
Explore core mathematics and college algebra, including natural, whole, integers, rational and irrational numbers, real numbers, the number line, and scientific notation, plus commutative, associative, and distributive properties.
Explore roots and radicals and the laws of indices, including how to work with the radical symbol, square roots, combining like radicals, and exponent rules.
Explore polynomials: define degree, identify monomials, binomials, and trinomials; learn adding, subtracting, multiplying, and factoring including greatest common factor and difference of squares.
Learn to work with rational expressions, simplifying by factoring and canceling common factors and multiplying, dividing, adding, and subtracting them, including using the least common denominator.
Solve linear equations in one variable using addition and multiplication properties to isolate the variable, clear fractions with a least common denominator, and explore word problems and no-solution cases.
This lecture explains linear inequalities and absolute value, defines symbols, shows solving rules including sign changes with negatives, graphs solutions on number lines, and solves absolute-value equations like |x-2|=8.
Explore the coordinate plane, axes, origin, and quadrants. Learn to determine slope using rise over run from two points and form the equation of a line.
Master college algebra techniques to solve systems of linear equations by elimination or substitution, then represent them with matrices and determinants, and apply Cramer's rule to find x and y.
Explore quadratic equations through factoring, the zero product property, the quadratic formula, and solving radical equations, then graph parabolas by locating vertex, intercepts, and orientation.
Solve and graph quadratic inequalities by finding boundary points, using solid or open circles, testing regions on the number line, with examples like (x-3)(x+2)>0 and 9x^2-2<=-3x.
Explore logarithmic functions as the inverse of exponentials, including common and natural logs, change-of-base, and practical calculations with examples and real-world applications.
COURSE DESCRIPTION
This course will expose students to the principles of algebra for the college level. Students will get an understanding of numerical and algebraic relationships and be able to formulate problems into mathematical terms, select, apply and communicate appropriate techniques of solution and interpret the solutions in terms of the problem.
GENERAL OBJECTIVES
At the end of the course students should be able to:
Think logically and critically
Reason using abstractentities
Have confidence to apply mathematical skills to develop appropriate solutions
Appreciate the use of algebra in making generalizations
Appreciate the use of algebraic techniques in solving problems
COURSE LEARNING OUTCOME
Identify and apply models and solve real-world situations with quadratic expressions using a variety of methods, including, but not limited to, arithmetic, algebraic, geometric, higher-order thinking, or statistical methods
Evaluate basic algebraic information by a variety of methods, including, but not limited to, verbal, numerical, graphical or symbolic.
Demonstrate the ability to develop convincing mathematical arguments, using mathematical reasoning skills and logic in order to solve algebraic problems
Demonstrate an in depth understanding and interpret algebraic models, such as formulas, graphs, tables or schematics, and draw inferences from them
Develop the view that algebra is an evolving discipline, interrelated with human culture and understand its connections to other disciplines.