This final project discusses a decreasing sequence (an) of nonnegative terms, the- re exist subsequences (nk) of (n) such thatP1k=1(nk+1−nk)ank andP1n=1 an ha- ve the same convergence. Then for P1n=1 an converges if and only if P1k=1 qkaqk converges for 1 < q ∈ N. Using these results, an extension of the ratio test is formed. Keywords: Sequence, series, convergency, divergency
This final project discusses the sensitivity analysis of transportation problems in triangular fuzzy numbers. The optimal solution of the transportation problem is obtained after converting the triangular fuzzy number in the transportation problem into a crisp number. When the optimal solution obtained remains the same for a long time, a sensitivity analysis is carried out to determine chan…
This nal project discusses the determinant of interval matrix with the calculation used is a combination of some interval arithmetic which has a shorter interval value than others. Assuming that a shorter interval value is an optimal value. The method used in determining the determinant of interval matrix is the modied Crout's method in the article of Nirmala and Ganesan [Journal of Phys…
This nal project discusses the modication of the fourth order multistep Adam- Bashforth and Adam-Moulton method by changing the integral boundaries of [xn; xn+1] to [xn−2; xn+1] to solve initial value problems. In generally, the com- parison results show that the numerical solution obtained with the modication of the fourth order multistep Adam-Bashforth and Adam-Moulton method has an…
This research is a development purposed is to produce mathematics learning devices such as syllabus, lesson plans, and student worksheet by using discovery learning on curved face three dimensional (cylinder, cone, and ball) material for the 9th grade of junior high school. This research is motivated by the incompatibility instruments which arranged by teacher based on 2013 Curriculum. The…
This final project discusses the premium of contingent endowment life insurance using Gompertz’s law. In this project, the number of insurance participants is limited to two people aged x and y years. The premium of contingent endowment life insurance are divided into two parts, namely the premium of contingent endowment joint life and last survivor status life insurance. In contingent e…
The background of this research is the existence of curriculum change that claiming teacher to can develop the learning devices and also still the limited learning devices that matching with 2013 curriculum.This research aims to produce products in the form of mathematics learning devices such as syllabus, lesson plan and student worksheet.The development model in this research is 4-D mode whic…
This research is motivated by the lack of mathematics teaching materials that introduce Malay Culture, namely traditional Malay games for students in accordance with the demands of the 2013 curriculum. The purpose of this research is to produce mathematics teaching materials in the form of books using the tradisional Malay Riau games. This research is a research and development (R&D) using the …
This research is motivated by the limited mathematics learning devices that are in accordance with the 2013 Curriculum. This research purposed is to produce mathematics learning devices such as syllabus, lesson plans, and student worksheets by using problem based learning on sets material for the seventh grade of junior high school. The development model used in this research is the 4-D model w…
This study is aimed to produce mathematic learning tools consisting of a Syllabus, Lesson Plan (LP), and Students' Worksheet (SW) in the material Linear Equation System of Three Variables in class X which applies valid and practical Problem Based Learning models. This developmental model used is the 4-D model which consists of 4 stages of development, namely define stage (definition), design st…
The research was based on the limited innovative mathematics learning device as a means of supporting learning in the 2013 Curriculum. The purpose of this research is to produce mathematics learning device in the form of syllabus, Lesson Plan (LP), and Student Activity Sheet (SAS) based on cooperative learning models type think pair square material of the sine and cosine rules of class X SMK/MA…
This research was conducted due the limited learning instruments in accordance with the 2013 Curriculum, especially the application of learning models and learning approaches. The purpose of this research is to develop the mathematics learning instruments: syllabus, lesson plans, and student worksheets using Problem Based Learning model with Melayu cultural context on circle’s topic for 8th g…
This research aims to produce the mathematics learning instruments which includes syllabus, learning implementation plans (RPP) and student activity sheets (LAS) model discovery learning on the material of quadrilateral and triangles to facilitate the mathematical representation students abilities of SMP/MTs that are valid and qualified of the practicality. The development research model used i…
This research aims to produce mathematics learning instrument which includes syllabus, learning implementation plans (RPP) and student activity sheets (LAS) based on the Discovery Learning on the sine and cosine rules topic of students of Vocational high school that are valid and practical. This research development model is a 4-D model which consists of the stages of define, design, developmen…
Most students have difficulty for learning mathematics because of mathematical abstract objects. Teachers can link everyday life with math material to make it easier for students to learn mathematics. One of the learning concepts that can connect learning material with everyday life is Contextual Teaching and Learning approach. Mathematical communication skills are needed to make it easier for …
Learning activities should be considered needs of students and the demands of the curriculum. The mathematics learning objectives and the demands of the current curriculum is to developing student’s higher order thinking skills. In fact the higher order thinking skills of junior high school students are categorized sufficient and still need to be improved. Efforts to improve the quality of st…
This research is motivated by the limited mathematics learning devices that are in accordance with the 2013 Curriculum. This research purposed is to produce mathematics learning devices such as syllabus, lesson plans, and student worksheets by using problem based learning on linear system with two variables material for the eighth grade of junior high school. The development model used in this …
This final project discusses the application of the Varignon’s theorem to the parallelo-hexagon by connecting the midpoints of the two sides which are close to the midpoint of the two sides in front of them so that they form a rectangle in the parallelo-hexagon. Proof is described in three alternatives, using the concept of congruence, geometrical transformation, and using parallelo-hexag…
This final project discusses the reciprocal addition formula of multiplying the m-th and n-th of Fibonacci numbers, where m and n are respectively even and odd integers, using the floor function. The reciprocal addition formula obtained is proven by using the Fibonacci number identities, the properties of the Fibonacci numbers, and algebraic calculations. This final project is a review of …
This nal project discusses the determinant of interval matrices by using arithmetic operations on interval numbers. Next, an analysis of the interval arithmetic is provided, assuming the shortest interval is the best. At the end, using the results of interval arithmetic analysis, the calculation of the determinant of interval matrix is given along with some of its properties. Keywords: In…