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Algebra 1 Textbook - Algebra I: Expressions, Equations, and Applications by Paul A. Foerster
Algebra 2 Textbook - Algebra and Trigonometry: Functions and Applications by Paul A. Foerster
Important Class Details
Algebra 1 - This course emphasize basic algebraic concepts and skills, as well as higher level reasoning involving problem solving and proof.
- Polynomials: terminology, evaluation, algebraic combinations, degree, long division
- Factoring: prime and common factors, difference of squares, quadratic trinomials, factoring by grouping
- Rational expressions: dividing by monomials, simplifying by factoring, algebraic combinations, least common multiples, combinations of rational expressions
- Linear equations: roots, literal equations, solutions of equations with rational expressions, story problems
- Linear inequalities
- Graphs and the Cartesian coordinate system
- Positive integral exponents and roots
- Graphs of linear functions
- Functions: notation, evaluation, inverse of functions
- Lines: slope, various forms for equations of lines, parallel and perpendicular lines
- Variation: direct, inverse, joint
- Quadratic equations: solutions by factoring, completing the square, the quadratic formula
- Story problems involving linear and quadratic equations
Algebra 2 - This course covers algebraic and trigonometric concepts intended to prepare students for a high school level pre-calculus course. Students will need a TI-83+ Graphing Calculator.
- Factoring of sums and differences of cubes
- Exponents: zero, negative exponents, laws of exponents, rational exponents, exponential growth and decay
- Radicals: rules, notation, combinations, rationalizing the denominator
- Complex numbers
- Logarithms: definition, properties, antilogs, computations
- Quadratic equations: solutions by factoring, quadratic formula, character of solutions, equations involving “disguised quadratics”
- Inequalities: solutions, graphing linear and quadratic inequalities
- Simultaneous equations: solutions by graphing, elimination, and substitution; linear programming in two variables
- Simultaneous inequalities: solutions by graphing
- Direct and inverse variation
- Conic sections in simple positions: basic features of graphs of circles, parabolas, ellipses and hyperbolas, algebraic solutions of quadratic systems, translation of axes
- Polynomial and rational functions: remainder theorem, factor theorem, synthetic division, fundamental theorem of algebra, factors and zeros, Descartes rule of signs, rational solutions of polynomial equations
- Graphs of rational functions: intercepts, asymptotes, symmetry, asymptotic behavior
- Binomial theorem
- Sequences and series: arithmetic and geometric sequences, infinite geometric series, summation notation, sums of arithmetic and geometric series
- Matrices: determinants and inverses of 2 x 2 and 3 x 3 matrices; Cramer’s rule
- Problem solving in an algebraic setting
- A brief introduction to trigonometry: sines, cosines, and tangents; solutions to right triangles
Credit Class: GATE MSU Academic Programs are conducted as an opportunity for students to gain high school level credit. GATE mathematics classes are designed to align with Michigan HSCE requirements as well as Common Core. Parents are responsible to communicate with their child’s school before applying to any academic program to address the question of issuing credit and placement of their student in their class curriculum and/or schedule. The GATE Summer Mathematics students are not able to opt into a MSU CHAMP program using any credit obtained from any GATE Summer Mathematics class cannot be used as a substitute for any class in the MSU CHAMP program.
Please note that how the school records your credit/grade for GATE programs is completely up to each individual school. We recommend asking your school how they will record the grade before your student begins the program.
GATE does not guarantee any credit acceptance for any programs, it is the responsibility of the student/family to determine this prior to the start of any program.