Algebra 2CP Fall Final Exam

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1 Fall Final Exam Review (Revised 0) Alebra CP Alebra CP Fall Final Exam Can You Solve an equation with one variable, includin absolute value equations (. and.) Solve and raph inequalities, compound inequalities, and absolute value inequalities (. and.) Translate an alebraic expression into a variable expression (.) Solve a ormula or a variable (.) Set-up and solve a word problem usin one or more variables (.) Find the value o a unction at a number and at an expression (.) Find the slope, x-intercept and y-intercept o a linear equation (. and.) Find the slope o a line iven two points (.) Write a linear equation iven various inormation (.) Graph linear equations and inequalities and absolute value equations and inequalities (.-.7) Graph and solve a system o linear inequalities (.) Determine the number o solutions and solve a system o equations involvin two variables (. and.) Use the properties o exponents, includin neative exponents, to simpliy expressions (.) Add, subtract, multiply and divide monomials and polynomials (.) Divide polynomials by binomials, includin usin lon division and synthetic division (.) Factor polynomials (includin the sum/dierence o squares) usin the methods demonstrated in class (.) Simpliy radicals by usin perect cubes, squares, etc (7. and 7.) Simpliy radicals that have variables with exponents (7.) Simpliy expressions with ractional powers and apply laws o exponents to those powers (7.) Graph a square root unction and ive its domain and rane (7.) Add, subtract, multiply and divide with radicals, includin usin the conjuate to rationalize a denominator (7.) Solve a radical equation (7.7) Use y = a(x h) + k or y = ax + bx + c to ind the vertex, axis o symmetry, y-intercept and a raph (.) Find the zeros o a quadratic unction (. and.) Add, subtract, multiply and divide expressions containin i, includin simpliyin expressions (.) Solve a quadratic eqn. by actorin, completin the square, square root property and quadratic ormula (.-.) Use the discriminant ind the nature o the roots o a quadratic equation (.) Solve and raph a quadratic inequality (.8) Determine the maximum or minimum value or a parabola (.) Lookin at a raph determine i the raph represents on odd-deree polynomial or an even-deree polynomial and tell the number o real zeros and imainary zeros (.) Given a actor o a polynomial and ind the remainin actors (.9) Find all real zeros o a polynomial usin the raphin calculator an tell how many complex zeros exist (.8-.9) Find the sum, dierence, product and quotient o unctions (7.) Find the composition o unctions (7.) Find the inverse o a unction and raph the unction and its inverse (7.) Simpliy rational expressions (8-) Add, subtract, multiply and divide rational expressions (8-) and (8-) Find the asymptotes, the intercepts, and holes in the raph o a rational unction (8-) Reconize and solve direct, joint and inverse variation problems (8-) Solve rational equations (remember to check or excluded values) (8-)

2 Fall Final Exam Review (Revised 0) Alebra CP ) I q 0., r., s, and t r s t q ) Combine like terms: aba b, evaluate: ) Write an alebraic expression or the verbal expression: Seven less than the product o and some number. 8s s ) Solve: ) Solve the ollowin or the variable b : A hb b ) I x and y, evaluate: xy x 7) Solve: 9x 8) Solve: y 9) Write and solve an inequality or: The sum o twice a number and is at most 7. 0) Jane has $00 in her account. She spends $0 on roceries, $90 on a DVD player, and $ on as. Write an inequality to show Jane's expenditures and how much she has or other expenses, e. ) Graph the solution set o x 0 or x ) Solve: x ) Solve: m ) Given:,,,,,,, Determine the domain, rane, an i it's a unction or not ) Find i x x x ) Write the ollowin in Standard Form and identiy the intercepts: y x 7) Graph the equation: x 7y 8) Find the slope between:, and, 9) Write the slope o the line parallel to: y x 0) Find the equation o the line passes throuh, and is perpendicular to ) Graph: x y 8 ) Graph: y x y x 7 ) Solve the system: x y and y x ) Solve the system: x 7y and x y ) Graph: y x and x ; y x y 0.x y x 7 y x x, y x y ) Graph, ind the vertices o the easible reion, and then ind the maximum and minimum values or the reion: 7) Jim has bills in some combination o $, $, and $0. Those bills total $. He has twice as many $ bills than $0 bills. Write (not solve) a system o equations to represent this. 8) The table shows the minimum t Wae wae rom the Dept o Labor. Let t 0 $. be the number o years since $.80 Write a prediction equation and 0 $. estimate the wae or 0. $.7 9) Graph: y x x $. 0) Determine whether the ollowin has a maximum or a minimum, then ind that value: y x 8x ) Factor: 8x x 0x ) Factor: a a ) Factor: d d ) Factor: x 0x ) Factor: x x ) Factor: x 9y 7) Factor: x x 8) Factor: x 8 9) Factor: 8a 7 0) Solve: x 0x 8 0 ) Solve: x x 0 ) Solve: x x 9 ) Write an equation iven the roots: ) Simpliy: m ) Simpliy: 7 8 ) Simpliy: i 7) Multiply: i i, 8) Divide: 7 i i 9) Solve or m and n : 8mi ni 0) Solve: x x 0 0 ) What value should be added to each side to complete the square: x x

3 Fall Final Exam Review (Revised 0) Alebra CP ) What are the nature o the roots o the equation: x x 0 ) Find the vertex: x x ) Graph: y x x ) Solve: x x ) Simpliy: a b cab 7) Simpliy: 8 8m n m n 8) Express in Scientiic Notation: ) Simpliy: x 7x x 0) Simpliy: x x x ) Divide: x x x ) Reasonably raph: y x x ) Simpliy: a b a b ) Determine whether the deree o the unction is odd or even. How many dierent real zeros does the equation have? ) Given that x is a actor o x x x x, ind the remainin actors. ) List all real zeros o: x x x 0x 7) List the possible rational zeros o the ollowin: x x x x 8) Find x, iven: 9) Find x, iven: 70) Find x, iven: x x x x x x x x x x x x 7) Find x i x x 7) Given,,,,,,, Is R R, ind a unction? R. 7) Simpliy: 0 0 a b 7) Simpliy: ) Simpliy: 8 7) Simpliy: x x 77) Write in radical orm: 7 m 78) Write as a rational exponent: a 79) Simpliy: 9a 7 b 80) Simpliy: 8) Solve: x 0x 0 8) Solve: x x 0 8) Find and raph the real roots o: x x 8 0 8) Find the raph, domain, and rane o y x 8) Solve: 9x x 8) Solve: x 87) Solve: a 88) Simpliy: a b c a b c m n 89) Simpliy: 0m n 90) Simpliy: x x x x x x x 9) Simpliy: x x x x x 9) Simpliy: x x x 9) Simpliy: 9) Solve: s s 9) Solve: 9) Solve: x x x x x 8 x x x x x x x x x 8 x 97) Solve: x x

4 Fall Final Exam Review (Revised 0) Alebra CP 98) Indicate the least common denominator o the ollowin: a bc a c 99) Determine the equation(s) o any asymptotes and x any hole(s) in: x x x 00) Determine the equation(s) o any asymptotes x x and any hole(s) in: x x 0) Some variable y varies directly with the cube o x. I x when y, ind the constant o proportionality, k. 0) While standin on snow, the pressure (P, in pounds per square inch) varies inversely with the total area, A (in square inches) o the soles o your ootwear. Suppose the pressure is 0. pounds per square inch while wearin 00 in soled snow shoes. What would be the pressure while wearin 0 in soled boots? 0) I y varies jointly as x and z, and y when x. and z, then ind y when x.8 and z. 0) Identiy the type o unction represented in each raph: ANSWERS ). ) 9a b ) n 7 ) s ) A b b h ) 7) x or 8) y 9) x 7; x 0) 0 90 e 00 ) ) ) x m or m ) D:,,, R:,, yes ) ) x y 7) ;, 0 0, ; and 8) m 9) m 0) y x 9 ) ) ), ) 7, ) ),,,,,,, Max: 7 at,, ; Min: at o t 7) o 0t t 8) y 0.07x.890 $. in 0 9) 0) Maximum; at x x x x ) ) aa 7 ) d 7d ) x ) x x ) x yx y 7) x x 8) x x x 9) aa a 9 0) x, ) x 7 ) x 8,

5 Fall Final Exam Review (Revised 0) Alebra CP ) x x ) m i ) ) i 7) 0i 7i 8) 0 9) m ; n 0) x i ) 9 ) Real Roots ), ) ) x 8 ) 0a b c 9n 7) 7m 8) ) 0x x 0) x x 7x ) x 8x 9 x ) ) a b ab ) Even; dierent real zeros ) x x ) x,, 0 (double root) 7),,,,, 8) x x 9) x x 70) x 8 7) y x,,,,,,, ; 7) no 7) a b 7) 8 0 7) 7) 0 x 77) 7 m or 7 m 78) 79) a ab 9ab 80) 7 8) x, 8) x 9 8) x, 8) D: x and R: y 8) x or 8) No Real Solution 87) a a c 88) b 8m 89) n x 90) x x 9) x x 9) x 9) x 7 x x x 8 9) s, 9) x., 9) No Real Solutions 9 97) x ) a bc 99) Hole: x ; Asym: x 7; y 0 00) Hole: x 0) k 8 0).87 psi 0) y 8. 0) Cubic Function Square Root Function

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