Mathematics
Meet our math teachers, Mrs. Hughes, Mr. Moye, Miss Gabhart, and Mrs. Fourman!
Our mathematics students can choose between two tracks: Traditional and Advanced. The Traditional Track starts in seventh grade with Basic Math 7 and concludes in the senior year with Precalculus. The Advanced Track begins with Pre-Algebra in the seventh grade and ends with Advanced Placement Calculus in the senior year.
Please note that Algebra I through Precalculus can be taken as honors classes.
Basic Math 7
Maintaining skills in fundamental operations (see grades 4-6)
Fractions and decimals
Factoring
Problem-solving strategies
Factorial
Ratio and proportion
Application of percent
Personal finances
Metric system
Probability
Basic geometric concepts
Development and use of formulas
Reading and constructing graphs
Introduction to statistics
Introduction to algebra
Negative numbers
Powers and roots
Time zones, latitude, and longitude
Introduction to plane and solid geometry
Pythagorean rule
Sine, cosine, tangent
Pre-Algebra
Maintaining skills in fundamental operations (see grades 4-7)
Principles of mathematics
English and metric measures
Basic algebraic concepts
Signed numbers
Powers and roots
Like and unlike terms
Multiplying and dividing monomials
Problem-solving strategies
Word problems solved algebraically
Reading and constructing graphs
Graphical scale drawings
Statistics and probability
Business math
Earning income
Banking
Stocks and bonds
Insurance
Basic plane and solid geometric concepts
Properties of geometric figures
Constructing geometric figures
Perimeter, area, surface area, and volume
Pythagorean rule
Sine, cosine, and tangent
Scientific notation
Algebra I
Linear equations in one variable
Algebraic numbers
Graphs
Formulas
Positive and negative numbers
Fundamental operations
Special products and factoring
Fractions
Ratio, proportion, and variation
Linear systems of equations
Powers and roots
Exponents and radicals
Quadratic equations
Numerical trigonometry
Mathematics in an Age of Science
Geometry
Basics of Geometry
Reasoning and Proof
Perpendicular and Parallel Lines
Congruent Triangles
Properties of Triangles
Quadrilaterals
Transformations
Similarity
Right Triangles and Trigonometry
Circles
Area of Polygons and Circles
Surface Area and Volume
Algebra II
Algebra II is the bridge between Algebra I and higher level mathematics such as Trigonometry and Calculus. Students will be studying concepts mastered in Algebra I in more depth, as well as focusing on new concepts necessary in upper level mathematics courses. For the Christian student, studying Algebra II and all mathematics can easily demonstrate the existence of a Creator with purpose, design, and order. Specifically, over the course of a year, students will study equations, functions, inequalities, and their graphs, matrices, conic sections, sequences and series, probability and statistics, and basic trigonometry.
Pre-Calculus:
Pre-Calculus is a year-long, academically rigorous course, with one semester a continuation of the Algebra curriculum, and the other semester covering trigonometry. The fundamental objectives are to help students truly understand the fundamental concepts of algebra, trigonometry, and analytical geometry, and to foreshadow important ideas of calculus. The use of technology will be strongly emphasized, as will standard analytical techniques. The course will use graphical, numerical, and algebraic modeling of functions.
Advanced Placement Calculus AB
AP Calculus AB is a course designed by the College Board. The College Board defines AP Calculus AB as a full high school academic year of work and is comparable to calculus courses in colleges and universities. Students at GCA who take AP Calculus will be expected to take the AP Exam in May. The purpose of taking the AP Exam is to attempt to gain college credit, placement, or both. Students can expect a short time of review of materials covered in pre-calculus, however the majority of the year will be spent on differential and integral calculus.
From the College Board Website:
Calculus AB [is] primarily concerned with developing the students' understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multirepresentational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally.
Broad concepts and widely applicable methods are emphasized. The focus of the course is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types. Thus, although facility with manipulation and computational competence are important outcomes, they are not the core of [the] course.
Technology should be used regularly by students and teachers to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results.
Through the use of the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling, the course becomes a cohesive whole rather than a collection of unrelated topics.
Goals:
• Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations.
• Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems.
• Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.
• Students should be able to understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
• Students should be able to communicate mathematics and explain solutions to problems both verbally and in written sentences.
• Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral.
• Students should be able to use technology to help solve problems, experiment, interpret results, and support conclusions.
• Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
• Students should develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.