Liberal Arts Mathematics 1
Liberal Arts Math 1 is designed to help students meet the requirements of Florida's state standards for mathematics. In addition to addressing and assessing the proficiencies specified within the content standards of the traditional pathway, the course provides students opportunities to apply knowledge and skills to complex real world situations through the completion of performance tasks modeling the structure and approach used in sample tasks produced by the Partnership for Assessment of Readiness for College and Careers (PARCC – www.parcconline.org) and the Smarter Balanced Assessment Consortium (SBAC – www.smarterbalanced.org).
Organized in two semesters and designed to accommodate a standard school year, Liberal Arts Math 1 includes comprehensive semester and final exams.
Liberal Arts Math 1 is a full year, high school credit course. Within the Liberal Arts Math 1 course, students will explore basic algebraic fundamentals such as evaluating, creating, solving and graphing linear, quadratic, and polynomial functions. The course also focuses on skills and methods of linear, quadratic, coordinate, and plane geometry. In addition, students will gain solid experience with geometric calculations and coordinate graphing, methods of formal proof, and techniques of construction. Furthermore, students will explore similarity and congruence of polygons, as well as area and volume of three-dimensional solids. Lastly, students will extend their knowledge of statistical data represented in distributions and graphical interpretations.
Upon successfully completing the course, the student should have mastered the following concepts:
- Solve and graph single variable, absolute value, and linear equations and inequalities.
- Evaluate and solve quadratic equations and inequalities using graphing, factoring, quadratic formula, and completing the square.
- Solve linear, quadratic and exponential systems of equations using graphing, substitution or elimination.
- Interpret and apply the relationship between the independent and dependent variable in linear, exponential, and quadratic functions through algebraic modeling and applications.
- Understand and know how to apply the distance, midpoint, and slope formulas as well as the Pythagorean Theorem.
- Form an equation of a line using the slope-intercept, point-slope and standard forms of a line.
- Apply basic fundamental rules of exponents.
- Be able to construct a formula or equation necessary to solve algebraic word problems involving area, perimeter, and linear systems of equations, basic probability and statistical reasoning, distance, and compounding interest.
- Evaluate rational expressions and solve equations with rational expressions.
- Simplify and perform operations with radical expressions such as addition and subtraction, multiplication and division.
- Perform operations with polynomials such as addition and subtraction, multiplication, long division and factoring.
- Understand defined terms, axioms, postulates, and theories.
- Apply rules of formal logic and construct proofs in two-column format.
- Know how to solve for angles given parallels, perpendiculars, and transversals.
- Demonstrate how to solve for sides and angles of triangles, quadrilaterals, and polygons.
- Understand trigonometric ratios and know how to use them to solve for unknown sides and angles in given triangles as well as application word problems.
- Calculate perimeter, area, and volume of figures and solids.
- Make geometric constructions on paper.
- Represent results of motion geometry (translation, rotation, reflection, dilation).
- Represent data with plots on the real number line (dot plots, histograms and box plots).
- Apply statistical concepts to describe the center (median and mean), spread (interquartile range and standard deviation) and shape of a data distribution.