Polynomials, FOIL, and Factoring EOC REVIEW

1 EOC REVIEWYou must be able to work with polynomials on the EOC:Distribution and FOIL:Rewrite each using distribution:1. )3(2 xx2. )3(5 xx3. )3)(5( xxPractice:Distribute. Simplify where )7(5xxx 2. )5)(72( xx3.)35)(35( xxPractice:Special )7)(7(xx 2. 2)72( )3(yx Factoring : each by Factoring the GCF:1. xx3022 2. 255269yxyx 3. 1642 xFactoring: Easy : 3532 xxPractice: Easy 542 xx2. 862 xx3. 72 xxPolynomials, FOIL, and FactoringEOC REVIEWF actoring: Special : 494292 xx2. 6492 xPractice: Special 252042 xx2. 11212 xFactoring: Hard Ones (Magic Number).Example: 1022 xx2. 211152 xxPractice: Magic 9272 xx2. 51362 xxFactoring: Solving a quadratic by : Solve for 0)12)(3( xx2. 030112 xxPractice: Solve by for 1522 xx2. 2592 xPolynomials, FOIL, and FactoringEOC REVIEWD irect Variation is just Slope-Intercept Form (without the intercept).If a problem states: y varies directly as x,That means y=kx for some value k is called the constant of variation.

2 You can think if it as can also say that x varies directly as y: this means x=kyExample 1:When y=6, x=2, solve for x when y=-9 if y varies directly as 2:The distance it takes to stop a moving train varies directly with the speed it istraveling. A train that is moving 50mph requires 10,000 feet to stop. Howmany feet will be required to stop a train moving 45mph?Practice:Solve each using direct variation. In each problem, y varies directly as When y=8, x=5. What is the constant of variation?2. When x=2, y=7. Find y when x= The skid marks left by a vehicle can be used to determine the speed withwhich it was traveling. If an 18-wheeler leaves 200-foot skid marks, it wastraveling approximately 60mph. How fast was an 18-wheeler traveling if it left240-foot skid marks?Proportional Reasoning can also be used for most of these problems:Example 1:The mass of an element varies directly as its volume. If 10cm3 of Carbonweighs grams, how much will 12cm3 weigh?

3 A. Solve using a Solve using diect What is the constant of variation?d. What do we call the constant of variation in this problem?Practice:The amount of stretch of a rubber band varies directly as the force applied toit. If a 10-gram weight stretches a rubber band by 8cm, how much will a rub-ber band stretch when weighted with a 14-gram weight?Direct VariationEOC REVIEWThe distance between coordinates on the plane can be found usingthe pythagorean )()(yyxxd The midpoint between two points (x1 , y1) and (x2 , y2) is found byaveraging the x and y 2,22121yyxxExample: Find the midpoint and distance between (4,3) and (-2, 5).Practice: Find the midpoint and distance for each pair of points. Leave thedistances in radical (8, -2) and (4, -5)2. (-3, -6) and (7, 3)3. (8, 9) and (3, 1)Parallel lines have the same lines have negative reciprocal : Which lines are parallel? Which are perendicular?a. 732 yxb.

4 732 yxc. 723 yxd. 732 xyExample: The points A(0,7) B(5,8) C(8,2) and D(3,1) form a quadrilateral ABCD a parallelogram?Practice:1. What is the equation of a line perpendicular to 75 yx through thepoint (9,1) in Standard Form?2. Points A(4,3) B(-8,1) and C(5,-3) are graphed on the plane to form a righttriangle. Which vertex is the right angle of triangle ABC?3. What is the approximate perimeter of triangle ABC above (to the tenth)?Distance/Midpoint REVIEWIf an equation is linear, it has a constant EOC problems will ask you to find an answer using a :In 1970, the average life expectancy in the was years. In 2000, theaverage life expectancy was years. Assuming the trend is linear, what willbe the average life expectancy in 2020?The oak tree in your backyard is 15 feet tall. When you planted it 2 years ago,it was just 7 feet tall. If the growth can be modeled by a linear equation, howtall will the tree be in 5 years?

5 PracticeAssume all growth or depreciation is linear for the following:1. In the year 2000, a 40-inch LCD television cost about $2,500. In 2008, youcan buy the same television for about $1,100. Assuming a linear rate of depre-ciation, how much less does the television cost this year than last year?2. Attendance at Lincoln high school has increased linearly for the past 10years. 5 years ago, Lincoln had 1,235 students. Now Lincoln has 1,705 stu-dents. If the growth continues, how many students will attend Lincoln in 3years?3. The height of a burning candle can be expressed by a linear equationwhere h is the height and m is the number of minutes the candle has beenburning. If a 15-inch candle burns for 35 minutes, it will be 8 inches tall. Whatequation can be written for the height h of a 15-inch candle that has beenburning for m minutes?Practice: Write a linear equation in slope-intercept form for each:1. A restaurant takes 1 hour to prepare and bake 16 pizzas.

6 To prepare andbake 20 pizzas takes the same restaurant takes 76 minutes. Whatequation can be used to represent the time in minutes m to bakep pizzas?2. The length of a particular snake is 16 inches at age 1 and 30 inchesat age 3. Assuming the snake grows at a linear rate, how long was itat birth?Linear RegressionEOC REVIEWE xponential growth: trpV)1( Amountprincipalrate (percent as a decimal)time (usually in years)Examples:How much will $400 be worth in 5 years at 7% interest (to the cent)?How long will it take for your money to double earning 6% interest?A. yearsB. 10 YearsC. 12 YearsD. 120 yearsPractice:1. The value of an automobile depreciates exponentially. If the rate of depre-ciation on your 7 year-old car is 20%, and the purchase price was $16,000,approximately how much is the car worth today?A. $18,380B. $13,890C. $3,748D. $3,3552. Approximately what interest rate must you earn on an investment to doublethe value of your money every 15 years?

7 A. 4%B. 5%C. 6%D. 7%3. In 2001, the population of Poughkeepsie was 12,500. In 2007, the popula-tion had increased by 1,170. Assuming that the growth rate is exponential,what is the annual rate of growth?A. :1. How long will it take an investment to triple in value if it is earning annually?A. 17 yearsB. 20 yearsC. 23 yearsD. 26 years2. Allentown has a population of 50,000 and a annual population growthrate. Brighton has 40,000 and a growth rate of If these growth ratescontinue, approximately how many years will it take for the populations to beequal?A. 25 yearsB. 50 yearsC. 75 yearsD. 100 years3. An aggressive species of vine grows in length by 20% daily. If the vine is 8inches long when planted, about how long will it be after two weeks of growth?A. 4 feetB. feetC. 7 feetD. feetExponential Growth/DepreciationEOC REVIEWThe vertex: abx2 To find the y-coordinate, plug-in Roots (solutions, zeros) aacbbx242 Examples:Find the roots and vertex for the following quadratic equation:3442 xxySolve for x: 101332 xxA.

8 5,32B. 5,32C. 5,32D. 5,32 Practice:1. The formula for the height of a ball h after t seconds is givenby the formula: 464162 tthWhat is the maximum height of the ball?A. 4 feetB. 60 feetC. 64 feetD. 68 feet2. Find the roots: 151642 xxhA. 25,23B. 25,23C. 25,23D. 25,233. The length of a rectangle is 4 inches greater than twice the the rectangle has an area of 70in2, what is its perimeter?A. 34inB. 38inC. 40inD. 74inQuadraticsEOC REVIEWE xamples:Where would the graphs of the two equations below intersect?A. 34 xyB. 923 yxWrite and solve a system of equations to solve the following:At a local bakery, 3 pastries and 5 doughnuts cost $ the same bakery, 4 pastries and one doughnut cost $ much would 2 pastries and 2 doughnuts cost?A. $ $ $ $ :1. Solve for x in the following system of equations: 42 yx 853 yxA. 127 xB. 712 xC. 1328 xD. 2813 x2. Micah has 4 more pencils than he has erasers.

9 If he has a total of 42 pen-cils and erasers, how many pencils does he have?A. 19B. 21C. 23D. 25 Practice:1. The perimeter of a rectangle is 31 inches, and the width is 10 inchesless than twice the length. What is the width of the rectangle?A. 7inB. 8inD. Adult tickets to a theme park cost $19 and childrens tickets cost $ cashier collected $632 from 40 park many adult attendants paid the cashier?A. 8B. 16C. 24D. 32 Systems of EquationsEOC REVIEWF ormulas you must know:Fill-in the following formulas. These are all formulas that you must be able to use on the EOCtest Tuesday. You will be quizzed on these formulas Wednesday so memorize these!1. Point-Slope Form: _____2. Slope-Intercept Form: _____3. Standard Form: _____4. Slope (given two points): _____5. Distance Formula (given two points): _____6. Midpoint Formula (given two points): _____7. Quadratic Formula: _____8. X-coordinate of the vertex of a quadratic: _____9.

10 Slope of a standard form linear equation: _____10. Direct Variation: _____11. Exponential Growth: _____Go sample items if you are looking for something to REVIEW tonight but GET AGOOD NIGHT S REST!Name_____ Period _____Formulas