High Mathematics for College Liberal Arts

Major Topics and Concepts

Segment 1

• Solve and graph mathematical problems that are modeled with linear functions.
• Interpret key features and determine constraints of linear functions in a real-world context.
• Classify exponential functions as representing growth or decay, given a mathematical or real-world context.
• Write exponential functions from a mathematical context given as a graph, a written description, or a table.
• Graph an exponential function, given a table, equation, or written description.
• Determine the constant percent rate of change using the properties of exponents, given an exponential function.
• Write and graph exponential functions, given a real-world context.
• Interpret key features of exponential functions in a real-world context.
• Compare key features of linear and nonlinear functions, each represented algebraically, graphically, in tables, or written descriptions.
• Determine whether a linear, quadratic, or exponential function best models a given real-world situation.
• Compare simple, compound, and continuously compounded interest over time.
• Solve real-world problems involving simple, compound, and continuously compounded interest.
• Explore the relationship between linear growth and simple interest.
• Explore the relationship between exponential growth and compound interest.
• Explore the relationship between exponential growth and continuously compounded interest.
• Solve mathematical problems involving congruence in two-dimensional figures.
• Solve mathematical problems involving similarity in two-dimensional figures.
• Solve real-world problems involving congruence or similarity in two-dimensional figures.
• Determine symmetries of reflection, symmetries of rotation, and symmetries of translation of a geometric figure.
• Solve mathematical problems involving right triangles using trigonometric ratios.
• Solve mathematical problems involving right triangles using the Pythagorean Theorem.
• Solve real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.
• Solve mathematical problems involving the area of two-dimensional figures.
• Solve mathematical problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones, and spheres.
• Solve real-world problems involving the area or surface area of figures.
• Solve mathematical problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones, and spheres.
• Solve real-world problems involving the volume of three-dimensional figures.
• Apply previous knowledge of scale drawings and scale factors to determine properties of figures.
• Determine how dilations affect the area of two-dimensional figures.
• Determine how dilations affect the surface area or volume of three-dimensional figures.

Segment 2

• Determine if given data is numerical or categorical.
• Determine if given data is univariate or bivariate.
• Determine an appropriate visual model to represent a given data set, depending on the type of data given.
• Interpret data given as a visual model and determine quantities from the display.
• Calculate and compare the appropriate measures of center and measures of variability of two data sets based on the effect of outliers.
• Interpret notable features of the shape of the data distributions for given sets of data.
• Fit a linear function to bivariate numerical data and interpret the slope and y-intercept of the model.
• Solve real-world problems using linear models in the context of a given set of data.
• Fit an exponential function to bivariate numerical data and interpret the percent rate of change.
• Solve real-world problems using exponential models in the context of a given set of data.
• Determine the power set of a given set.
• Determine if one set is a subset of another set.
• Determine if two sets are equivalent.
• Prove set relations involving equivalence.
• Explore relationships and patterns between sets using Venn diagrams.
• Apply Venn diagrams to make arguments about sets.
• Describe unions, intersections, or complements as subsets of a sample space using characteristics of the outcomes.
• Determine the complement of a set, the union of two sets, and the intersection of two sets.
• Determine the independence of events by calculating the product of their probabilities.
• Create two-way tables to organize data and determine relative, joint, and marginal frequencies.
• Interpret the joint and marginal relative frequencies as empirical probabilities.
• Apply probabilities to determine whether characteristics in the population are approximately independent.
• Calculate the conditional probability of two events and interpret the result in terms of its context.
• Interpret the independence of two events using conditional probability.
• Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
• Apply the addition rule for probability and interpret the results in terms of the model and its context.
• Apply the general multiplication rule for probability and interpret the result in terms of the context.
• Apply the addition and multiplication rules for counting to solve mathematical and real-world problems, including problems involving probability.
• Perform the set operations, including the difference and product of two sets.
• Prove set relations including DeMorgan’s laws.
• Translate propositional statements into logical arguments using propositional variables and logical connectives.
• Determine truth values of simple and compound statements using truth tables.
• Identify and accurately interpret conditional, biconditional, and quantified statements.
• Find the converse, inverse, and contrapositive of a statement.
• Represent logic operations, such as AND, OR, NOT, NOR, and XOR, using logical symbolism to solve problems.
• Determine whether two propositions are logically equivalent.
• Construct logical arguments using laws of detachment, syllogism, tautology, contradiction, and Euler diagrams.
• Judge the validity of arguments and give counterexamples to disprove statements.
• Given a mathematical situation, calculate the appropriate permutation.
• Given a mathematical situation, calculate the appropriate combination.
• Given a real-world situation, calculate a permutation or combination for the scenario.

Besides engaging students in challenging curriculum, the course guides students to reflect on their learning and evaluate their progress through a variety of assessments. Assessments can be in the form of practice lessons, multiple-choice questions, writing assignments, projects, research papers, oral assessments, and discussions. This course will use the state-approved grading scale. Each course contains a mandatory final exam or culminating project that will be weighted at 20% of the student’s overall grade.***

***Proctored exams can be requested by FLVS at any time and for any reason in an effort to ensure academic integrity. When taking the exam to assess a student’s integrity, the exam must be passed with at least a 59.5% in order to earn credit for the course.  

To achieve success, students are expected to submit work in each course weekly. Students can learn at their own pace; however, “any pace” still means that students must make progress in the course every week. To measure learning, students complete self-checks, practice lessons, multiple choice questions, projects, discussion-based assessments, and discussions. Students are expected to maintain regular contact with teachers; the minimum requirement is monthly. When teachers, students, and parents work together, students are successful.