This study aims to describe the types of mistake and causes of the XI grade students of SMA Negeri 31 Jakarta TP. 2019/2020 made a mistake in solving the problem of an algebraic function derivative application. The method of this research is a qualitative descriptive study. The data was obtained by conducting tests and interview online. The respondents were drawn from 6 XI class in SMA Negeri 31 Jakarta. Each student's work was analyzed to describe the types of mistakes using the Newman analysis procedure, then an interview was conducted to describe the factors that caused students to make mistakes. Based on the results of the study, it can be concluded that the types of mistakes found when students solve problems in the application of algebraic function derivatives are 1) reading mistakes, that is, incorrectly writing the functions listed in the questions, 2) mistakes in understanding, in the form of misinterpreting what is known and asked about, 3) transformation mistakes, in the form of students' inability to choose procedures to solve problems appropriately, 4) process skill mistakes, in the form of incomplete student work, miscalculation, 5) conditioning mistakes, in the form of students' inability to show the final answer. The contributing factors are that students do not understand the derivative application material of algebraic functions, students are in a hurry to solve the problems, different types of questions given are different from the questions exemplified by the teacher, and rarely make conclusions at the end of the answer. Keywords: analysis of mistakes, newman procedure, application of derivative algebraic functions.

This study aims to add alternative learning options to trigonometry material at the high school level by applying the problem based learning model. In developing the learning model, this research uses a learning design. Learning development is done by analyzing the needs and analyzing students. Performances objectives and learning outcomes are reviewed in detail and adjusted to the learning objectives that have been set. The results of this study indicate that the learning design by applying the problem based learning model can be one of the recommendations for teachers in implementing trigonometry learning. This is because in the learning process, students are asked to solve problems in the real life, so it can help students develop problem-solving skills in trigonometry.