and 16. Use formulas to solve for a specific variable. 2.2 Ex: use the formula A h( ), to solve for b 1.

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1 Math A Intermediate Algebra- First Half Fall 0 Final Eam Stud Guide The eam is on Monda, December 0 th from 6:00pm 8:00pm. You are allowed a scientific calculator and a 5" b " inde card for notes. On our inde card be sure to write an formulas ou needed for an of the problems listed. I will not provide ou with an formulas on the eam. The Final Eam is comprehensive; however, not all of the problems that appeared in the previous eams will appear in the final. Use this stud guide to know which math concepts ou need to review. For the Final Eam, ou will need to be able to:. Compare numbers, including fractions and decimals using inequalit smbols... Given roster notation or set-builder notation graph the set on the number line and vice versa... Identif important sets of numbers... Epress in set builder notation each set of numbers that are indicated on the number line.. 5. Know how to simplif numbers with eponents, absolute values, simplif statements using the order of operations and how to complete inequalit statements (including fractions and decimals.. &. 6. Know how to add, subtract, multipl, and divide positive and negative numbers (including fractions and decimals, while simplif epressions and using the order of operations.. &. 7. Translate phrases into mathematical statements.. &. 8. Eponents..6 Know the difference between and (!! 9. Evaluate an algebraic epression variables given specific values for the variables.. 0. Simplif epressions using the rules of eponents, including epressions with both positive, negative, and zero eponents..5. Convert decimal numbers to scientific notation and convert scientific notation to decimal numbers..6. Multipl and divide numbers in scientific notation. 6.. Simplif epressions b using the distributive propert and combining like terms... Solve linear equations using the addition propert and multiplication propert of equalit.. 5. Solve a geometric problem b plugging in what ou know and solving for what ou don t know.. 6. Use formulas to solve for a specific variable.. E: use the formula A h( b b, to solve for b. 7. Use linear equations to solve application problems, such as, solving miture problems, motion problems, problems involving mone, and so on..,. 8. Solve inequalities and graph the solution sets on a number line Solve compound inequalities that have solutions as ranges depending on the word and or or Solve inequalities and equations involving absolute value..6. Plot and label ordered pairs, determine if a point is on a line, and read the inputs and outputs of graphs... Determine whether an ordered pair is a solution to the equation, and complete and tables... Graph linear and nonlinear equations b plotting points. Plot at least points for the graph... Interpret graphs. Decide which graph illustrates the stor.. 5. In a relation (or function, the set of values for the independent variable is called the domain. The set of values for the dependent variable is called the range..

2 6. Decide which relations are functions. For functions, each element of the domain can onl have ONE element of the range, but it is ok for two different elements of the domain to have the same element of the range.. 7. Use the vertical line test to determine whether a graph represents a function.. 8. Understand function notation.. 9. Graph horizontal lines, vertical lines, and lines through the origin.. 0. Graph an equation using intercepts. Must also plot a rd point used as a check point... Given two points, find the slope of the line passing through those two points, or state that the slope is undefined... Given the graph of a line, find the slope of the line or state that the slope is undefined... Graph the line with the given slope and going through the given point. Plot at least points... Given an equation, determine the slope and intercept of the line represented b that equation.. 5. m b, where m slope,and b -intercept (0, b 6. Find an equation of the line using the slope and intercept from a graph.. 7. When discussing real-life situations or when creating mathematical models, it is often useful to discuss slope as a rate of change.. 8. Use the slope-intercept form to construct models from graphs.. 9. Write the equation of the line given a point on the line, and the slope of the line m..5 ( * To write an equation given a point and a slope: Given, and m use m, then solve for to get into m b form. ( ( 0. Write the equation of the line given two points on a line, and,..5 ( * To write an equation given points:.given (, and (, use m to calculate m, (.Then use m, then solve for to get into m b form. (. Recognize parallel and perpendicular lines..5. Use the point-slope form to construct models from graphs..5. Find the sum, difference, product, and quotient of functions..6. Graph the sum of functions Graph linear inequalities. Use a test point to determine the shaded region (the solution Solve a sstem of linear equations graphicall. This includes sstems that have one unique solution, no solution, or an infinite number of solutions.. 7. Solve a sstem and a sstem of linear equations b the substitution method. This includes sstems that have one unique solution, no solution, or an infinite number of solutions.. &. 8. Solve a sstem and a sstem of linear equations b the addition method. This includes sstems that have one unique solution, no solution, or an infinite number of solutions.. &. 9. Solve application problems involving and sstems of linear equations. Man of the application problems ou see here are repeats of Chapter problems, ecept ou are using two variables to solve the problem instead of one variable. I will not provide an formulas or charts so be sure to write an formulas/charts ou needed for HW on our inde card Solve sstems of linear inequalities b graphing each inequalit and finding which region satisfies both inequalities Solve sstems of linear inequalities b graphing that involve absolute value Add and subtract polnomials. 5.

3 5. Multipl polnomials (distributing, FOILing, Divide polnomials b monomials (write the denominator under each term of the numerator and reduce Divide polnomials using long division (fill in all missing terms with 0, 0², 0³, Divide polnomials using snthetic division Factor b using general factoring procedures * Factor a polnomial b factoring out the GCF of all the terms. * Factor a polnomial using a combination of factoring methods. * For terms: - the difference of squares a b ( a b( a b - the sum of cubes a b ( a b( a ab b - the difference of cubes a b ( a b( a ab b * For terms: a b c - with leading coefficient : find two numbers that add to b and ac. Just use these numbers. - with leading coefficient not : find two numbers that add to b and ac. Replace the b term using the numbers ou found and factor b grouping. Finding numbers: a b c Both numbers are positive *Perfect square trinomials: * For terms: a b c Both numbers are negative a a ab b ( a b ab b ( a b a b c Bigger number is positive a b c Bigger number is negative - factor b grouping - group and factor the first terms, then factor remaining terms. NOTE: For the factoring problems above, the onl instructions I will give ou on the eam will sa: Factor the polnomial completel. It will be up to ou to figure out which factoring tool or method to use. There will not be an prime polnomials, so do not state prime. 58. Use factoring procedures to solve application problems There are several tpes: use the Pthagorean Theorem to find the unknown sides of a right triangles; use the equation to find its -intercepts on a graph; find an equation given its -intercepts; given the area of a rectangle within a rectangle, find its dimensions of a uniform border. use the equation given to find the height of a projectile or the time it takes for the projectile to be at a certain height; Practice Problems for the Final To stud for the final do the following problems AND look at the problems that were on the eams (but onl those similar to those in this handout. For those of ou who have the Chapter Test Prep Video cd that came with the book, ou can view it to see someone working out each of the problems that are in the Chapter Tests.

4 Final Eam Review Intermediate Algebra Name. Epress the set in roster form. - 6 { I and }. Consider the following set of numbers. a. List the rational numbers. 6, 5, 6, 0, 0.7,, 8,.9, b. List the irrational numbers.. Arrange the numbers from smallest to biggest. - (-0.87, -,.8,, Simplif: ( 9 9( 5. Simplif: 9 ( 5 6. Simplif: 5 ( Simplif: [( ( 5 7] [( 6 (8] 8. Simplif: Evaluate for = 5 and = 6 : ( 0. Simplif.. Multipl. 7 5 ( z ( 6 z. Simplif. 6ab c 5 8a bc

5 . Convert the following to standard form Simplif. 6 7 (.5 0 (.0 9 (60 5. Simplif. 7(9 ( 6. Simplif Solve for. (6 {5 [6 ( ( ]} 8. Solve for. 5 ( Solve for. 7 ( ( 6 0. Solve ( for.. A ield sign on a particular road has an area of 50 in². What is the length of the base if the height is inches? Remember: A bh. You are choosing between two long-distance telephone plans. One plan has a monthl fee of $5 with a charge of 5 per minute. The other plan has a monthl fee of $0 with a charge of 0 per minute. For how man minutes of long-distance calls will the costs for the two plans be the same?. If French roast coffee sells for $8.50 per pound and vanilla hazelnut coffee sells for $.50 per pound, how man pounds of vanilla hazelnut should ou mi with 9 pounds of French roast to get a blend that is sold for $ per pound?

6 . Sa ou were running 6 miles an hour, and our friend was running miles an hour. How long did it take to get mile ahead of our friend? Rate Time Distance You friend 5. Solve the inequalit, epress our answer in interval notation, and graph the solution. 0 or Solve the inequalit, epress our answer in interval notation, and graph the solution Solve and epress our answer in interval notation. 8. Solve the following

7 9. Determine if the following graphs represent a function. It does represent a function, then state the domain. 0. Graph Write the equation of the line.. Write an equation of the line that goes through the point (, - and perpendicular to the line 9.

8 . The population of the United States, in millions, in 980 was 6.5 million, and in 990 was 50 million. This information is shown in the following graph. a. Determine a linear function that can be used to estimate the population of the United States, P, in millions, in terms of t ears after 960. b. Use the function determined in part a to determine the population of the United States in 0. c. Use the function determined in part a to estimate the ear at which the population of the United States will be 500 million.. Let f ( and g ( 5 a. Find ( f g( b. Find ( f g( c. Find ( f g( 5. Graph

9 6. Find the inequalit that describes the shaded region. Solve the following linear sstem b graphing Solve the following linear sstems b the method of our choice. 8. z 8 z 0 z 9. You invested $0,000 in two funds paing % and 5% annual interest. At the end of the ear, the interest from the 5% investment eceeded the interest from the % investment b $0. How much mone was invested at each rate? Let = Let = Equations

10 0. Jesse, Maria and Charles went to the local craft store to purchase supplies for making decorations for the upcoming dance at the high school. Jesse purchased three sheets of craft paper, four boes of markers and five glue sticks. His bill, before taes was $.0. Maria spent $0.0 when she bought si sheets of craft paper, five boes of markers and two glue sticks. Charles, purchases totaled $.0 when he bought three sheets of craft paper, two boes of markers and one glue stick. Determine the unit cost of each item? Let = Let = Let = Equations: Solve the following sstem of linear inequalities b graphing... Indicate whether monomial, binomial, or trinomial, and state the degree: 5 z z. Subtract: 5 (6 8 ( 9 7 Tpe of polnomial Degree of polnomial. Multipl: ( ( Divide: 6 z 6 z 8 z z

11 6. Divide using long division: 7. Divide using snthetic division: ( 6 ( Factor. a b b 9. Factor. ( 7( 50. Factor. 8 ( 5 ( 5 5. Factor Solve for r. 5r r 5. Solve for k. ( k 7 k ( k

12 5. Find the area of the shaded region in factored form: 55. Find the difference of the volumes of the two cubes in factored form: Find the missing lengths b using the Pthagorean Theorem, a b c, and then factoring Find an equation whose graph will have the -intercepts,0 and, A rectangular garden measures 6 feet b feet. A path of uniform width is to be added so as to surround the entire garden. The landscape artist doing the work wants the garden and path to cover an area of 60 square feet. How wide should the path be? 6

13 59. You throw a ball straight up from a rooftop 60 feet high with an initial speed of 8 feet per second. The function h ( t 6t 8t 60 describes the ball s height above the ground, h(t, in feet, t seconds after ou threw it. a. Find the time it takes for the ball to hit the ground. b. Find the time it takes the ball to be at a height of 9 feet. 60. A 5-ft ladder is leaning against a building. The ladder reaches up the wall feet more than the distance of the ground between the base of the ladder to the building. Find the length the ladder reaches up the wall and the distance of the ground between the base of the ladder to the building. 5 feet

14 Answers:. {-, 0,, }. a. 6,5, 6,0,0.7,.9, b., , 0.87,.8,.875, z 9 a b 8c , No Solution b 5inches 00 minutes 5 lbs of Vanilla Hazelnut ½ hour (, (6, (, 5] (, 5] [,, a. function { } b. function { } c. not a function 5

15 . a. P ( t.5t b. P ( c. t 6. ears so, 096. a. b. c ,, z 9. $6,000 invested at % interest. $,000 invested at 5% interest. 0. $.75 for sheet of craft paper, $.60 for a bo of markers, $.95 for a glue stick... Trinomial Degree: z z ( a b ( a b 9. ( ( 50. ( 5( ( (9 5. ( ( 9 5. r, r k 5, k 5 5. A shaded ( ( The path has a uniform width of ft all the wa around. 55. ( ( a. It will hit the ground at 5 seconds. b. It will be at a height of 9 feet at second and seconds = 9 distance on ground is 9 feet and distance up the wall is feet.