This final project discusses the effect of weak disorder on the thermalization process in the Fermi–Pasta–Ulam–Tsingou (FPUT) model, which is one of the classical systems in nonlinear dynamics based on Hamiltonian mechanics. In this study, two types of weak disorder are introduced, namely mass disorder and quadratic potential disorder. The research is conducted numerically through ti- me …
This final project discusses the prospective reserve of endowment life insuran- ce using Benktander type II distribution and Hull-White interest rate model for x-years old single participants with n years coverage period and h years premium payment period. The calculation of reserve is determined using the prospective method, which is calculation of reserve based on the present value of all pas…
Life insurance companies provide protection to address risks that may occur to life insurance participants. Companies need to prepare reserve costs to address these risks. These reserve costs are used to cover the needs of the insurance company and the insurance participants. These reserve are obtained from pre- miums paid by insurance participants and are used to cover the needs of the insuran…
Endowment last survivor life insurance is a type of life insurance product that provides financial protection for two individuals and offers benefits either upon the death of both insureds or upon their survival to the end of the insurance period. In the event of a claim, the insurance company must allocate sufficient reserve funds. Reserve have an important role in ensuring the financial stabi…
This final project discusses a new modification on Heun’s method based on a contraharmonic mean for solving an initial value problem with high efficiency. The process begins by deriving the formula for the method discussed followed by stability analysis, consistency analysis, local truncation error (LTE). From the numerical results presented it can be seen that this method is more stable …
This study aims to improve students' mathematical problem-solving skills through the implementation of a cooperative learning model using the Power of Two method on the topic of linear equations and inequalities in one variable. The subjects of this study were 36 eighth-grade students from class VIII2 at SMP Negeri 11 Pekanbaru. The research employed a Classroom Action Research (CAR) approach c…
This study was motivated by the low level of Learning Objective Achievement Criteria (KKTP) among ninth-grade students at SMP Babussalam Pekanbaru. Based on the summative test scores obtained from the mathematics teacher on the topic of similarity with essay-type questions in the second semester of the 2024/2025 academic year, only 6 out of 24 students achieved the LAC criteria, representing a …
This research is a Classroom Action Research that aims to improve the learning process and improve students' Mathematical Reasoning Ability through the application of Problem Based Learning. This research was conducted in two cycles on 35 Junior High School (SMP) students. The learning tools used include teaching modules equipped with Student Worksheets, teaching materials and data collection i…
This research was motivated by the fact that the mathematics learning outcomes in class VIII.2 of SMPN 13 Pekanbaru were low, with only 39.53% of students reaching the Learning Objectives Achievement Criteria. This study aimed to improve students' mathematics learning outcomes by implementing the Problem Based Learning (PBL) model. This research is a collaborative Classroom Action Research…
Kemampuan Pemecahan Masalah Matematika (KPMM) merupakan kemampuan yang dimiliki oleh peserta didik dalam menyelesaikan permasalahan matematika dengan indikator-indikator KPMM, yaitu: (1) memahami masalah; (2) merencanakan pemecahan masalah; (3) melaksanakan rencana pemecahan masalah; (4) menafsirkan hasil yang diperoleh. Hasil observasi, wawancara, dan tes awal KPMM peserta didik kelas X T…
One of the mathematical skills that students must master is problem-solving skills. The results of a preliminary study indicate that students' mathematical problem-solving skills are still low. In addition to cognitive abilities, there are affective abilities that must also be developed, one of which is the character of the critical reasoning dimension. Changes in the times and rapid technologi…
Abstract: This study aims to improve the learning process and improves students’ mathematical problem solving abilities by implementing the problem based learning model. The subjects of this study were students of class VIII.1 of SMP YLPI P. Marpoyan in the first semester of the 2024/2025 academic year. This study consisted of two cycles, the first cycle containing two meetings with the mater…
This final project discusses the determination of solutions to the nonlinear Dio- phantine equation x3 + y3 = z2 over the ring of Gaussian integers for the special case x ≠ y. The solution approach employs exponential properties, elementary algebra, and a method of separating the real and imaginary parts of complex expressions. Since the analytical method used here is based on simple algebra-…
Penelitian ini dilatarbelakangi oleh rendahnya kemampuan komunikasi matematis peserta didik serta keterbatasan Lembar Kerja Peserta Didik (LKPD) yang dirancang khusus untuk memfasilitasi kemampuan komunikasi matematis berdasarkan Kurikulum Merdeka. Sebagai fasilitator pembelajaran, guru perlu menyediakan LKPD yang mendukung kemampuan komunikasi matematis, khususnya bagi peserta didik fase D. Ke…
Penelitian ini dilatarbelakangi oleh rendahnya kecakapan pemecahan masalah matematis peserta didik. Proses pembelajaran masih berpusat pada guru, sehingga peserta didik cenderung pasif dalam kegiatan pembelajaran di kelas dan belum mampu untuk memecahkan masalahnya sendiri. Peserta didik kurang memahami soal-soal pemecahan masalah disebabkan karena peserta didik kesulitan memahami informasi pad…
Penelitian ini dilatar belakangi oleh rendahnya kemampuan pemahaman konsep matematis siswa di Indonesia dan masih terbatasnya penggunaan LKPD yang disusun berdasarkan Kurikulum Merdeka oleh guru sebagai sarana penunjang pembelajaran. Sebagai fasilitator pembelajaran, guru perlu menyediakan LKPD yang mendukung pengembangan kemampuan pemahaman konsep matematis, khususnya siswa fase E. Kemampuan p…
Abstract: This study aims to produce a valid and practical Problem Based Learning (PBL) module to facilitate the mathematical problem-solving ability of phase D students on the topic of curved-surface solid shapes. This research employed the Research and Development (R&D) method using the 4D development model (Define, Design, Develop, Disseminate). The research instruments consisted of expert v…
This study aims to determine the effect of self-efficacy on the learning achievement of class XI students in chemistry subjects at SMAN 12 Pekanbaru. This type of research is a survey research with a quantitative approach. Data collection methods in this study are questionnaires and documentation. The validated self-efficacy questionnaire was distributed to a sample of 140 students selected thr…
This study aims to determine the improvement of students' problem-solving ability in acid-base material through the application of the Problem Based Learning (PBL) learning model in class XI of SMAN 7 Pekanbaru. This study uses a quantitative method with a one group pretest-posttest pre-experimental design. The research sample consisted of 36 students selected through a simple random sampling t…
This study aims to determine the influence of interpersonal intelligence and learning independence on students' chemistry learning outcomes in grade X of SMA/MA or equivalent. This research employed a quantitative approach using a survey method. The sample consisted of 152 grade X students from SMA Negeri 15 Pekanbaru. The instruments used were questionnaires and documentation of students’ ch…