Chapter R1, Problem 1GA

To determine

The goals of taking this course and discuss them with your group members.

Explanation of Solution

The main goals of taking this course can be summarized as below:

(1) Linear equations and Inequalities in one variable:

After learning this topic, if we have given a linear equation with one variable,

• We will be able to clear fraction
• We will be able to use the distributive property
• We will be able to use the addition and multiplication properties

If we have given a literal equation, then we'll be able to

• Solve for any given variable

If we have given an inequality with one variable, then we'll be able to:

• Solve the inequality algebraically
• Describe the solution of inequality using inequality notation and interval notation
• Solve and graph the solutions of absolute value inequality

(2) Linear equations in two variables and Functions:

After learning this topic, if we have given a linear equation with two variable, we will be able to:

• Understand and Transform the equation of line in different form like: slope-intercept form, point-slope form or standard form
• Identify the slope and y-intercept of any equation of line
• Graph the equation of line using slope and y-intercept

If we have given an inequality with two variables, then we will be able to:

• Solve the solution graphically
• Write the solution in interval notation using the parentheses and square bracket as per the inequality sign

If we have given a function in any of the algebraic, table, graph or in context form, we will be able to:

• Identify a function as a relationship of the dependent variable and independent variable
• Demonstrate the proper use of the function notation
• Identify domain and range of the function from algebraic equation or from the graph
• Evaluate the function value at any point
• Identify dependent and independent variables in context

(3) System of Linear equations and Inequalities:

After learning this topic, if we have given a system of linear equation with two variable, we will be able to:

• Solve the system of equation by substitution method, addition method or graphing method
• Compare the real life models expressed by linear functions
• Identify the number of solutions, that is, one solution, infinitely many solutions or no solution
• Interpret the solution of system given in context

If we have given linear inequalities with two variables, we will be able to:

• Solve the equalities using the graphing method
• Solve the compound inequalities

If we have given linear inequalities with three variables, we will be able to:

• Solve the system of equations algebraically
• Solve the system of equations using matrices

(4) Polynomials:

After learning this topic, if we have given polynomials, we will be able to:

• Identify the degree of the polynomial and the like terms in the polynomial
• Perform the basic operations on polynomials, like addition, subtraction, multiplication and division of polynomials
• Factor by grouping
• Factor trinomials using splitting the middle term
• Factor binomials and trinomials
• solve equations using zero product rule and square root property

(5) Rational Expressions and Rational equations:

After learning this topic, if we have given a rational expression or equation, we will be able to:

• Simplify the rational expressions and equations
• Perform the basic operations like addition, subtraction, multiplication and division of rational expressions
• Simplify the complex fractions

(6) Radicals and Complex numbers:

After learning this topic, if we have given a radical number or expression, we will be able to:

• Simplify the radical expression using the exponent rules
• Perform the basic operations, like addition, subtraction, multiplication and division of radical expressions
• Rationalize the radicals in rational expressions
• Change simple rational exponents to radical form and vice versa

If we have given a complex number, then we will be able to

• Write the complex number in standard form
• Perform the basic operations, like addition, subtraction, multiplication and division of complex numbers
• Find the complex conjugates to divide the complex numbers

(7) Quadratic Equation, Function and Inequalities:

After learning this topic, if we have given a quadratic equation or expression, we will be able to:

• Factor the quadratic equations
• Solve the quadratic equation to find the zeros of the equation
• Solve the quadratic equations using different methods, like quadratic formula, splitting the middle term, completing the square method or graphically
• Identify the shape of the parabola by identifying the dependent and independent variable
• Identify the vertex of the parabola

(8) Exponential and Logarithmic functions:

After learning this topic, if we have given an exponential function, we will be able to:

• Identify the growth or decay factor
• Determine the growth or decay rates
• Identify the exponential growth/decay and continuous growth/decay
• Identify the increasing or decreasing graph of given exponential function

If we have given a logarithmic equation, we will be able to:

• Expand the logarithmic expression using the logarithmic rules
• Combine the logarithmic expression using the logarithmic rules
• Differentiate between regular log and natural log
• Graph the logarithmic functions

(9) Conic sections:

After learning this topic, we will be able to:

• Find the distance between any two points, midpoint of line segment connecting two points
• Identify and differentiate between different conics, like circle, parabola, ellipse and hyperbola
• Solve the system of non linear equations with two variables
• Graph the solutions of two non linear inequalities

(9)Binomial expansions, Sequences and Series:

After learning this topic, we will be able to:

• Expand a binomial of higher order
• Identify the series and sequences and their general terms
• Use of Arithmetic and Geometric sequence and series in real life applications.