Integrated Math II (3014) WV is a full year high school mathematics course intended for the student who has successfully completed Integrated Math I (3012) WV. 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.
CURRICULUM CONTENT AND SKILLS FOCUS:
UNIT 1: 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.
UNIT 2: SIMILARITY, CONGRUENCE, PROOFS: PART II
Students will use properties of parallelograms to prove statements involving triangles, rectangles, rhombuses, trapezoids, as well as state key properties of similarity and use facts about similarity to calculate side measures of similar polygons.
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY
Students will express trigonometric functions as ratios of a given angle, 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.
UNIT 4: CIRCLES AND VOLUME
Students 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.
UNIT 5: EXTENDING THE NUMBER SYSTEM
Students will add, subtract, and multiply polynomials; 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.
UNIT 7: QUADRATIC FUNCTIONS PART I
Students will solve quadratic equations by factoring, using the quadratic formula, or by completing the square, and they will find the discriminant of a quadratic equation and use it to determine what kinds of solutions a quadratic equation has.
UNIT 8: QUADRATIC FUNCTIONS PART II
Students 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. They will find the common difference of an arithmetic sequence and extend it to the nth term.
UNIT 9: MODELING GEOMETRY
Students will find properties and measures of shapes using the coordinate plane and know properties of triangles. They will 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.
UNIT 10: APPLICATIONS OF PROBABILITY
Students will determine the theoretical probability of a single event, compound events, independent events, and mutually exclusive events. They will explain the concept of conditional probability as found in everyday situations.