S: Math 080 Intermediate Algebra
BC: James Edward Hardee III
FC: A YEAR IN REVIEW | Math 080 Exam Review Study Guide
1: Dividing Fractions | - When dividing fractions I must remember to ... KEEP CHANGE CHANGE - Which means to keep the first fraction, change the sign to multiplication and then flip the second fraction. | - If I can factor any of the expressions I need to do this next. - Then I remove all the factors of 1. - Then I need to simplify. | Then...
2: "Families are like fudge ... mostly sweet with a few nuts." | Adding Rational Expressions | Steps to solving an addition expression. 1. Find the least common denominator of the fractions. - to do this you want to get the same denominator on both sides of the addition sign in the expression. - You may need to multiply one numerator by the denominator of the other expression so that the denominators are the same for both expressions. 2. Once the denominators are the same then you can simply add the numerators.
3: For example: | x+4 + x-7 x+2 x+5 x+4 . x+5 + x-7 . x-2 x-2 x+5 x+5 x-2 x^2 + 9x +20 + x^2-9x+14 (x-2)(x+5) (x-2)(x+5) 2x^2 + 34 = 2(x^2+17) (x-2)(x+5) (x-2)(x+5)
4: Functions and Graphs of Functions | - To graph a function I find the ordered pairs using the function and plot them on the graph. - The y axis is the vertical axis and the x axis is the horizontal axis. | For example: f(x) = x+2 x f(x) -4 -2 0 2 2 4 | Then I will graph these points on a graph.
5: "The friends we meet on the path of life make the trip worth while." | To determine if a graph is a function or not I will use the vertical line test. - This means that if it is possible that a vertical line placed on the graph can pass over the graphed line more than once then it is not a graph of a function.
6: Equations of Lines | - One way of describing a line is using the slope intercept formula. The formula is... y = mx + b m= the slope of the line. This is also known as rise over run. Most of the time slope is expressed as a fraction. b= is the y in the y intercept ordered pair. For example (0,b) - Another way to describe a line is using the point slope formula ... y - y1 = m(x-x1) - For this equation you substitute in the slope for m=5 and a point in the line such as (1, 5) y-5 = 5(x-1)
7: Things to remember... - If the line is a horizontal line then there is a slope of 0. - If the line is a vertical line then the line has a slope that is not defined. - If two lines are parallel to each other then they have the same slopes and different y intercepts. - If two lines are perpendicular then the products of their slopes is -1. Also one of the lines can be vertical and one can be perpendicular.
8: Solving Systems of Inequalities | - A. Matrix - I set my equations as x, y and the constant. - Then set D equal to the x and y numbers in a matrix. x y D=[1 3] 2 3 - Then I cross multiply and always put a minus in the middle. - Then I set Dx equal to c and y in a matrix form. - Then I cross multiply and always put a minus. Then I repeat this step with Dy equal to x and c in a matrix form. - To find x coordinate solve dx/d. To get y point solve dy/d. - B. Graphing - I put the equations into slope intercept form and then graph the points. - Then find the coordinates of the point of intersection. - Then I check my answer
9: C. Substitution - I solve one of the given equations for a x or a y. - Then I can substitute that equation for the x or y in another equation. - Then I substitute that answer into another equation. - I should then end up with an answer for x and y. D. Elimination - In this method I can take one equation and multiply it by whatever number I need to so that either the x or the y will cancel in the other equation. - Then I add the equations and solve for the variable that is left. - If there are three variables then I solve for another variable just as I did that one.
10: Inequalities | - An inequality contains a greater than, less than or equal to symbol in them. - The solution of the inequality is what makes the inequality true. - When you have to divide to solve an inequality then you have to flip the signs. - An intersection between two number or groups of numbers is what they have in common. The intersection is shown by using an upside down U in between the two numbers. - If two numbers or inequalities are joined by the word and then it is called a conjunction. - The word or means union. A union is shown by using a U. This means that the answer can be in at least one of the individual sentences.
11: - Absolute value is when there are two straight lines down beside the numbers or the variables. This means that the product is always a positive number even if the calculation turns out to be negative. - When graphing an inequality then I use a dotted line if the equation says greater than or less than. - If the inequality is greater or equal to or less than or equal to then I will use a solid line.
12: Radicals | - The square root symbol makes an equation be a radical. - The number or expression under the radical is known as the radicand. - Numbers can also be under a third root, fourth root or so on. - Numbers under the square root can also be written to an exponent. For example: - If 7 was to the 5th root it could also be written as 7^1/5. -
13: - The pothagorean theorem also involves squares and powers. - This equation is . . . a^2 + b^2 = c^2 - I can use the rules of squares and powers to help me solve this to find the lengths of the sides of a right triangle.
14: Quadratic Formula | - In order to solve equations using this formula I need to have them in this formate... ax^2 +bx +c =0 - Then I can plug the a, b and c into the formula above and solve. - I need to remember the rules for solving radical expressions that I have previously mentioned.
15: Completing the Square | 1. Check for descending order. 2. a must be 1. If not you must divide the equation by that number so it will be 1. 3. Move c to the right. 4. Multiply b times 1/2 and then square it and add it to both sides. *** 5. Factor the left side combine like terms on the right side. 6. Take the square root of both sides and remember plus or minus on the right side.