# Introductory Algebra

**COURSE DESCRIPTION: **

A beginning algebra course covering most elementary topics of algebra. This includes the real number system, solving equations and inequalities, polynomials, fractional equations, and radical expressions. This is an adaptor course designed for students with no algebra background or for students who need review.

**COURSE COMPETENCIES: **

During this course, the student will be expected to:

**1. Compute with integers. **

1.1 Compare integers using <, >, or =.

1.2 Name the additive inverse of any integer.

1.3 Write the absolute value of any integer.

1.4 Determine the sum of two integers .

1.5 Determine the difference of two integers.

1.6 Determine the product of two integers.

1.7 Determine the quotient of two integers.

1.8 Use the order of operations to evaluate numerical expressions.

**2. Simplify algebraic expressions **

2.1 Evaluate an expression for a given value of the variable.

2.2 Use the commutative or associative property to simplify a given expression.

2.3 Use the distributive property to simplify an expression.

2.4 Use the properties of 0 or 1 to simplify an expression.

2.5 Identify the value of a given expression with exponents.

2.6 Implement the order-of-operations rules.

**3. Solve first-degree equations and inequalities in one variable . **

3.1 Classify statement as identity, contradiction, or conditional.

3.2 Solve linear equations/inequalities involving one-step transformations using
the addition property of equality.

3.3 Solve linear equations/inequalities involving one-step transformations using
the multiplication property of equality.

3.4 Solve linear equations/inequalities involving two transformations.

3.5 Solve linear equations for one variable in terms of other variables.

**4. Write models for verbal problems that produce first-degree equations
and inequalities in one variable. **

4.1 Translate phrases and sentences written in words into their algebraic form.

4.2 Write an equation to solve a given word problem.

5. Simplify expressions involving integer exponents.

5.1 Define a positive exponent.

5.2 Define the zero exponent.

5.3 Define a negative exponent .

5.4 Use exponent rules for products, quotients, and powers.

**6. Compute with polynomials. **

6.1 Define polynomial.

6.2 Evaluate a polynomial, given values for the variable.

6.3 Classify a given polynomial according to number of terms.

6.4 Identify degree of term and/or polynomial.

6.5 Find the sum/difference of two polynomials.

6.6 Find the product of two polynomials.

6.7 Calculate the square of a binomial.

6.8 Apply the order of operations to simplify polynomials.

6.9 Find the quotient of two polynomials.

**7. Factor polynomials.
**7.1 Remove the greatest common monomial factor.

7.2 Factor by grouping.

7.3 Factor a trinomial which is the product of two binomials with integral coefficients.

7.4 Factor a binomial which is the difference of two squares.

7.5 Factor polynomials completely.

**8. Operate on rational expressions.
**8.1 Identify whether an algebraic expression is rational or irrational.

8.2 Determine whether two rational expressions are equivalent .

8.3 State the restrictions on the variables in a given rational expression.

8.4 Simplify a rational algebraic expression.

8.5 Express the sum/difference of two rational expressions in simplest form.

8.6 Express the product/quotient of two rational expressions in simplest form.

8.7 Solve equations containing rational expressions.

**9. Graph a linear equation in two variables.
**9.1 Plot a given ordered pair of rational numbers on a graph.

9.2 Name the coordinates, given a point on a graph.

9.3 Determine ordered pairs which satisfy a given linear equation.

9.4 State the x- intercept and y -intercept for a linear equation.

9.5 Graph a linear equation on a coordinate plane.

**10. Write the equation of a specified line.
**10.1 Define slope.

10.2 Determine the slope, given two points.

10.3 Determine the slope, given the equation of a line.

10.4 Write an equation for a line given the slope and the y-intercept.

10.5 Write an equation for a line given the slope and one point (not the y-intercept).

10.6 Write an equation for a line given two points.

10.7 Determine the slope of a line parallel/perpendicular to a given line.

**11. Solve systems of linear equations.
**11.1 Recognize parallel, intersecting, and coinciding lines when given
systems of two simultaneous equations.

11.2 Solve system of equations by graphing method.

11.3 Use elimination method to solve system.

11.4 Use substitution method to solve system.

**12. Compute with radical expressions.
**12.1 Simplify a single radical.

12.2 Rationalize a denominator.

12.3 Express sums/differences of algebraic square roots in simplest terms.

12.4 Express products/quotients of algebraic square roots in simplest terms.

12.5 Recognize between which two integers a square root of a number lies .

**13. Solve quadratic equations in one variable.
**13.1 Use factoring to solve quadratic equations.

13.2 Use the quadratic formula and/or completing the square.

13.3 Write models for verbal problems that produce quadratic equations.

14. Use algebraic techniques appropriate to real-world and mathematical problem situations.

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