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Mathematics

“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”
~Stan Gudder, Professor of Mathematics, University of Denver
The mathematics faculty develop the logical, quantitative, and critical thinking skills in each student, all within a traditional course sequence.  All courses aim to utilize technology as an accompaniment to mathematical knowledge. Using a balance between the concrete and the abstract, the department presents mathematics as both a real-world tool and theoretical discipline. Students are asked to demonstrate their knowledge symbolically and verbally through discussions, written work, assessments, presentations, and projects. Here at Bishop we require that students take a math class during all four years of their time here. We are unique from other High Schools in that respect, but the goal is preparedness for college and we want to not only meet but exceed the admission requirements for the UC and CSU systems.

List of 14 items.

  • Algebra AB

    Two Semesters: Grade 9
    Through the study of algebra, the student will develop an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations. Students communicate precisely about quantities, logical relationships, and unknown values through the use of signs, symbols, models, graphs, and mathematical vocabulary. Regular opportunities are provided for students to communicate through oral and written explanations of math concepts. Topics include inequalities in one variable, multiple variable equations, and solving and graphing linear equations.
  • Algebra BC

    Two Semesters: Grade 9-10
    This course prepares students for their continuing study of algebra-based mathematics, especially Algebra II. Topics include quadratic equations and inequalities with multiple variables, systems of linear equations and inequalities, properties of exponents and radicals, and rational expressions and equations.
  • Geometry

    Two Semesters: Grades 9-11
    PREREQUISITE: Successful completion of Algebra I and/or Department Approval
    This is the study of Euclidean geometry, plane and solid, with emphasis on application and practical problems. Concepts include congruent triangles, parallel lines, quadrilaterals, circles, similar figures, the Pythagorean Theorem and special triangles, perimeter, area, volume, regular polygons, and right-triangle trigonometry.   A system of logical thought is developed through basic geometric concepts and their application. 
  • (H) Geometry

    Two Semesters:     Grades 9-10
    PREREQUISITES: Second Semester Grade of 90% or higher in Algebra 1 and/or Department Approval
    An honors section of Geometry is offered, in which students apply the concepts of Geometry at a more advanced level and at a faster pace.
  • Algebra II

    wo Semesters:     Grades 9-12
    PREREQUISITE: Successful completion of Algebra I and Geometry and/or Department Approval  
    This is a second year course in Algebra, emphasizing linear, quadratic, polynomial, exponential, and logarithmic functions as well as complex numbers, solving systems of equations, and matrix algebra. Emphasis is placed on understanding key mathematical ideas and applying them to problem solving. Students will be introduced to graphing calculators and will use them extensively. Trigonometry is not covered in this course, however it is offered as a stand-alone semester course (see course listing for Trigonometry).
  • (H) ALgebra iI

    Two Semesters:    Grades 9-12
    PREREQUISITE:  Second semester grade of 90% or higher in Geometry, or 80% or higher in (H) Geometry and/or Department Approval, which may include a placement exam.
    An honors section of Algebra II is offered, in which students apply the concepts at a more advanced level and at a faster pace.  Additional content includes an introduction to conic sections, polar graphing, the unit circle, and trigonometric functions.  Concepts will be reinforced with extensive use of graphing calculators.
  • Probability and Statistics (PSTAT)

    Fall Semester: Grades 10-12
    PREREQUISITE: Successful completion of Algebra II or (H) Algebra II/Trigonometry and/or Departmental Approval
    This course explores random phenomena using probability including addition and multiplication rules, conditional probability and independence. Simulation of random behavior, discrete random variables and their probability distributions: expected value and standard deviation. Exploration of data through graphical and numerical displays including but not limited to graphical displays of distributions with univariate data (dot plot, stem plot, bar charts, histogram, frequency tables, relative and cumulative frequency), summarizing distributions of univariate data (mean, median, mode, standard deviation, range). Graphical comparisons utilizing back to back stem plots, parallel box plots, within group and between group variation, clusters, gaps, outliers, and shape will be discovered. 
  • Trigonometry

    Spring Semester: Grades 10-12
    PREREQUISITE:  Successful completion of Algebra II and/or Departmental Approval
    The trigonometry course introduces students to the both right triangle and circular trigonometry. Trigonometric functions and their inverses are studied thoroughly. Parametric and polar equations is also as well as complex numbers in both rectangular and polar form are also covered.
  • Precalculus

  • (H) Precalculus

    Two Semesters: Grades 11-12
    PREREQUISITE: Second semester grade of 90% or higher in Algebra 2, or 80% or higher in Trigonometry, and/or Department Approval.
    This course is designed to prepare students for Calculus.  Topics covered will include functions, logarithms, vectors, matrices, polar graphs and equations, sets, logic and trigonometry.  Concepts will be reinforced with extensive use of graphing calculators.
  • Calculus

    Two Semesters:   Grades 9-12
    PREREQUISITE:  Departmental Approval 
    The college preparatory calculus course covers differentiation and integration techniques of basic functions. Applications of calculus are also included.
  • AP Calculus AB

    Two Semesters:   Grades 9-12
    PREREQUISITE:  Departmental Approval and/or Placement Exam.
    This challenging and demanding course is for students who want to take the college equivalent of a semester’s worth of calculus. Topics covered include differentiation and integration techniques, slope fields, and solids of revolution. The AP exam is required for all students enrolled in this course. Applications of calculus are also included. The AP exam is required of all students. 
  • AP Calculus BC

    Two Semesters:   Grades 9-12
    PREREQUISITE:  Departmental Approval and/or Placement Exam.
    This challenging and demanding course is for students who want to take the college equivalent of a year’s worth of calculus. Topics covered include differentiation and integration, parametric, polar and vector functions, differential equations, Euler's method, L'Hôpital's rule, slope fields, hyperbolic functions, applications of integrals, improper integrals, polynomial approximations, series and Taylor series. The AP exam is required for all students enrolled in this course.
  • AP Statistics

    Two Semesters:    Grade 11-12
    PREREQUISITE:  Departmental Approval
    This course is a college-level introduction to statistics that covers the following areas: exploration and interpretation of data (categorical, quantitative, univariate, bivariate), graphs to represent statistics (bar graphs, pie charts, histograms, ogives, scatterplots), normal distributions, sampling methods, experiments and design, simulations, probability, random variables, binomial and geometric distributions, sampling distributions and statistical inference. The AP exam is required for all students enrolled in this course.