# MTH 104 INTERMEDIATE ALGEBRA WITH TRIGONOMETRY

Students will be required to spend one additional hour
each week on a supplemental learning activity determined by

instructor. Creating open expressions and using those expressions to write
equations involving one or two variables to

solve problems and applications will be integrated throughout this course
(especially in * topics). Examples from other

disciplines will be incorporated whenever possible. A comprehensive departmental
final exam testing the degree of

mastery of the following course objectives is required.

**1. Sets of Numbers**

1.1 Review classifying a given real number as being a counting

or natural number, whole number, integer, rational or

irrational number.

1.2 Introduce the concept of imaginary and complex numbers.

1.3 Write complex numbers in a + bi form; add, subtract,

multiply, and divide complex numbers is a + bi form.

**2. Properties of Real Numbers**

2.1 Review identifying and using the Commutative, Associative,

Distributive , Identity, and Inverse Properties.

***3. Equation Solving Techniques**

3.1 Review solving linear equations in one variable.

3.2 Review solving literal equations and formulas for a single

variable.

3.3 Solve quadratic equations in one variable.

3.3a Review solving by factoring

3.3b Solve by using the square root method.

3.3c Solve by completing the square where a = 1.

3.3d Solve by the quadratic formula.

3.3e Use the discriminant to classify the roots.

3.4 Solve rational equations.

3.5 Solve radical equations involving one radical term.

**4. Polynomials**

4.1 Review adding and subtracting polynomials .

4.2 Multiply polynomials.

4.3 Review division of a polynomial by a monomial .

4.4 Divide a polynomial by a binomial using long division.

**5. Factoring**

5.1 Review the following factoring techniques: Factor a

monomial GCF from a polynomial, factor a polynomial

containing four terms by grouping, factor the difference of

two squares, factor trinomials of the form ax^{2} + bx + c.

5.2 Factor perfect square trinomials.

5.3 Factor the sum and difference of two cubes.

**6. Rational Expressions**

6.1 Review simplifying rational expressions.

6.2 Review multiplying and dividing rational expressions.

6.3 Review adding and subtracting rational expressions with like

denominators .

6.4 Add and subtract rational expressions with unlike

denominators.

6.5 Simplify complex fractions.

**
*7. Inequalities in one variabl**e

7.1 Review the solution of a linear inequality in one variable,

express the solution using set notation and interval notation,

and graph the solution on the real number line.

7.2 Solve compound linear inequalities, express the solution

using set notation and interval notation, and graph the

solution on the real number line.

**8. Absolute Value**

8.1 Review the concept of absolute value as distance from zero

on the real number line.

8.2 Solve a linear absolute value equation in one variable.

8.3 Solve a linear absolute value inequality in one variable,

express the solution using set notation and interval

notation, and graph the solution on the real number line.

9. Functions

9.1 Introduce the use of function notation.

***10. The Cartesian Coordinate System **

10.1 Review graphing linear equations in two variables by

plotting points .

10.2 Review slope and its relationship to horizontal, vertical,

parallel and perpendicular lines.

10.3 Review graphing linear equations using the slope and y-intercept.

10.4 Write the equation of a line using the slope- intercept form

and the point-slope form.

10.5 Graph linear inequalities in two variables.

10.6 Use the vertex, axis of symmetry, and intercepts to graph

a quadratic equation of the form y = ax^{2} + bx + c.

***11. Systems of Equations**

11.1 Review solving systems of linear equations in two

variables graphically and algebraically .

11.2 Solve a system of three linear equations in three variables

algebraically.

12. Exponents and Radicals

12.1 Review simplifying exponential expressions with integer

exponents.

12.2 Simplify exponential expressions with rational exponents.

12.3 Review simplifying square root radical expressions.

12.4 Simplify cube root radical expressions.

12.5 Perform arithmetic operations on square root and cube

root radical expressions.

***13. Trigonometry**

13.1 Review the use of the Pythagorean Theorem.

13.2 State the sine, cosine, and tangent ratios in terms of

opposite side, adjacent side and hypotenuse of a right

triangle.

13.3 Use special triangles (30°-60°-90°, 45°-45°- 90°) to find

sine, cosine, and tangent ratios of special angles.

13.4 Find any angle or side of a right triangle given one acute

angle and one side, or two sides.

13.5 Solve realistic applications involving right triangles.

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