Bunker Hill Community College

MAT195 Objectives

MAT195 COLLEGE ALGEBRA COURSE OBJECTIVES

1. Solve linear inequalities in one variable.
2. State the definition of absolute value and use the definition to evaluate or simplify expressions involving absolute value.
3. Solve equations involving absolute value.
4. Solve inequalities involving absolute value.
5. Draw the graph of a function of the form y =  |x – a| .
6. Find the slope of a line containing two given points.
7. Write the equation of a line given the slope and a point, or given two points.
8. Draw the graph of a line given the equation.
9. Draw graphs of linear inequalities in two variables.
10. Draw graphs of systems of two linear inequalities in two variables.
11. Determine whether or not a given graph is the graph of a function.
12. Find the equation of  the inverse relation for a linear or quadratic function, state whether it is a function, and draw the graphs of both the function and the inverse.
13. Solve applied problems involving direct and inverse variation.
14. Solve systems of two linear equations in two variable by graphing.
15. Solve systems of two linear equations in two variables algebraically.
16. Solve systems of three linear equations in three variables algebraically.
17. Solve applied problems involving systems of linear equations in two or three variables.
18. Use the rules for exponents to simplify expressions involving positive integral exponents.
19. Simplify expressions containing zero exponents.
20. Find the value of powers or simplify expressions involving positive, zero and negative integral exponents.
21. Identify a perfect trinomial square and write it as the square of a binomial.
22. Factor sums or differences of odd powers.
23. Factor differences of even powers, and state that sums of some even powers cannot be factored.
24. Given an appropriate polynomial in four terms, factor the polynomial by grouping.
25. Reduce a rational expression to lowest terms.
26. Multiply and divide rational expressions and reduce to lowest terms.
27. Draw the graph of a function of the form y = a/x .
28. Find the least common multiple of two or more polynomials.
29. Add and subtract rational expressions and reduce to lowest terms.
30. Simplify complex fractions.
31. Solve equations involving rational expressions.
32. Solve applied problems using equations involving rational expressions.
33. Find the value of a power involving rational exponents where the value is a rational number.
34. Simplify expressions involving rational exponents.
35. Use rational exponents to simplify expression involving radicals.
36. Find the distance between two given points.
37. Draw the graph of a function .
38. Use the rules for radicals to simplify radicals by removing factors and by rationalizing the denominators.
39. Add and subtract expressions containing radicals.
40. Multiply an expression containing radicals by a single radical term and multiply   two two-term expressions containing radicals.
41. Rationalize a one-term or two-term denominator or numerator containing square roots.
42. Solve equations involving radical expressions.
43. Write the square root of a negative number as an imaginary number.
44. Add and subtract complex numbers.
45. Multiply imaginary numbers, an imaginary number by a complex number or two complex numbers.
46. Divide imaginary numbers, a complex number by an imaginary number, or two complex numbers.
47. Write a quadratic equation in standard form and identify a, b, and c.
48. Solve equations of the form ax2 + c = 0 when the equation has real number solutions, or state that the equation has no real number solutions.
49. Solve quadratic equations where the solutions are complex numbers.
50. Use the quadratic formula to solve quadratic equations when the equation has real number solutions, or state that the equation has no real number solutions.
51. Use the quadratic formula to solve area and volume problems.
52. Find the vertex of a parabola and determine whether the vertex is a maximum or minimum.
53. Draw the graph of a quadratic function.
54. Given an appropriate formula, solve problems describing the motion of an object due to gravity.
55. Solve quadratic inequalities in one variable.
56. Find the equation and draw the graph of a parabola, ellipse, circle, and hyperbola (the hyperbola centered at the origin only).
57.  Draw the graph of a function of the form y = ax.
58. Use the definition of a logarithm to write an exponential statement in logarithmic form, or a logarithmic statement in exponential form.
59. Find the value of a logarithmic expression, where the value can be found by inspection from the exponential form.
60. Draw the graph of a logarithmic function.