Network of Sacred Heart Schools

Curriculum Detail

SHP Courses by Department

To learn more about each department's requirements and philosophy, please visit the SHP Departments page.

Math

  • Algebra 1

    Algebra 1 is designed to build a strong foundation in algebraic thinking and problem-solving skills. Students will explore linear, quadratic, and absolute value functions through multiple representations, developing fluency in solving equations and inequalities. The course incorporates the study of function notation, systems of equations, and polynomial operations (e.g. factoring and distributing). Lessons from our CPM curriculum involve collaborative problem-solving, critical thinking, and the application of mathematical practices. By the end of the course, students will be prepared to analyze and model real-world situations using a variety of algebraic concepts and techniques.

  • Geometry

    This course is designed to deepen and extend students’ existing understanding of geometric concepts, both preparing them for subsequent course work in mathematics and allowing them to be able to recognize geometric principles in the world around them. Students will establish triangle congruence criteria using rigid motions and build a formal understanding of similarity based on dilations and proportional reasoning. Students will also develop the concepts of formal proof, explore the properties of two- and three-dimensional objects, work within the rectangular coordinate system to verify geometric relationships and prove basic theorems about circles. Throughout the course there is a committed and consistent effort to review and maintain algebraic skills.  An emphasis is placed on student discovery and hands-on or digital exploration before formalizing concepts.

    Prerequisite:    
    Freshmen: Satisfactory SHP placement exam results;
    Sophomores: C- or higher in Algebra 1 (spring semester)

     

  • Geometry Jump

    This course covers the same material as a full-year high school Geometry course in a very intensive fashion. The main purpose is to develop understanding of concepts in plane, solid and coordinate geometry, the skills to apply these concepts to solve problems, and the ability to construct formal arguments and proofs. Topics include angles, parallel lines, triangles and other types of polygons, congruence, similarity, circles, various types of solid figures, area, volume, coordinate geometry, and basic right triangle trigonometry. Throughout the course there is a committed and consistent effort to review and use algebraic skills in the context of solving geometrical problems. This is a UC approved course.

    No more than two (2) excused or unexcused absences are allowed; SHP will call parents if attendance becomes an issue and a third absence will result in withdrawal from the course.

    Prerequisite:
    For rising sophomores at SHP only: A- or higher in both semesters of Algebra 1 AND departmental approval

  • Geometry Honors

    This course is a more rigorous, fast-paced Geometry course designed for students with demonstrably strong Algebra 1 skills and inquisitive mathematical minds. Students are introduced to the topics of plane, solid, and analytic geometry while continuing to use and extend some of the concepts learned in algebra. Students learn about angles, parallel lines, triangles and other types of polygons, congruence, similarity, transformations, circles, various types of solid figures, area and volume, coordinate geometry, and right triangle trigonometry. More emphasis is placed on constructing deductive justification for theorems and other assertions than in the regular Geometry course. The TI-84 graphing calculator is used extensively to accompany understanding algebraic and geometric contents from graphing and finding intercepts to transformation and simple programming.

    Prerequisite:
    Freshmen:  Satisfactory SHP placement exam results;

    Enrollment in the second semester of Geometry Honors requires completion of the first semester of this course with a grade of B- or higher

  • Algebra 2

    This course is designed to extend and deepen students’ understanding of various previously learned algebraic concepts as well as introduce them to new algebra topics. Students study relations, functions and their graphs, systems of equations and inequalities, quadratic and other polynomial functions, powers and roots, exponential and logarithmic functions, complex numbers, rational functions, matrices,  unit circles, trigonometric functions, and inverse relations. Extensive use of the graphing calculator allows the emphasis to be on problem-solving and exploration and analysis of real-world applications.
     
    Prerequisite:
    C- or higher in Geometry or Geometry Honors (spring semester) OR
    A- or higher in both semesters of Algebra 1 at SHP  AND
    C- or higher in Geometry Jump or equivalent over the summer

  • Applications for Advanced Algebra

    Applications for Advanced Algebra is a year-long project-based class that will be an alternative course to Statistics and Precalculus following Algebra 2. This course emphasizes hands-on data collection, creating mathematical expressions/equations, and identifying key features based on data and the question at hand. Tools such as data collection, presentation, and analysis are at the heart of every unit. Each unit will parallel a concept rooted in Geometry, Statistics, Algebra 2, or Precalculus. Students will be tasked to collect data from their own life experiences and showcase relationships using creative assessments. Assessments will include project presentation, graphical representations, and analysis of collected data using spreadsheet functions, computational statistical analyses, and other online tools. 
     
    Prerequisite:
    C- or higher in Algebra 2 (spring semester)

  • Algebra 2 Trig Honors

    This course is a more rigorous, fast-paced version of Algebra 2 that also includes a solid introduction to analytic trigonometry. The topics covered in this course include those in the regular Algebra 2 course, but at a more challenging level. Students study relations, functions and their graphs, systems of equations and inequalities, quadratic and other polynomial functions, direct and inverse variation, powers and roots, exponential and logarithmic functions, complex numbers, rational functions, and sequences and series. In addition, other topics covered include inverse relations, matrices, linear programming, and an extensive study of trigonometry and its applications. Extensive use of the graphing calculator allows the emphasis to be on problem-solving and exploration and analysis of real-world applications.
     
    Prerequisite:
    Freshmen: Satisfactory SHP placement exam results;
    Sophomores: B- or higher in Geometry Honors (spring semester) OR
    A in Geometry (spring semester) AND
    Departmental approval based on unit tests, final exam, and honors placement test

    Enrollment in the second semester of Algebra 2 Trig Honors requires completion of the first semester of this course with a grade of B- or higher

  • Precalculus

     

    This course is designed for students who wish to take a math course that continues to solidify and expand upon their understanding of various mathematical concepts encountered in Geometry and Algebra 2. The primary focus is the study of functions, their properties, and their graphs. Functions covered include polynomial functions, absolute value, power, rational, exponential, logarithmic, and trigonometric functions. Other topics include conic sections, sequences and series, analytical trigonometry, and trig identities.  Mathematical notation, precision, and applications are emphasized. 

    Prerequisite:
    C or higher in Algebra 2 (spring semester) AND
    70 or higher on the spring semester final exam OR 
    C- or higher in Algebra 2 Trig Honors (spring semester) OR
    B- or higher in  Applications for Advanced Algebra (spring semester) AND
    Departmental approval based on placement test     OR
    C+ or higher in Statistics (spring semester) AND departmental approval based on placement test

  • Precalculus AB Honors

     

    This course is designed to prepare students for college-level calculus, as well as introduce them to other interesting topics in mathematics. The primary focus is an in-depth study of functions, their properties, and graphs. The types of functions studied are polynomial, power, rational, exponential, logistic, logarithmic, piecewise-defined, circular, trigonometric, inverse trigonometric, and functions involving absolute value. Other topics include conic sections, sequences and series, analytical trigonometry, and trig identities.  Extensive use of the graphing calculator allows the emphasis to be on a variety of problem-solving approaches (numerical, graphical, and algebraic) and through mathematical modeling while building a deeper understanding of algebraic techniques. 

    Prerequisite:
    A- or higher in both semesters of Algebra 2 AND 
    Departmental approval based on unit tests, final exam, and honors placement test     OR
    C- or higher in Algebra 2 Trig Honors (spring semester)

    Enrollment in the second semester of Precalculus AB Honors requires completion of the first semester of this course with a grade of B- or higher
     

  • Precalculus BC Honors

    This course is designed for students with exceptional math ability who plan to enroll in AP Calculus BC the following year. The first 70% of this course is a more rigorous, fast-paced version of Precalculus AB Honors, and includes and extends many of the topics in that course. The primary focus of the precalculus portion of the course is an in-depth study of functions, their properties, and graphs. The types of functions studied are polynomial, power, rational, exponential, logistic, logarithmic, piecewise-defined, circular, trigonometric, inverse trigonometric, and functions involving absolute value. A significant amount of time is spent on a variety of topics in trigonometry. In addition, students will encounter the following topics: vectors; parametric equations; polar coordinates; complex numbers; and sequences and series. Students are expected to study these topics in greater depth and investigate problems that require more complex thinking than in the other precalculus courses. Extensive use of the graphing calculator allows the emphasis to be on a variety of problem-solving approaches (numerical, graphical, and algebraic) and on the exploration of real-world data and situations through mathematical modeling while building a deeper understanding of algebraic techniques. The last 30% of this course is devoted to covering the following calculus topics: limits; continuity; conceptual and formal definition of the derivative; graphing derivatives; derivatives of algebraic and trigonometric functions; and some applications of the derivative.

    Prerequisite    :
    B+ or higher in Algebra 2 Trig Honors (spring semester) 

    Enrollment in the second semester of Precalculus BC Honors requires completion of the first semester of this course with a grade of B- or higher

  • Calculus

    This course is designed for students who wish to study the concepts of calculus and gain experience with its methods and applications. This course covers many topics in differential and integral calculus of elementary functions. It covers at least as much material as a standard first semester of college calculus. Topics include a review of basic concepts of analytic geometry and functions; limits and continuity; derivatives of algebraic, trigonometric, exponential, and logarithmic functions; applications of the derivative; The Fundamental Theorem of Calculus; integration; and applications of the definite integral. This course is not intended to prepare the student for the AP Calculus AB Exam in May, since some AP Calculus AB topics will not be covered.
     
    Prerequisite:
    B or higher in Precalculus (spring semester) with a grade of B or higher OR
    C or higher in Precalculus AB Honors (spring semester) OR
    C- or higher in Precalculus BC Honors (spring semester)

  • Statistics

    This course provides an introduction to statistical ideas and statistical reasoning.  It is designed for the student who wants to learn about statistics, but who does not seek preparation for the AP Statistics exam.  This course includes, but may not be limited to the following topics: descriptive statistics, creating and interpreting graphical displays, linear regression, basic probability, the normal distribution, the binomial distribution, sampling distributions, basic statistical inference, significance tests, confidence intervals, and Chi-square procedures. In addition, strong emphasis is placed on sampling and experimental design. These ideas are explored through projects and activities.

    Prerequisite:    
    C- or higher in Algebra 2 or Algebra 2 Trig Honors (spring semester)
     

  • AP Calculus AB

    This advanced math course covers many topics in differential and integral calculus of elementary functions and is designed to prepare the student for the AP Calculus AB Exam. It covers at least as much material as a standard first semester of college calculus. Topics include a review of basic concepts of analytic geometry and functions; limits and continuity; derivatives of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions; applications of the derivative; The Fundamental Theorem of Calculus; integration; and applications of the definite integral.

    Prerequisite    :
    B+ or higher in Precalculus AB Honors (spring semester)  OR
    C+ or higher in Precalculus BC Honors (spring semester) AND
    Completion of the AP Calculus AB summer assignment by the deadline indicated in the summer assignment

  • AP Calculus BC

    This is an advanced math course for exceptional math students. This course gives a thorough examination of the calculus of functions of a single variable and is designed to prepare the student for the AP Calculus BC Exam. It covers at least as much material as a standard first year of college calculus. Students taking this course will have already covered a significant amount of differential calculus in Precalculus BC Honors. Thus, the first semester is devoted primarily to completing the coverage of all of the AP Calculus AB topics in differential and integral calculus of elementary functions, although a few topics not included in the AP Calculus AB curriculum such as improper integrals will be covered. The second semester covers topics including but not limited to infinite sequences and series, parametric,  polar, and vector calculus along with AP exam preparations.
     
    Prerequisite:
    B+ or higher in Precalculus BC Honors (spring semester) OR
    C+ or higher in AP Calculus AB (spring semester) AND
    Completion of the AP Calculus BC summer assignment by the deadline indicated in the summer assignment 

  • AP Statistics

    This course is for the motivated math student who wishes to learn about the world of statistics and take the AP Statistics exam. It is a college-level course designed to educate students about producing data through samples and experiments, organizing the data, and using elements of probability to make inferences from the data. Topics include: designing experiments; performing surveys; descriptive statistics; visual representations of data like histograms and box plots; skewness; measures of central tendency and spread; elementary probability; conditional probability; Central Limit Theorem; normal distribution; binomial distribution; sampling distributions, statistical inference: significance tests; one/two sample tests of hypotheses; t-distribution; confidence intervals; Chi-square procedures; and linear regression.
     
    Prerequisite:    
    B or higher in both semesters of Precalculus OR
    C- or higher in Algebra 2 Trig Honors, Precalculus AB Honors, Precalculus BC Honors (spring semester) OR
    For rising seniors only: A- or higher in Algebra 2 AND
    Departmental Approval

  • Advanced Topics in Math Honors

    Advanced Topics in Math, Honors (fall semester)
    This semester-long Honors course is designed for students who have a strong foundation in mathematics and who wish to deepen and expand their knowledge of the discipline. It includes the following main areas of study:
    • Basic set theory and logic
    • Number theory (divisibility, prime numbers)
    • Introductory abstract algebra (group theory)
    • Matrix and linear algebra
    The order of the topics has been carefully chosen to form a coherent sequence, which should provide an excellent foundation for college-level mathematics courses. A primary goal of the course is to develop skills in mathematical abstraction, conjecture, and problem-solving. A heavy emphasis is on constructing formal written proofs.
     
    Prerequisite: 
    B+ or higher in AP Calculus AB (spring semester) OR
    C- or higher in AP Calculus BC (spring semester) OR
    For rising seniors only: A- or higher in Precalculus BC Honors 

  • Multivariable Calculus Honors

    Multivariable Calculus (spring semester)
    This semester-long Honors course is designed for students who have a strong foundation in mathematics and who wish to deepen and expand their knowledge of calculus involving multiple variables. It includes the following main areas of study:
    • Quadric surfaces
    • Vectors
    • Calculus of vector-valued functions
    • Differentiation of multivariable functions
    • Applications
    A primary goal of the course is to develop skills in mathematical abstraction, conjecture, and problem-solving. A heavy emphasis is on constructing formal written proofs.
     
    Prerequisite: 
    B+ or higher in AP Calculus AB (spring semester) OR
    C- or higher in AP Calculus BC (spring semester) OR
    For rising seniors only: A- or higher in Precalculus BC Honors AND 
    taking AP Calculus AB or BC concurrently. 
Where Scholarship and Values Matter
Founded by the Society of the Sacred Heart, SHS is a Catholic, independent, co-ed day school for students in preschool through grade 12