
Concept explainers
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
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)
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)
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.
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