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. …
This thesis discusses modification of the Japanese Theorem on hexagon and heptagon with diagonal lines formed from one point as proven by using Carnot Theorem. In addition, this thesis also discusses other modification of the Japanese Theorem on hexagon and heptagon with diagonal lines formed from points that can form the same quadrilateral and triangle which are then proven by using the m…
This research is motivated by the demands of the 2013 curriculum on teachers. Teachers are required to not only teach and educate, but must be able to become facilitators so that the role of education becomes more meaningful. Teachers must be able to design learning processes that are interactive, inspiring, fun, challenging and motivating students to actively participate in the learning p…
human beings who are able to keep up with the pace of development of science and technology in the 21st century. One of the four 21st century skills that are quite important is the ability to think critically. On the other hand, when viewed from the achievement of the national examination (UN) in the field of mathematics in 2019, is 45.52 is quite low. Especially about the material questions Pr…
This research is motivated by the importance of students' mathematical understanding abilities in Indonesia, especially in Riau Province and the limited number of Student Worksheets that facilitate mathematical understanding abilities. The ability of mathematical understanding is important for students to have because it becomes a prerequisite in learning further mathematical concepts and …
This study aims to produce electronic LKPD assisted by google slides on linear programming material that can facilitate valid and practical KPMM for class XI high school students. Based on the results of observations and interviews with several schools in Pekanbaru, information was obtained that the electronic LKPD was not yet available. This research is a research and development (R&D) using t…
Death is the end of life in a biological organism. All living things will eventually die. Humans are also living beings, so humans also experience death. Babies are humans, so babies will also experience death. Infant mortality is influenced by two factors, namely factors before and after birth, which before birth is the consumption of pregnant vitamins, births assisted by medical personnel, wh…
The final project presents a new approach to evaluate the cubic roots of a quadratic matrix order 2 by using the Cayley-Hamilton’s theorem. In addition, this final project also aims to show how the Cayley-Hamilton’s theorem can be used to determine the explicit formula of each cubic roots of quadratic matrix. In its application several examples are given to determine the cubic roots of …
This final project discusses the interactions among three population consisting of prey 1, prey 2, and predator population. The model described involves the prey 1 population influenced by Allee effect. Prey 1 and prey 2 population have a mutuality according to Holling functional response, while the predator population has alternative food sources. In the model observed, there are eight eq…
This final project discusses of the multi-item inventory problem with backorder using assignment model as mixed integer linear programming problem with branch-and-bound method. This model aims to determine optimal policy of inventory problem by meeting the specified constrains. The mathematical model for this problem is designed using the LINGO 18.0 application. The solution of the assignm…
This final project discusses the inventory management of resources with discount of raw materials. In this discussion, it is used the economic order quantity model with discount to determine how much to order, so as to minimize the total inventory costs. The result of this problem is the total inventory cost which is smaller than the previous policy. Keywords: Inventory, inventory manageme…
This nal project discusses the multiplication of a Pell numbers and a Pell-Lucas numbers generating a power numbers. The power numbers is the repeated product of a numbers, with a positive, zero, or negative integer power. Power numbers are obtained if they satiss the condition n > m > 0, and n ≡ m(mod 4) or n ≡ m+2(mod 4) and satiss the solution of (N,M) for N ≤ 14 and M ≤ 7. K…
This nal project discusses the properties of BI -algebra and properties of ideals in BI -algebra. By using the binary operations and implication algebra are obtained by conditions that show the properties of BI -algebra and Ideals in BI -algebra. This nal project is a review of article from Saeid et al. [Analele Stiintice ale Universitatii Ovidius Constanta, 2017, 177-194]. Keywords: BI…
This research is motivated by the low ability to solve mathematical problems and the limited learning tools based on the 2013 Curriculum, especially those that apply the Problem Based Learning (PBL) model. Based on these conditions, it is necessary to develop learning tools in the form of syllabus, lesson plans, and LKPD to assist teachers in learning. The purpose of the research is to pro…
This nal project discusses the solution of solid transportation problem of triangular fuzzy numbers. Triangular fuzzy numbers are converted into rm numbers and paramaters. Furthermore, to nd the optimal solution, an approach for solving the solid transportation problem is used. Based on the comparison of two forms, it is concluded that the parameter form can be used as an alternative in…
This study aimed to develop valid and practical quadrilateral and triangular based on acontextual approaches to facilitate the mathematical probelm solving ability of seventh-grade students of SMP/MTs. This research model used ADDIE model covering the Analysis, Design, Development, Implementation, and Evalution stages. Based on the validation results, it was obtained that the mathematics module…