This research is development research (R&D) with the aim of producing learning media using Articulate Storyline 3 that meets valid and practical requirements to help Grade VIII students of SMP/MTs in understanding the material on the System of Two Variable Linear Equations and facilitating Mathematical Problem Solving Ability. This study applies the ADDIE development model which consists of fiv…
This final project presents a proof of the butterfly and double butterfly theorems on parabola and ellipse using Haruki’s lemma. In addition, this final project also shows the use of modifications of Haruki’s lemma on a parabola and Haruki’s lemma on ellipse for each proof step. Keywords: Butterfly theorem, double butterfly theorem, Haruki’s lemma on parabola, Haruki’s lemma on e…
ABSTRACT This final project discusses a fifth-order convergence method to solve nonlinear equations by modifying Newton’s method using variational iteration techniques. It is analytically shown that the resulting method has fifth-order convergence. The computational results support the results of the analytical study. Numerical computation shows that the resulting method is comparable to…
ABSTRACT This final project discusses the development of the concept of a mixtilinear incircles in a cyclic quadrilateral. The development carried out is to show the various relationships formed between the mixtilinear incircles radii that can be constructed on the cyclic quadrilateral. In any triangle ABC, three different mixtilinear incircles can be constructed. In this final project, po…
This research is motivated by the low mathematical problem solving ability of students. One of the efforts that can be made by teachers to improve mathematical problem solving skills is to design the learning process. The learning process can take place well if the teacher is able to develop learning tools. Based on observations and interviews conducted with three mathematics teachers, nam…
This final project discusses Gradient Descent method with the explicit stepsize formula for solving systems of nonlinear equations. Gradient Descent method with the explicit stepsize formula has linear convergence and if the Jacobian matrix has a special structure then it is equivalent to Newton’s method which quadratic convergence. At the end of the discussion, some numerical examples a…
ABSTRACT This nal project discusses the multiplicative functions commutable with sums of squares. In this nal project, suppose that k be an integer greater than or equal to 3. It is shown that if a multiplicative functions f satises f(x2 1 + x2 2 + · · · + x2 k) = f(x1)2 + f(x2)2 + · · · + f(xk)2 for all positive integers xi, then f is the identity function. This nal project i…
The final project discusses the development of converse Leon Anne’s Theorem in crossed quadrilateral. This theorem initially applies to a convex quadrilateral with the balance property obtained if the area of two opposite triangles is half the area of the quadrilateral. In the case of the a crossed quadrilaterals, balance property is obtained from the difference of the area of two certain…
This final project discusses the annual premium on whole life insurance for insurance participants aged x years using a composite model method that where there are parameters in the model is estimated using maximum likelihood method. Premium payments stop if the insurance participant die. The solution to the problem is to obtain by determining the annuity continuous and single premium, the…
ABSTRACT This final project discusses the combination of the Halley and Potra-Ptak (MHP) methods which are the result of the combination of two iteration methods, namely the Halley and Potra-Ptak methods to solve nonlinear equa- tions. The convergence analysis shows that the MHP has a convergence order of nine. Basin of attraction from MHP and other comparison iteration methods are provid…
This research aims to produce valid and practical learning tools, namely Syllabus, RPP, and Student Activity Sheets on the Three Variable Linear Equation System material for class X SMA. This research is motivated by the importance of learning tools that can facilitate students' mathematical problem solving abilities. This research use 4D model which consists of 4 stages were definition, design…
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This study aims to produce an E-LKPD with discovery learning-based flat-sided geometrical materials that can facilitate the mathematical understanding ability of eighth grade students of SMP/MTs and meet the valid and practical requirements. This type of research is development research with ADDIE development model consisting of analysis, design, development, implementation, and evaluation stag…
ABSTRACT This final project discusses a new modified simplex method for solving a quadratic fractional programming problems. The method based on linear programming problem for finding an optimal solution to a quadratic fractional programming problem, where the numerator of objective function can be factorized into two linear functions. An illustration in the form of an example is given to …
This research is motivated by the low mathematical reasoning ability of students and the low quality of the learning tools used by the teacher. Based on the preliminary analysis, researcher obtained information that the mathematics learning tools used by the teacher were not in accordance with the rule of the Kurikulum 2013. Thus, it is necessary to design a mathematics learning tools that is i…
This final project discusses the nonnegative integer solution of nonlinear Diophantine equation (8n)x + py = z2 subject to some odd prime numbers p for natural numbers n. That is solved by Catalan conjecture, exponential property, and congruency. These properties aim to determine the value (nx, y, z). Analytically different solutions are obtained based on the values of n and p taken in the…
Abstract: This study aims to produce mathematics learning tools through the application of a Problem Based Learning model mathematical problem solving skill for three-variable linear equation systems to facilitate valid and practical. This research consists of four stages of 4-D development research, namely Define, Design, Develop, and Disseminate. The validity of the learning device is assesse…
This nal project discusses the properties of BP-algebra and its relation to BP- algebra with BF-algebra, BH-algebra, and B-algebra 0 commutative. Their relationship is proven by showing that the properties of BP-algebra, BF-algebra, BH-algebra, and B-algebra 0 commutative are interrelated. If (X; ∗; 0) BP- algebra with (x∗y)∗z = x∗(z∗y) and then (X; ∗; 0) is B-algebra and if (X…
This thesis discusses the modification of the Cross’ Theorem on a convex quadrilateral and an expanded nonconvex quadrilateral by constructing a square pointing outward on each side of the Cross’ Theorem quadrilateral. The proof process is done using the sine and cosine rules. The result obtained is that the total area of flat figures that are opposite each other formed from the Cross�…
Education is a complex activity that includes various components that are related to one another. Learning is an activity that is inseparable from human life, by learning humans can develop the potentials that they are born with. Learning geography is one of the subjects in high school. The quality of education is currently experiencing challenges as a result of the corona virus outbreak. …