# Academics

## Math

The Mathematics Department at La Salle High School focuses on meeting students where they are in their mathematical abilities and progressing them through a curriculum to reach their full potential. Each student will begin his journey based on where he previously left off or where a placement test indicates he should begin. From this point, students are given the opportunity to develop four years of critical thinking and mathematical skills that focus on deductive reasoning and inductive thinking. This journey could entail courses such as Algebra 1, Geometry, Algebra 2, Pre-Calculus, AB Calculus and AP Statistics, among other courses. At the conclusion of the students' La Salle experience, they should be competent in their abilities to think deductively, reason inductively and be prepared for a college experience.

#### Integrated Math / Algebra 1(CP)

This is a 2-year course that focuses on increasing student mathematical skill sets and addressing the building blocks of Algebra 1. The major topics of this course are computations involving linear, quadratic and exponential functions. Students will use hands-on materials and calculators in solving problems where Algebra concepts are applied. After completing this course sequence, students should take CP or ACP Geometry, determined by teacher recommendation.

Prerequisite: Recommendation 2 Full-year courses – 1 credit each

Key Skills:

- Compute operations using integers and rational numbers with and without a calculator.
- Solve linear equations and inequalities using various methods.
- Identify, write and graph linear functions.
- Solve systems of linear equations and inequalities using various methods.
- Perform operations on polynomials which includes factoring of quadratics.
- Solve and graph quadratic functions using various methods.
- Apply properties of exponents and apply exponential functions.
- Introduction to statistical modeling.

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- Algebra 1 Common Core (Pearson)
- TI-84 Plus calculator or TI-30 calculator or higher recommended

#### Algebra 1(ACP)

This course focuses on the development of Algebra 1 skills and applications. Prior to beginning this course, students are expected to have mastered topics including but not limited to operations on integers, fractions and decimals. Topics of this course include but are not limited to linear, quadratic and exponential functions. Students will be expected to solve problems with and without the use of a calculator. After completing this course, students should take ACP Geometry or CP Geometry, determined by teacher recommendation.

Prerequisite: Recommendation Full-year course – 1 credit

Key Skills:

- Solve linear equations and inequalities using various methods.
- Identify, write and graph linear functions.
- Solve systems of linear equations and inequalities using various methods.
- Perform operations on polynomials which includes factoring of quadratics.
- Solve and graph quadratic functions using various methods.
- Apply properties of exponents and applications of exponential functions.
- Introduction to statistical modeling.

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- Algebra 1 (McGraw Hill)
- TI-84 Plus calculator or TI-30 calculator or higher recommended

#### Algebra 1(HP)

This is a rigorous course designed for freshmen who have had some exposure to algebra curriculum in the 8th grade. This honors course will focus on deep dive of Algebra 1 skills and applications. Prior to beginning this course, students are expected to have mastered topics including but not limited to operations on integers, fractions and decimals. Topics of this course include but are not limited to linear, quadratic and exponential functions. Students will be expected to solve problems with and without the use of a calculator. After completing this course, students should take HP Geometry, determined by teacher recommendation.

Prerequisite: Recommendation Full-year course – 1 credit

Key Skills:

- Solve linear equations and inequalities using various methods.
- Identify, write and graph linear functions.
- Solve systems of linear equations and inequalities using various methods.
- Perform operations on polynomials which includes factoring of quadratics.
- Solve and graph quadratic functions using various methods.
- Apply properties of exponents and applications of exponential functions.
- Introduction to statistical modeling.

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- Algebra 1 (McGraw Hill)
- TI-84 Plus calculator or TI-30 calculator or higher recommended

#### Geometry (CP)

This course focuses on the development of inductive and deductive reasoning skills with an emphasis on application of geometric topics. This course will focus on the relationship between geometric topics and algebraic techniques with minimal time spent on direct proofs. Topics include but are not limited to lines, angles, triangles, quadrilaterals, polygons, congruence, similarity, right triangle trigonometry, transformations, probability and circles. After completion of this course, students should take CP Algebra 2.

Prerequisite: Algebra 1 Full-year course – 1 credit

Key Skills:

- Define and determine the building blocks of geometry including points, lines and planes, measuring segments and angles, angle pairs, and midpoint and distance in the coordinate plane.
- Develop reasoning skills including inductive and deductive reasoning, conditionals,

bi-conditionals, and proving angles congruent.

- Develop skills related to parallel and perpendicular lines including properties of parallel lines, parallel lines and triangles, equations of lines, and slopes of parallel and perpendicular lines.
- Develop and expand on skills related to angles and triangles including proving triangle congruence.
- Define and compute measurements of the relationships that occur within triangles, focusing on triangle inequalities.
- Develop skills necessary to prove polygons and quadrilaterals.
- Develop skills for solving proportions created in similar figures.
- Develop skills for working with right triangles including the Pythagorean Theorem, special right triangles and right triangle trigonometry.
- Understand rigid transformations and dilations.
- Develop an understanding of angles, lines and angles within a circle along with writing the equation of a circle in a coordinate plane.
- Explore and perform calculations of probability.

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- Geometry Common Core (Pearson)
- TI-84 Plus calculator or TI-30 calculator or higher recommended

#### Geometry (ACP)

This course focuses on the development of inductive and deductive reasoning skills with an emphasis on application of geometric topics. This course is more rigorous than CP Geometry and will include some formal direct proofs, but mostly focus on the relations between geometric topics and algebraic techniques. Topics include but are not limited to lines, angles, triangles, quadrilaterals, polygons, congruence, similarity, right triangle trigonometry, transformations, probability and circles. After completion of this course, students should take ACP Algebra 2 or ACP Pre-Calculus, determined by teacher recommendation.

Prerequisite: Algebra I Full-year course – 1 credit

Key Skills:

- Define and determine the building blocks of geometry including points, lines and planes, measuring segments and angles, angle pairs, and midpoint and distance in the coordinate plane.
- Develop reasoning skills including inductive and deductive reasoning, conditionals,
- bi-conditionals, and proving angles congruent.
- Develop skills related to parallel and perpendicular lines including properties of parallel lines, parallel lines and triangles, equations of lines, and slopes of parallel and perpendicular lines.
- Develop and expand on skills related to angles and triangles including proving triangle congruence.
- Define and compute measurements of the relationships that occur within triangles, including mid-segments, bisectors, medians and altitudes along with triangle inequalities.
- Develop skills necessary to prove polygons and quadrilaterals along with performing computations in coordinate geometry.
- Develop skills for solving proportions created in similar figures.
- Develop skills for working with right triangles including the Pythagorean Theorem, special right triangles, right triangle trigonometry, the Law of Sines, and the Law of Cosines.
- Understand rigid transformations, dilations and similarity transformations.
- Develop an understanding of angles, lines and angles within a circle along with writing the equation of a circle in a coordinate plane.
- Explore and perform calculations of probability.

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- Geometry Common Core (Pearson)
- TI-84 Plus calculator or TI-30 calculator or higher recommended

#### Geometry (HP)

This is a rigorous course designed for freshmen who have had an accelerated Algebra 1

curriculum in the 8th grade. This honors course will focus on writing formal geometric proofs

using deductive and inductive reasoning. Instruction will be fast-paced with high expectations of

students working independently both in and out of the classroom. Topics from Euclidean

Geometry are included but not limited to lines, angles, triangles, quadrilaterals, polygons, congruence, similarity, right triangle trigonometry, transformations,probability and circles. After completion of this course, students should takeHonors Algebra 2 or ACP Algebra 2, determined by teacher recommendation.

Prerequisite: Recommendation

Key Skills:

- Define and determine the building blocks of geometry including points, lines and planes, measuring segments and angles, angle pairs, and midpoint and distance in the coordinate plane.
- Develop reasoning skills including inductive and deductive reasoning, conditionals, bi-conditionals, and proving angles congruent.
- Develop skills related to parallel and perpendicular lines including properties of parallel lines, parallel lines and triangles, equations of lines, and slopes of parallel and perpendicular lines.
- Develop and expand on skills related to angles and triangles including proving triangle congruence.
- Define and compute measurements of the relationships that occur within triangles, including mid-segments, bisectors, medians and altitudes along with triangle inequalities.
- Develop skills necessary to prove polygons and quadrilaterals along with performing computations in coordinate geometry.
- Develop skills for solving proportions created in similar figures.
- Develop skills for working with right triangles including the Pythagorean Theorem, special right triangles, right triangle trigonometry, the Law of Sines, and the Law of Cosines.
- Understand rigid transformations, dilations and similarity transformations.
- Develop an understanding of angles, lines and angles within a circle along with writing the equation of a circle in the coordinate plane.
- Explore and perform calculations of probability.

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- Geometry Common Core (Pearson)
- TI-84 Plus or similar calculator required

#### Algebra II (CP)

This course extends Algebra 1 topics using more complex Algebra skills. Topics include but are not limited to linear functions, quadratic functions, polynomial functions, radical functions, exponential functions and logarithms, as well as rational functions. After completion of this course, students should take CP College Algebra.

Prerequisite: Geometry Full-year course – 1 credit

Key Skills:

- Solve and write linear equations and inequalities.
- Solve and graph absolute value functions.
- Solve systems of equations and inequalities.
- Solve and graph quadratic functions using various methods.
- Solve polynomial functions algebraically.
- Simplify and solve radical equations.
- Perform operations on functions.
- Solve exponential and logarithmic equations.
- Simplify rational expressions and solve rational equations.

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- Algebra 2 Common Core (Pearson)
- TI-84 Plus or similar calculator required

#### Algebra II (ACP)

This course extends Algebra 1 topics using more complex Algebra skills. This course is more rigorous than CP Algebra 2 and topics include but are not limited to linear functions, quadratic functions, matrices, polynomial functions, radical functions, exponential functions and logarithms, rational functions, and trigonometric functions. After completion of this course, students should take ACP Pre-Calculus or CP College Algebra, determined by teacher recommendation.

Prerequisite: Geometry Full-year course – 1 credit

Key Skills:

- Solve and write linear equations and inequalities.
- Solve and graph absolute value functions.
- Solve systems of equations and inequalities, including 3-variable systems.
- Perform operations with matrices and use matrices to solve systems.
- Solve and graph quadratic functions using various methods, including complex numbers and quadratic systems.
- Solve polynomial functions algebraically and graphically, including the fundamental theorem of algebra.
- Simplify, graph, and solve radical equations.
- Perform function operations, including inverses.
- Solve and graph exponential and logarithmic equations, including natural logarithms.
- Simplify rational expressions and solve rational equations.
- Perform calculations involving arithmetic sequences and series as well as geometric sequences and series.

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- Algebra 2 Common Core (Pearson)
- TI-84 Plus or similar calculator required

#### Algebra II (HP)

This is a rigorous course designed to prepare students for Honors Pre-Calculus and AP Statistics. Instruction will be fast paced with high expectations. Students will be expected to work independently both in and out of the classroom. Topics include but are not limited to linear functions, quadratic functions, matrices, polynomial functions, radical functions, exponential functions and logarithms, rational functions, sequences and series, probability and statistics, periodic functions, and trigonometry. After completion of this course, students should take either ACP Pre-Calculus or Honors Pre-Calculus and AP Statistics, determined by teacher recommendation.

Prerequisite: Honors Geometry or Recommendation Full-year course – 1 credit

Key Skills:

- Solve and write linear equations and inequalities.
- Solve and graph absolute value functions.
- Solve systems of equations and inequalities, including 3-variable systems.
- Perform operations with matrices including use matrices to solve systems.
- Solve and graph quadratic functions using various methods, including complex numbers and quadratic systems.
- Solve polynomial functions algebraically and graphically, including the fundamental theorem of algebra.
- Simplify, graph, and solve radical equations.
- Perform function operations, including inverses.
- Solve and graph exponential and logarithmic equations, including natural logarithms.
- Simplify rational expressions and solve rational equations.
- Perform calculations involving arithmetic sequences and series as well as geometric sequences and series.
- Introduce the unit circle and interpret the sine, cosine and tangent functions.
- Perform calculations with probability, including permutations, combinations, conditionals and standard deviation.

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- Algebra 2 Common Core (Pearson)
- TI-84 Plus recommended

#### College Algebra with Trig (CP)

This course is an extension of the Algebra 2 curriculum. The topics that were introduced in

Algebra 2 will be built upon and applied to financial, real-word problems. Topics will include how to write checks, balance checking/saving accounts and transaction records. Topics will also cover mortgages, auto loans and installment loans. This math course will help connect Algebra to real world situations. By building on prior math concepts from other courses, this class will review Algebra mechanics and strengthen problem solving skills. From money management to advanced math topics, the course will cover fundamentals and beyond. These topics will be extended, with an emphasis on financial situations for the real world.

Prerequisite: Algebra II or CP Geometry Full-year course – 1 credit

Key Skills:

- Define, identify, and apply trigonometric equations and applications.
- Solve linear equations and inequalities using various methods to calculate salaries and taxes as they deal with pay.
- Identify, write and graph linear and exponential functions to show different pay schedules.
- Rearrange formulas to highlight a quantity of interest, using methods to solve equations for simple and compound interest, present value and periodic deposit investments.
- Calculate equations that include finance charges, monthly payments, average daily balances and credit card entries.
- Understand basic vocabulary of credit terms.
- Choose and interpret basic vocabulary of stocks and the stock market.
- Create and explain graphs of stock and trade volumes from ticker information
- Perform operations on rational expressions to calculate items like monthly rent and leasing, moving expenses and mortgages.
- Define, calculate, and graph different equations of taxes: property, sales, income
- Create and perform calculations within an excel sheet for life expenses and starting a career.

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- Financial Algebra: Advanced Algebra with Financial Applications (Cengage, 2018)
- TI-84 Plus calculator or TI-30 calculator or higher recommended

#### Pre-Calculus (ACP)

This course is an extension of the Algebra II curriculum. The topics that were first introduced in Algebra 2 will be built upon, extended, and applied to more complex and in-depth problems. The topics covered include but are not limited to linear, quadratic, and polynomial functions, complex numbers, exponential and logarithmic functions, rational functions, systems of equations, and unit circle trigonometry. There will be an emphasis on applying topics to real world situations. After completion of this course, students should take ACP Calculus Foundations or ACP Statistics determined by teacher recommendation.

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Prerequisite: Algebra II Full-year course – 1 credit

Key Skills:

- Solve linear equations and inequalities and apply using various methods.
- Identify, write and graph linear functions and apply linear functions.
- Solve systems of linear equations and inequalities and apply using various methods.
- Perform operations on matrices and solve matrix equations and apply.
- Solve and graph quadratic and polynomial functions and apply using various methods.
- Apply properties of exponents and applications of exponential and logarithmic functions and their graphs.
- Graph rational functions.
- Define, identify, and apply arithmetic and geometric sequences and series.
- Solve probability problems involving combinations and permutations.
- Define, identify, and apply trigonometric equations and applications.
- Graph trigonometric functions.
- Solve equations and applications of conic sections.

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- Larson Pre-Calculus (Houghton Mifflin)
- TI-84 Plus or similar calculator required

#### Pre-Calculus (HP)

This is a rigorous course designed to prepare students for AP Calculus and/or AP Statistics. Instruction will be fast-paced with high expectations. Students will be expected to work independently both in and out of the classroom. Topics include but are not limited to linear, quadratic, and polynomial functions, exponential and logarithmic functions, rational functions, periodic functions and trigonometry, conics, and vectors. The class has an emphasis on real world applications and extended thinking. After completion of this course, students should take AP Calculus, AP Statistics, or ACP Calculus Foundations, determined by teacher recommendation.

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Prerequisite: Algebra 2 or Recommendation Full-year course – 1 credit

Key Skills:

- Solve linear equations and inequalities and applications using various methods.
- Identify, write and graph linear functions and application of linear functions.
- Solve systems of linear and nonlinear equations, inequalities, and apply using various methods.
- Solve and graph quadratic and polynomial functions and apply using various methods.
- Apply properties of exponents and apply to exponential and logarithmic functions and their graphs.
- Graph rational functions and solve rational equations.
- Define, identify, and apply arithmetic and geometric sequences and series.
- Solve probability problems involving combinations and permutations.
- Define, identify, and apply trigonometric equations and applications.
- Analytic Trigonometry.
- Graph trigonometric functions.
- Solve equations and applications of conic sections.
- Perform the dot product and operations on vectors.
- Graph polar functions and solve polar equations.
- Introduce limits and the derivative.

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- Larson Pre-Calculus (Houghton Mifflin)
- TI-84 Plus or similar calculator required

#### Statistics (ACP)

This course is a first look into the world of Statistics. The topics in this course include but are not limited to probability, frequency distributions, data descriptions, confidence intervals, hypothesis testing, correlation and regression, and nonparametric statistics. Emphasis will be placed on applications requiring a conceptual understanding of these topics.

Prerequisite: College Algebra or beyond Full-year course – 1 credit

Key Skills:

- Identify and classify different types of data.
- Organize, represent, and graph data using different types of distribution.
- Distinguish between the different types of central tendencies.
- Describe different data sets accurately using different descriptors and tests.
- Use different hypothesis testing on data.
- Computation of correlation and regression.
- Apply knowledge of these topics to develop, implement, and interpret results of surveys.
- Research, organize, and present different data analysis techniques.

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- Elementary Statistics (McGraw Hill)
- TI-84 Plus or similar calculator required

#### Statistics (AP)

This course is the equivalent of an introductory college-level course. Instruction will be fast- paced with high expectations. Students will be expected to work independently both in and out of the classroom. Topics in this course include but are not limited to probability, frequency distributions, data descriptions, confidence intervals, hypothesis testing, correlation and regression, and nonparametric statistics. Students will collect, analyze, graph, and interpret real-world data. Examples from real research will be reviewed and evaluated by students to learn the process of designing and analyzing research studies. This course will follow the College Board learning objectives and students will be required to take the AP College Board test.

Prerequisite: Algebra 2 with recommendation Full-year course – 1 credit

Key Skills:

- Describe categorical and quantitative data sets with both numeric and visual representations.
- Describe a datum’s location within a dataset.
- Describe relationships between variables.
- Design and analyze studies and experiments.
- Determine probabilities and utilize probability rules.
- Determine probabilities based on combining two random variables based on their distributions.
- Determine probabilities based on random variable distributions in both binomial and geometric settings.
- Determine a mean and proportion of a sample based on a population distribution.
- Estimate a mean or proportion of a population based on a random sample.
- Evaluate a mean or proportion of a population based on a random sample.
- Compare populations based on random samples taken from each population.
- Use Chi-Squared Goodness of Fit tests to analyze categorical data of a population based on a random sample.
- Perform regression analyses to formulate predictive equations.

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- The Practice of Statistics - 4th Edition (Starnes, Yates, and Moore)
- TI-84 Plus or similar calculator required

#### Calculus Foundations (ACP)

This course is an introduction to the principle ideas of differential and integral calculus along with an integrated review of functions. Topics covered include but are not limited to limits, differentiation, and integration of algebraic, exponential, and logarithmic functions. Emphasis will be placed on the use of calculus in solving real-world problems, including examples from business, economics, and the social and natural sciences. Juniors who take this course are recommended to take ACP or AP Statistics in their senior year. This is a course that will prepare students for Calculus at the college level.

Prerequisite: Pre-Calculus Full-year course – 1 credit

Key Skills:

- Determine derivatives for functions including algebraic, exponentials, and logarithmic functions.
- Solve application problems using derivatives, including but not limited to extreme values and marginals.
- Use basic integration techniques to solve simple differential equations.
- Integrate selected functions and solve business and economic applications using these results.
- Apply the Fundamental Theorem of Calculus to evaluate definite integrals.
- Demonstrate the connection between area and the definite integral.

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- Larson Calculus An Applied Approach (Houghton Mifflin)
- TI-84 Plus or similar calculator required

#### Calculus (AP)

Advanced Placement Calculus AB is designed to develop the topics of differential and integral calculus. Instruction will be fast-paced with high expectations. Students will be expected to work independently both in and out of the classroom. Emphasis is placed on limits, continuity, derivatives and integrals of algebraic and transcendental functions of one variable. Upon completion, students should be able to select and use appropriate models and techniques for finding solutions to derivative-related problems with and without technology. This course is equivalent to a Calculus I college-level course. This course will follow the College Board learning objectives and students will be required to take the AP College Board test.

Prerequisite: Pre-Calculus with recommendation Full-year course – 1 credit

Key Skills:

- Apply the definition of limit to evaluate limits by multiple methods.
- Use derivatives to analyze and graph algebraic and transcendental functions.
- Select and apply appropriate models and differentiation techniques to solve problems involving algebraic and transcendental functions; these problems will include but are not limited to applications involving optimization and related rates.
- Apply the definition of indefinite integral to solve basic differential equations.
- Apply the properties of definite integral to evaluate basic integrals.
- Use the fundamental theorem of calculus to evaluate integrals involving algebraic and transcendental functions.

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- Larson Calculus for AP (Houghton Mifflin)

- TI-84 Plus or similar calculator required