Analytic Geometry is a full year high school mathematics course intended for the student who has successfully completed Coordinate Algebra. This course is designed to prepare students for college-level and real-world mathematical reasoning. The concepts covered in this course integrate the topics of Advanced Algebra, Geometry, Trigonometry, and Statistics. Throughout the course, students will explore higher order strategies necessary for analyzing multi-level linear, quadratic and polynomial functions and equations, investigate geometric proofs involving similarity and congruence in triangles and quadrilaterals as well as special angle relationships formed by parallel lines and transversals. Students are exposed to several branches of mathematics and will explore ways in which each one can be used as a mathematical model in understanding the world.
- Similarity, Congruence, Proofs: Part I:Student will identify different types of angles and solve for missing angle measures, as well as use corresponding parts of congruent triangles to prove triangles are congruent using different postulates and theorems.
- Similarity, Congruence, Proofs: Part II:Student will use properties of parallelograms to prove statements involving triangles, rectangles, rhombus, trapezoids, as well as state key properties of similarity, and use facts about similarity to calculate side measures of similar polygons.
- Right Triangle Trigonometry: Student will express trigonometric functions as ratio of a given angle, and use a table of sine, cosine, or tangent values to solve for a missing value, and use the inverse trigonometric functions (sin-1, cos-1, and tan-1) to find unknown angle measurements in right triangles.
- Circles and Volume: Student will identify, define, and calculate measures of the parts of a circle, or measures of different forms created by lines intersecting with a circle, as well as finding the surface area and volume of different conic sections.
- Extending the Number System: Student will add, subtract, and multiply polynomials, and perform long division of polynomials, factor trinomials using the difference of two squares, the difference of two cubes, and perfect square trinomials, and perform operations with complex numbers including using FOIL to multiply, divide, and find multiplicative inverses using complex conjugates.
- Quadratic Functions Part I: Student will solve quadratic equations by factoring, using the quadratic formula, or by completing the square, and find the discriminant of a quadratic equation and use it to determine what kinds of solutions a quadratic equation has.
- Quadratic Functions Part II: Student will write a linear equation in slope-intercept form, identify the slope and y-intercept of a line from the given equation, and graph a line using the slope and y-intercept, and find the common difference of an arithmetic sequence, and extend it to the nth term.
- Modeling Geometry: Student will find properties and measures of shapes using the coordinate plane, and know properties of triangles, use the standard and general form of the circle formula to solve problems in the coordinate plane, and derive and apply the equation, find the directrix, the focus, and graph a parabola.
- Applications of Probability: Student will determine the theoretical probability of a single event, compound events, independent events, and mutually exclusive events, and explain the concept of conditional probability as found in everyday situations.