In this course, students study the relationship between input and output as functions, including quadratic, polynomial, rational, radical, exponential, inverse and logarithmic applications. Patterns in the transformation of functions are also examined in depth. Irrational and complex numbers are explored, in the context of larger concepts such as infinity and real numbers. The Unit Circle will provide the basis for the study of trigonometric functions, including their graphs and identities. The Laws of Sine and Cosine
are applied in conjunction with the Pythagorean theorem, in order to solve real-world engineering and physics problems.
In this course, students study the relationship between input and output as functions, including quadratic, polynomial, rational, radical, exponential, inverse and logarithmic applications. Patterns in the transformation of functions are also examined in depth. Irrational and complex numbers are explored, in the context of larger concepts such as infinity and real numbers. The Unit Circle will provide the basis for the study of trigonometric functions, including their graphs and identities. The Laws of Sine and Cosine are applied in conjunction with the Pythagorean theorem, in order to solve real-world engineering and physics problems.
This course covers all topics in the standard level Algebra II & Trigonometry but the intensive class explores the core families of algebraic functions: linear, quadratic, polynomial, radical, rational, exponential, logarithmic, and trigonometric more extensively. The course also moves at a brisker pace and tackles more challenging problems. Central themes include: interval notation, complex numbers, transformations, inverses, and using families of functions to model real world phenomena. Problems also require more abstraction and in the trigonometry segment of the course, students' mastery of the unit circle includes Radian measurement, and developing trigonometric models for physical processes.
This course covers all topics in the standard level Algebra II & Trigonometry but the intensive class explores the core families of algebraic functions: linear, quadratic, polynomial, radical, rational, exponential, logarithmic, and trigonometric more extensively. The course also moves at a brisker pace and tackles more challenging problems. Central themes include: interval notation, complex numbers, transformations, inverses, and using families of functions to model real world phenomena. Problems also require more abstraction and in the trigonometry segment of the course, students' mastery of the unit circle includes Radian measurement, and developing trigonometric models for physical processes.
This course explores the topics of limits, differentiation, integration, and elementary differential equations, focusing on the Fundamental Theorem of Calculus. Students learn the graphical foundation for the limit definition of the derivative, and apply rules of differentiation to solve real-world problems in Physics and Finance. In our study of Integrals, students find the area under a curve, solve kinematics problems, and calculate volumes of solids of revolution. Although graphing calculators are required, a strong foundation in Algebra and Precalculus is necessary. Conceptual understanding is paramount, but students are also asked to show their work algebraically and graphically.
This course explores the topics of limits, differentiation, integration, and elementary differential equations, focusing on the Fundamental Theorem of Calculus. Students learn the graphical foundation for the limit definition of the derivative, and apply rules of differentiation to solve real-world problems in Physics and Finance. In our study of Integrals, students find the area under a curve, solve kinematics problems, and calculate volumes of solids of revolution. Although graphing calculators are required, a strong foundation in Algebra and Precalculus is necessary. Conceptual understanding is paramount, but students are also asked to show their work algebraically and graphically.
This course covers limits, derivatives, integrals, and elementary differential equations. In addition, students study kinematics, sequences and series, and various approximation methods with a focus on the fundamental and advanced theorems of calculus. Students examine the different representations of functions: graphical, analytical, and algebraic. Calculators are used to graph and help analyze functions.
This course covers limits, derivatives, integrals, and elementary differential equations. In addition, students study kinematics, sequences and series, and various approximation methods with a focus on the fundamental and advanced theorems of calculus. Students examine the different representations of functions: graphical, analytical, and algebraic. Calculators are used to graph and help analyze functions.
This course consists of two parts: Calculus II and Multivariable Calculus. The year picks up where the Intensive Calculus class left off and starts with a discussion of solving first order differential equations by separation of variables as well as by using an integrating factor. The class then explores the topic of convergence and divergence of infinite series where students learn about the different methods in determining a series’s convergence or divergence as well as be able to approximate functions using Taylor and Maclaurin Series. Calculus II of a single variable ends with the topic of finding tangent lines and arc lengths of parametric curves as well as areas of polar curves.
The second semester introduces students to the realm of functions with multiple variables. The class first starts with an introduction to cylindrical surfaces then discusses operations on vectors such as dot and cross products as well as vector projections. The students learn how to write equations of planes in 3-space, find extreme values using partial derivatives, and optimize functions using Lagrange multipliers. The course ends with students learning about double integrals over rectangular as well as non-rectangular regions.
This course consists of two parts: Calculus II and Multivariable Calculus. The year picks up where the Intensive Calculus class left off and starts with a discussion of solving first order differential equations by separation of variables as well as by using an integrating factor. The class then explores the topic of convergence and divergence of infinite series where students learn about the different methods in determining a series’s convergence or divergence as well as be able to approximate functions using Taylor and Maclaurin Series. Calculus II of a single variable ends with the topic of finding tangent lines and arc lengths of parametric curves as well as areas of polar curves.
The second semester introduces students to the realm of functions with multiple variables. The class first starts with an introduction to cylindrical surfaces then discusses operations on vectors such as dot and cross products as well as vector projections. The students learn how to write equations of planes in three-dimensional space, find extreme values using partial derivatives, and optimize functions using Lagrange multipliers. The course ends with students learning about double integrals over rectangular as well as non-rectangular regions. Prerequisite: Calculus (Intensive) in 11th grade, or departmental approval.
This two-semester course provides an advanced introduction to statistics and data science: gathering information, interpreting patterns, drawing conclusions, and visualizing and presenting data. Students will be expected to use spreadsheets and more advanced statistical packages like SPSS and STATA. It is also an excellent way to practice and extend the skills acquired in Algebra while building the language proficiencies required for higher level math. Students will learn to use a variety of technological tools to manipulate and present data. They will be assessed by examinations and independent research projects.
Students will tackle univariate and bivariate descriptive statistics, probability theory and random variables, with a strong emphasis in high-level critical thinking concepts, including Simpson’s Paradox, Bayes’ Theorem, and Q-Q Plots. Students will become proficient in both Microsoft Excel and Tableau software programs. Armed with this foundation, students will proceed to study college-level statistical testing, including z-tests, t-tests, and p-tests.
This two-semester course offers an advanced, interdisciplinary introduction to data science and statistics, blending philosophy, mathematics, and technology. Students will explore the nature of knowledge and “proof,” learning to construct and critique data-supported arguments. They will master tools like spreadsheets and data visualization software to analyze and present data effectively. Topics include data visualization, descriptive statistics, probability, hypothesis testing, and linear regression.
The project-based curriculum emphasizes real-world applications, with projects such as personal data tracking, evaluating "Greatest of All Time" candidates, and analyzing social issues using systems thinking. Students will develop critical thinking, rigorous analytical skills, and ethical approaches to data. By course end, they will be equipped for advanced studies and practical applications across fields like business and social sciences. Prerequisite: B– or higher in Algebra II & Trigonometry (Intensive), A– or higher in Standard Level Algebra II & Trigonometry with teacher recommendation, or departmental approval.
The modern world is a data-driven world, requiring knowledge in how to gather information, design mathematical models to derive patterns, analyze and summarize data, and present inferences and conclusions from analysis. This is a course in univariate and bivariate descriptive statistics, probability theory, and random variables, with a strong emphasis in critical thinking skills and the use of technology. Students will learn not only the techniques of quantitative research, but also how to organize data in a way that can be tested and that provides meaning. Students will become proficient in Microsoft Excel.
The modern world is a data-driven world, requiring knowledge in how to gather information, design mathematical models to derive patterns, analyze and summarize data, and present inferences and conclusions from analysis. This is a course in univariate and bivariate descriptive statistics, probability theory, and random variables, with a strong emphasis in critical thinking skills and the use of technology. Students will learn not only the techniques of quantitative research, but also how to organize data in a way that can be tested and that provides meaning. Students will become proficient in Microsoft Excel.
This course is a project-based course that builds on the exploration of statistics and data in Intensive Data Science I. Students expand on their technology skills using the Python programming language for simulations, data visualization with matplotlib, and data analysis with pandas and scipy. Students also apply their learning to the principles and real-world applications of machine learning and AI. In the second semester, students will design and complete an independent project on their topic of interest related to statistics, programming, or machine learning.
This course is a project-based course that builds on the exploration of statistics and data in Intensive Data Science I. Students expand on their technology skills using the Python programming language for simulations, data visualization with matplotlib, and data analysis with pandas and scipy. Students also apply their learning to the principles and real-world applications of machine learning and AI. In the second semester, students will design and complete an independent project on their topic of interest related to statistics, programming, or machine learning.
Geometry is an inquiry-based course in the study of Euclidean concepts, along with topics in transformational, coordinate, and solid geometry, in order to build understanding of the relationships of shapes in 2-D and 3-D space. Utilizing problem-solving techniques, inductive and deductive reasoning, logical analysis, and geometric proofs, students examine lines, angles, triangles, polygons, polyhedrons, circles, cylinders, cones, and spheres. Basic trigonometry is used to solve problems in real-world scenarios. The course also weaves Algebra content into every unit in order to maintain Algebra I skills in preparation for Algebra II.
Geometry is an inquiry-based course in the study of Euclidean concepts, along with topics in transformational, coordinate, and solid geometry, in order to build understanding of the relationships of shapes in 2-D and 3-D space. Utilizing problem-solving techniques, inductive and deductive reasoning, logical analysis, and geometric proofs, students examine lines, angles, triangles, polygons, polyhedrons, circles, cylinders, cones, and spheres. Basic trigonometry is used to solve problems in real-world scenarios. The course also weaves Algebra content into every unit in order to maintain Algebra I skills in preparation for Algebra II.
The course begins with an inquiry-based study of Euclidean concepts, along with topics in coordinate and solid geometry, in order to build understanding of the relationships of shapes in 2D and 3D space. Utilizing engineering and physics-based problem-solving techniques, inductive and deductive reasoning, logical analysis, and geometric proof, students explore lines, angles, triangles, circles, polygons, polyhedrons, prisms, pyramids, and spheres. Some relevant Algebra II topics are introduced, including the Unit Circle and radian/degree conversion; solving simultaneous equations, linear functions and the derivation of fundamental trigonometric identities. Problem-solving and analysis using a graphing calculator is a feature of the course. Compass and straight-edge constructions are a prominent technique for proving mathematical theorems and making connections between mathematics, art, and philosophy.
The course begins with an inquiry-based study of Euclidean concepts, along with topics in coordinate and solid geometry, in order to build understanding of the relationships of shapes in 2D and 3D space. Utilizing engineering and physics-based problem-solving techniques, inductive and deductive reasoning, logical analysis, and geometric proof, students explore lines, angles, triangles, circles, polygons, polyhedrons, prisms, pyramids, and spheres. Some relevant Algebra II topics are introduced, including the Unit Circle and radian/degree conversion; solving simultaneous equations, linear functions and the derivation of fundamental trigonometric identities. Problem-solving and analysis using a graphing calculator is a feature of the course. Compass and straight-edge constructions are a prominent technique for proving mathematical theorems and making connections between mathematics, art, and philosophy.
This course extends many of the topics broached in Algebra II & Trigonometry and introduces some new concepts in quantitative analysis. The course begins with an exploration into trigonometry, including utilizing identities and deductive reasoning in trigonometric proof. New topics of study include: recursive relations, sequences and series, probability and combinatorics, the binomial theorem, and rational functions. The course work relies heavily on a problem-solving approach, which requires students to think creatively and make deeper connections to the material. Students will become skilled in the use of graphing calculators, as well as other on-line tools.
This course extends many of the topics broached in Algebra II & Trigonometry and introduces some new concepts in quantitative analysis. The course begins with an exploration into trigonometry, including utilizing identities and deductive reasoning in trigonometric proof. New topics of study include: recursive relations, sequences and series, probability and combinatorics, the binomial theorem, and rational functions. The course work relies heavily on a problem-solving approach, which requires students to think creatively and make deeper connections to the material. Students will become skilled in the use of graphing calculators, as well as other on-line tools.
This course focuses on strengthening the student’s understanding of the concepts involving the different types of functions such as linear, quadratic, rational, as well as square root functions. The students would be solving equations as well as making the connection between the algebraic solution and the different data representations such as graphs and tables. Aside from being able to do problems manually, the students will be taught how to use technology to support their claims as well as see it as a power tool that they can use to do further explorations. The second part of the course allows the student the opportunity to bridge the connection between Algebra and Geometry by using the techniques they have learned to solve equations to deal with geometric problems.
This course focuses on strengthening the students understanding of the concepts involving the different types of functions such as linear, quadratic, rational, as well as square root functions. The students would be solving equations as well as making the connection between the algebraic solution and the different data representations such as graphs and tables. Aside from being able to do problems manually, the students will be taught how to use technology to support their claims as well as see it as a power tool that they can use to do further explorations. The second part of the course allows the student the opportunity to bridge the connection between Algebra and Geometry by using the techniques they have learned to solve equations to deal with geometric problems.
This course revisits and extends all of the topics broached in Intensive Algebra II & Trigonometry, while introducing new concepts in quantitative analysis. The curriculum is designed to give advanced students a comprehensive foundation for further study in Calculus. The course begins with a deep exploration into trigonometry, including utilizing identities and deductive reasoning in trigonometric proof. New topics of study include: advanced probability and combinatorics, the binomial theorem, recursive relations, sequences and series, matrices, and conic sections. The course concludes with an introduction to limits and continuity, both necessary for differential and integral Calculus. The course work relies heavily on a problem-solving approach, which requires students to think creatively and make deeper connections to the material. Students will become skilled in the use of graphing calculators.
This course revisits and extends all of the topics broached in Intensive Algebra II & Trigonometry, while introducing new concepts in quantitative analysis. The curriculum is designed to give advanced students a comprehensive foundation for further study in Calculus. The course begins with a deep exploration into trigonometry, including utilizing identities and deductive reasoning in trigonometric proof. New topics of study include: advanced probability and combinatorics, the binomial theorem, recursive relations, sequences and series, matrices, and conic sections. The course concludes with an introduction to limits and continuity, both necessary for differential and integral Calculus. The course work relies heavily on a problem-solving approach, which requires students to think creatively and make deeper connections to the material. Students will become skilled in the use of graphing calculators.
Grace Church School is a co-educational independent school in downtown Manhattan, New York City providing instruction for over 800 students in junior kindergarten through twelfth grade.
