MA1010 Algebra and Trigonometry

Real number system, complex numbers, exponents and radicals, algebraic expressions and operations, linear and quadratic equations, inequalities, functions and graphs, polynomials and their zeros, rational functions, exponential and logarithmic functions, systems of equations, matrices, trigonometry and unit circles, trigonometric identities and functions. PREREQUISITE: None.

Lecture Hours

V

Lab Hours

0

Course Learning Outcomes

After successfully completing this course, the student will be able to:

• Understand the real number system, identify rational numbers and irrational numbers, and graph real numbers on the number line.
• Conduct operations on real numbers (absolute value, addition, subtraction, multiplication, division, division by zero).
• Evaluate expressions, including arithmetic expressions, exponential expressions, square roots, order of operations, and algebraic expressions.
• Know the properties of real numbers (commutative, associate, distributive, identity, inverse, multiplication properties of zero)
• Use the properties (computation, like terms, combining like terms, products and quotients, removing parentheses)
• Solve linear equations.
• Solve inequalities and represent the results in interval notation or graph.
• Solve compound inequalities and graph the solution set.
• Solve absolute value equations and inequalities.
• Graph lines in the coordinate plane.
• Compute the slope of a line.
• Know different forms of the equation of a line, including point-slope form, slope intercept form, standard form and be able to graph a line.
• Solve linear inequalities and graph them.
• Understand the definition of a function, its domain and range, linear and constant functions.
• Use the vertical line test.
• Understand the integral exponents (positive and negative exponents, product rule, zero exponent, changing the sign of an exponent, quotient rule).
• Understand the power rules (raising an exponential to a power, raising a product to a power, raising a quotient to a power, variable exponents).
• Conduct addition, subtraction, and multiplication of polynomials.
• Multiply binomials.
• Compute division of polynomials.
• Factor polynomials (factoring out the greatest common factor, factoring the difference of two squares, factoring perfect square trinomials, factoring a difference or sum of two cubes, factoring a polynomial completely).
• Factor quadratics.
• Solve equations by factoring.
• Identify radicals.
• Understand the rational exponents (roots, positive rational exponents, negative rational exponents, using the rule of exponents, simplifying expressions involving variables).
• Conduct operations with radicals/quotients, powers, and rationalizing denominators.
• Solve equations with radicals and exponents.
• Understand complex numbers (definition, addition, subtraction, multiplication, division, square roots of negative numbers, imaginary solutions to equations).
• Factor and complete the square.
• Develop the quadratic formula and use the formula.
• Graph linear and constant functions, absolute value function, quadratic functions, square root functions, and graph relations.
• Transform graphs (reflect, translate, stretch and shrink) and do multiple transformations.
• Understand exponential functions (definition, domain and range, graphing exponential functions, exponential equations, applications).
• Understand logarithmic functions (definition, domain and range, graphing logarithmic functions, logarithmic equations, applications).
• Use properties of logarithms (product rule, quotient rule, power rule, inverse properties).
• Understand the series (summation notation, changing the index).
• Understand angles and arc length.
• Know trigonometric functions of a general angle.
• Know trigonometric functions of an acute angle.
• Know variation and graphs of the trigonometric functions.
• Understand fundamental relations and identities of the trigonometric functions.
• Know sum, difference, and product formulas of the trigonometric functions.