatively analyzed, using three stages of analysis: data reduction, data display and concluding. The main findings of this research are (1) the subject of fact error made mistakes in writing vector symbols, (2) the subjects of concept error made mistakes in identifying an equation (plane equation or line equation), since his focus was only in the number of variables of the equation.Keywords: fact error, concept error, space analytic geometry

ANALISIS KEMAMPUAN BERPIKIR KRITIS PADA MATERI PERSAMAAN GARIS LURUS DIKAJI BERDASARKAN HABITS OF MIND

Habits of mind are one of the many factors that influence mathematical critical thinking skills. The purpose of this study was to describe students' mathematical critical thinking skills on straight line equation material studied based on habits of mind. The results obtained: 1) There are 3 categories of habits of mind that appear, namely 29.73% high categories with the ability to think critically mathematically can provide statements in the form of reasons; evaluates gradient values; make a statement and consider it; provide a coherent and detailed explanation; set the strategy to be used, 51.35% of the medium category with the ability to think critically in mathematics can provide a statement in the form of reasons; evaluates gradient values; make a statement and consider it; just write down the steps without explanation on the written test; have a strategy to solve the questions but not according to the indicators and 18.92% low category with the ability to think critically mathematically can give statements in the form of reasons evaluates gradient values, but calculations are wrong; unable to make a statement and consider it; just write down the steps without explanation; do not have a strategy to solve the problem. Keywords: Critical Thinking, Habits Of Mind, Straight Line Equations

DEVELOPMENT OF MATHEMATICS TEACHINGS BASED ON APOS THEORY: CONSTRUCTION OF UNDERSTANDING THE CONCEPT OF STUDENT STRAIGHT LINE EQUATION

This research is an ADDIE-based research and development. Data on the development process were collected using tools validated by materiel experts, design experts, student response questionnaires and teacher responses. The results of the implementation of the use of textbooks are seen from the student activity sheets and student learning outcomes, in this study using participants from class VIII students of MTs YPI Kuala Enok totaling 28 students with a random sampling technique. The results of this development research are: (1) SMP / MTs mathematics textbooks based on the APOS theory on straight line equation material are declared suitable for use in learning activities based on the validation results of material experts and design experts. Based on the results of student and teacher responses to textbooks, they are ranked very well. (2) The effectiveness of using SMP/MTs mathematics textbooks based on the APOS (Action, Process, Object, Schema) theory of straight line equation material seen from the student activity sheet can be concluded that in the process of learning student activities. In addition, on the basis of the results of all students, the criteria for completeness were achieved, an average score of 85. Thus, from the results of this analysis, it can be concluded that textbooks based on the APOS theory are effective in constructing an understanding of the concept of straight line equations.

Asosiasi Adversity Quotient dengan Hasil Belajar Matematika Peserta Didik Jenjang SMP

The purpose of this study was to determine whether there is a relationship between the students' adversity questions and the mathematics learning outcomes. This type of research is a quantitative research with correlational techniques. The research sample that was selected randomly to 50 students. The instrument to measure the adversity quotient variable used a questionnaire with a Likert scale and the variable instrument of mathematics learning outcomes used a multiple-choice form test, that had been tested for validity and reliability. The requirements test performed showed normal analysis results (Lilliefors test) and homogeneous (Fisher's test). The regression linearity test results of the regression line equation ?=1,947+0,795X. The test results used product trials when the r=0,605 was obtained. Reinforced the degree of significance with the test obtained the tvalue=5,267>2,01=ttable. This research conclusion that there is a significant positive relationship between adversity quotient and mathematics learning outcomes of seventh grade students at SMP Negeri 4 Cikarang Selatan with a contribution of 36,6%.

Contribution of the Application of Learning Methods and Learning Activities to the Results of Islamic Religious Education of SMP Swasta Sei Bejangkar

This study aims to identify and describe: (1) the positive and significant contribution of the application of the learning method to the learning outcomes of Islamic Religious Education, (2) the positive and significant contribution of learning activities to the learning outcomes of Islamic Religious Education, and (3) the positive and significant contribution of the application. Learning methods and learning activities together on the learning outcomes of Islamic Religious Education?.The research was conducted at the Sei Bejangkar Region Private Junior High School. This research is a quantitative study with a correlation research method. The population in this study was all students of class VIII which consisted of 2 classes with a total of 72. All students were used as research samples. The data collection instruments used was questionnaires and tests. The data analysis used is correlation and regression. The research findings show: (1) there is a positive and significant contribution between the application of learning methods and learning outcomes with a correlation number of 0.354 with the regression line equation Ŷ = 71.60 + 0.23 X1, (2) there is a positive and significant contribution between learning activities and outcomes. Learn with the correlation number 0.473 with the regression line equation Ŷ = 68.96 + 0.28X2. and (3) there is a positive and significant contribution between the application of learning methods and learning activities with learning outcomes with a correlation number of 0.549 with the regression line equation Ŷ = 138.80 + 0.18X1 + 0.25X2. The effective contribution of the variable application of learning methods to learning outcomes is 9.90%, while the effective contribution of learning activity variables to learning outcomes is 20.00%.

Accretion disks around a mass with quadrupole QUADRUPOLE

In this work, we consider the exterior static axisymmetric gravitational of compact objects. We investigate the properties of the q-metric which is the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. The geodesic line equation is derived from the field equations and the orbits of the test particle are investigated. We consider the stability properties of test particles moving along circular orbits around a mass with quadrupole. We show that the quadrupole modifies drastically the properties of an accretion disk made of such test particles.