SOL AII.a The student, given rational, radical, or polnomial epressions, will a) add, subtract, multipl, divide, and simplif rational algebraic epressions; Hints and Notes Rules for fractions: ) Alwas factor an squared terms completel watch for greatest common factors ) Addition & Subtraction of fractions require a common denominator ) When dividing fractions flip the second fraction and multipl 4) Comple Fractions simplif numeration, simplif the denominator, then divide Recommended:,,,4,6,8 PRACTICE AII.a. Simplif: a a a a a a a a. Simplif: F. G. J. a a a a. Simplif: m m m m m m m m m Henrico Count Public Schools EOC Algebra II Review 0-0
PRACTICE AII.a 4. Multipl: 6 4 5 F. 4 7. Divide: 4 8. Simplif: 7 5 4 8 60 G. J. 4 4 5 5 4 5 5. Multipl: 4 9 6 4 0 6. Divide: 4 5 4 5 4 7 4 7 5 5 7 0 0 4 4 F. 4 G. F. G. 9 5 5 7 J. 5 9. Simplif: 64 6 8 6 8 6 5 8 69 0 4 664 4 8 4 J. 5 Henrico Count Public Schools EOC Algebra II Review 0-0
SOL AII.b The student, given rational, radical, or polnomial epressions, will add, subtract, multipl, divide, and simplif radical epressions containing rational numbers and variables, and epressions containing rational eponents; HINTS AND NOTES PRACTICE AII.b. Simplif: 6 7 9. Simplif: 5 8 F. 4 5 Simplif Radicals ) Take root of coefficient ) Divide eponents of radicand b the inde; answer outside, remainder inside G. J. 5 4 7 4 Recommended:,, 4, 6, 8, 9, 0,, 4. Simplif: 4 6 6 6 4 6 6 5 4 6 4. Simplif: 6 5 4 5 6 F. G. J. Henrico Count Public Schools EOC Algebra II Review 0-0
HINTS AND NOTES Adding & Subtracting Radical Epressions Onl radical epressions with like radicands (stuff under the radical) can be added or subtracted. PRACTICE AII.b 5. Simplif: 5 49 0 5 5 4 0 5 4 74 6. Simplif: 8 7 4 6 6 F. 4 7 G. 6 7 74 Rationalize Denominator inde or root is radicand is The radicand contains no fractions in the answer. No radicals can be in the denominator of the answer. J. 6 7 6 6 7. Rationalize the denominator: 4 4 4 4 8. Rationalize the denominator: F. G. J. 4 4 Henrico Count Public Schools 4 EOC Algebra II Review 0-0
HINTS AND NOTES Multipling & Dividing Radicals n n n a b ab n n a b n a b PRACTICE AII.b 4 4 9. Multipl: 9 0. Divide: F. 9 8 8 8 5 6 5 Conjugate pairs: a + b and a b Use to rationalize denominators. G. 8 5 8 5 Properties of Rational Eponents J. 6 5. Simplif: 4 ( 4 )( ). m n m n a a a. ( a ) a m n mn. ( ab) m a m b m 9 8 8 8 6 6 8 6 6 8 4. 5. 6. a a a m m n a b a a m m mn a b m m. Simplif: F. G. 4 4 6 4 9 4 ( )( 6 ) J. 4 6 Henrico Count Public Schools 5 EOC Algebra II Review 0-0
HINTS AND NOTES PRACTICE AII.b. Simplif: 7 4 6 9 7 9 4. Simplif: 7 8 7 F. G. J. 4 5 6 4 5 6 6 4 4 9 8 5 Henrico Count Public Schools 6 EOC Algebra II Review 0-0
SOL AII.c The student, given rational, radical, or polnomial epressions, will write radical epressions as epressions containing rational eponents and vice versa. PRACTICE AII.c. Rewrite 6 5 using rational eponents. Don t Forget: a a b a b b 6 5 6 5 5 6 Recommended:, 4 5 6. Rewrite 8 7 using rational eponents F. 8 7 G. 7 8 7 8 J. 8 7. Simplif and write in simplest radical form: 0 7 7 0 4. Simplif and write in simplest radical form: 5 5 5 F. 6 G. J. 6 6 5 5 Henrico Count Public Schools 7 EOC Algebra II Review 0-0
SOL AII.d The student, given rational, radical, or polnomial epressions, will factor polnomials completel. Was to Factor: PRACTICE AII.d. Which is the factored form of 64? ) Greatest Common Factor w ( w) ) Difference of Squares (4 )(4 4 ) (4)(6 ) (4 )(6 4 ) (4 )(6 4 ) a b a b a b ( )( ). Factor: 00 F. ( 50)( 50) ) Sum of Cubes* a b ( a b)( a ab b ) 4) Difference of Cubes* a b ( a b)( a ab b ) * (a [same sign] b)(a [opposite sign] ab [alwas positive] b ) 5) Trinomials 6) Factor b Grouping (leading coefficient) four terms 7) Completing the square Recommended:,, 6, 8, 9 G. ( 0)( 0) ( 0)( 0) J. ( 5)( 4). Factor: 4. Factor: 9 6 9 6 9 ( 7 ) 5 8 ( 7 ) 6 ( 7 ) 6 (9 ) 7 4 F. ()( 4) G. (4)( ) ()( 4) J. ()( 4) Henrico Count Public Schools 8 EOC Algebra II Review 0-0
PRACTICE AII.d 5. Factor: ( )( ) ( )( ) ( )( ) ( )( ) 9. Factor: ( b 4) b 64 ( b4)( b4)( b 4) ( b 4)( b 4b 6) ( b 4)( b 4b 6) 6. Factor: 8u u F. (6u)( u ) G. (6u)( u ) (6u)( u ) J. (6u)( u) 0. Find the term that must be added to both sides of the equation so that the equation can be solved b the method of completing the square F. 6 G. 64 8. 7. 8. 5 represents the area of a rectangle. Which of the following could represent the length of one side of the rectangle? 4 5represents the area of a rectangle. Which of the following could represent the length of one side of the rectangle? F. G. J. J.. Find the term that must be added to both sides of the equation so that the equation can be solved b the method of completing the square 8 9 6-9 6 9. Henrico Count Public Schools 9 EOC Algebra II Review 0-0
AII. The student will investigate and appl the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the n th term, and evaluating summation formulas. Notation will include Σ and a n. Term Formulas A: a a ( n ) d G: n a a r n n Sum Formulas A: G: S n a a n ( ) ( n a ) r S r a IG: S r If ou forget the formulas, just list series out and count terms or add terms on calculator. Recommended,,, 4, 6 PRACTICE AII.. Insert two arithmetic means between - and., 0, 8, 9 4, 7. Evaluate: F. 984 G. 000 05 J. 050 5 n (n ). Which is an arithmetic sequence?, 5, 9, 4... 00, 50,.5,.6..., 0, 7, 4... -8, -4, -, -... 4. If a () n a? n F. G. 8 4 J. 7 which of the following represents 5. Which of the following represents (n )? 6 69 9 9 8 n 6. Find the net term in the sequence 8, 5,, -. F. - G. - -4 J. -5 Henrico Count Public Schools 0 EOC Algebra II Review 0-0
SOL AII. The student will perform operations on comple numbers,. epress the results in simplest form using patterns of the powers of i, and identif field properties that are valid for the comple numbers. Calculator (TI-8 or TI-84) Use i button on the calculator, however remember to use the parentheses to separate operations. EX. i i ( i) ( i) Don t Forget: i PRACTICE AII.. Simplif: i i 5i. Simplif: F. G. 47 65 65 i 47 65 65 i 4i i 5i 7 4i Recommended:, 4, 7, 8,0,, J. 47 65 65 i 47 65 65 i. Simplif: 7 i 8 i 57 i 65 57 i 65 57 i 65 57 i 65 Henrico Count Public Schools EOC Algebra II Review 0-0
PRACTICE AII. 4. Simplif: ( 5 i)(8 i) 46i F. G. 4i J. 4i 46i 5. Simplif: ( 7 i )( 9 4 i ) 7 59i 9 59i 9 67i 7 67i 6. Simplif: (8 i) (7 6 i) F. 0 i G. 0 i 69 8i J. 4 4i 7. Simplif: (6 6 i ) ( i ) 7 8i 7 8i 6 8i 5 4i 8. Simplif: ( 4 i) (5i 6) F. 4 i G. 9 4i 8 4i J. 5i Henrico Count Public Schools EOC Algebra II Review 0-0
PRACTICE AII. To simplif powers of i Change to ( i ) to (- ) ( i ) Power then change 9. Simplif: i i 44 i Eample i ( i ) i ( ) i ( ) i i 0. Simplif: F. G. J. i i 7 i Don t Forget: i. Write the given epression in terms of i : 8i i i 8 i 8.. Write the given epression in terms of i : 64. 8 F. G. 8i 8i J. 8. Simplif: i 07 i i Henrico Count Public Schools EOC Algebra II Review 0-0
SOL AII.4a The student will solve, algebraicall and graphicall, absolute value equations and inequalities. Graphing calculators will be used for solving and for confirming the algebraic solutions. To Solve Absolute Value Equations Set = to positive value Set = to negative value To Solve Absolute Value Inequalities. Write equation as is. Write equation, switch inequalit smbol, change to negative value PRACTICE AII.4a. Which graph represents the solution of - - 0 4 5 6 - - 0 4 5 6 - - 0 4 5 6-6 -5-4 - - - 0. Solve: 6 0 0 F. and G. 4 0 J. no solution 4 6 9? To Graph Absolute Value Inequalities GreatOR Than Less ThAND OR. (Open Left & Right) (Closed Left & Right). Solve: 4 5, 5,,, (Open Between) (Closed Between) Recommended:,,, 4 4. Solve and Graph: 5 9 F. 8 7 6 5 4 0 G. 8 7 6 5 4 0 8 7 6 5 4 0 J. 8 7 6 5 4 0 Henrico Count Public Schools 4 EOC Algebra II Review 0-0
SOL AII.4b The student will solve, algebraicall and graphicall, quadratic equations over the set of comple numbers; Graphing calculators will be used for solving and for confirming the algebraic solutions. Methods for Solving Quadratics. Factor. Complete the Square. Square Root Method 4. Quadratic Formula b b 4ac a negative number use i Calculator Hints: To Find Roots, Solutions, Zeros. Graph quadratic in =. Press nd Trace. Press # for zeros 4. Left Enter 5. Right Enter 6. (Guess) Enter Recommended:,,4,6,7,8,0, PRACTICE AII.4b. Solve:,, 4,,. Solve: F., G. i. i, 4 4 0 4 8 J. i, i. Solve:,,,. 4. Solve: F., G., 0 ( ) 8, J. No Solution Henrico Count Public Schools 5 EOC Algebra II Review 0-0
PRACTICE AII.4b 5. Solve: 4 0 4 4, 4, 4 4, 4 4 4, 6. Solve: 0 0 F. G. 5,,5 5, J. 5, 7. Solve: 6 5 i 5 8. Which statement is true for the quadratic 0 4 48? F. The product of the roots is 4. G. The product of the roots is 4. The sum of the roots is 4. J. The sum of the roots is. Henrico Count Public Schools 6 EOC Algebra II Review 0-0
PRACTICE AII.4b Describe nature of roots. You can graph the quadratic in the calculator look for the number of times the graph touches the -ais. Touches once One real solution Touches twice Two real solutions Does not touch Two Imaginar solutions. Use the discriminant b 4ac Discriminant > 0 Two real solutions Discriminant < 0 Two imaginar solutions Discriminant = 0 One real solution 9. Find the quadratic equation with roots and 5 7 6 0 5 7 6 0 5 7 6 0 5 7 6 0 0. Find the quadratic equation with roots and F. G. J. 5 0 5 0 5 0 5 0. Describe the nature of the roots of the equation 0. One real root Two imaginar roots One real root and one imaginar root Two real roots. Describe the nature of the roots of the equation 4 4 5 0. F. Two imaginar roots G. Two real roots One real root J. One real root and one imaginar root 5 5.. Henrico Count Public Schools 7 EOC Algebra II Review 0-0
SOL AII.4c The student will solve, algebraicall and graphicall, equations containing rational algebraic epressions; Graphing calculators will be used for solving and for confirming the algebraic solutions. PRACTICE AII.4c Solve a rational equation. Determine the least common denominator.. Eliminate the fraction(s) b multipling ALL terms b the least common denominator.. Simplif the terms. 4. Solve the resulting equation. 5. Check our answers to make sure the solution does not make the fraction undefined.. Solve: = 8 5 = = 4 5 = 4 = 4. Solve: m m+6 = m+9 m F. m = 5 Recommended:,,, 4 G. m = 5 m = J. m = 5. Solve: 5 4 = = 5 6 = 7 = 6 7 = 7 6 Henrico Count Public Schools 8 EOC Algebra II Review 0-0
PRACTICE AII.4c 4. Solve: a + = 5 a 5 a 5 a+5 F. a = 5 G. a = 40 a = 40 J. a = 0 5. Solve: 5 = 7 +4 + 8 = = 5 7 = 9 7 = 5 Henrico Count Public Schools 9 EOC Algebra II Review 0-0
SOL AII.4d The student will solve, algebraicall and graphicall, equations containing radical epressions. Graphing calculators will be used for solving and for confirming the algebraic solutions. PRACTICE AII.4d Solve a radical equation. Isolate the radical. Square or cube both sides. Check for etraneous solutions Solve a rational eponent equation. Isolate the epression with rational eponent. Raise both sides to reciprocal eponent power. Check for etraneous solutions. Solve: 4 0 5 0 and no solution. Solve: F. 7 G. 7 5 9 7 and 7 J. 0 and 7. Solve: 4 7 7 7 7 and Henrico Count Public Schools 0 EOC Algebra II Review 0-0
SOL AII.5 The student will solve nonlinear sstems of equations, including linear-quadratic and quadratic-quadratic, algebraicall and graphicall. Graphing calculators will be used as a tool to visualize graphs and predict the number of solutions. PRACTICE AII.5. How man solutions are there for this sstem? Number of solutions Number of points of intersection on graph 0 Remember ou can also plug in values to BOTH equations to see which ordered pairs make BOTH equations true!. Solve: 4 7 F. (-4, -4) G. (4, 5) (5, 8) J. (-4, -9). Which is the solution to the sstem below? {(0, 7),(0,7)} {( 7,0),(7,0)} {(0, 5),(0,5)} 4. Solve the sstem graphicall: 49 64 8 F. {(0, 8),(0,8)} G. {(0, 9),(0,9)} J. {( 8,0),(8,0)} Henrico Count Public Schools EOC Algebra II Review 0-0
SOL AII.6 The student will recognize the general shape of function (absolute value, square root, cube root, rational, polnomial, eponential, and logarithmic) families and will convert between graphic and smbolic forms of functions. A transformational approach to graphing will be emploed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions. = = PRACTICE AII.6. Which of the following is the graph of a quadratic? = = = =. Which of the following could represent =? F. G. J. Henrico Count Public Schools EOC Algebra II Review 0-0
For the functions below, use these rules to translate the graph: h>0 shifts right h units h<0 shifts left h units k>0 shifts up k units k<0 shifts down k units a<o reflects across ais change to, reflects across ais PRACTICE AII.6. Which of the following is most likel the equation represented b this graph? 4 4. Given the graph: 5 4 5 4 4 5 4 5 Write an equation for it using a translation of =. F. G. J. Henrico Count Public Schools EOC Algebra II Review 0-0
PRACTICE AII.6 5. Which most likel represents the equation of the graph below? 6. What could be the graph of + = ( + )? F. G. 4 4 4 J. 4 4 4 4 Henrico Count Public Schools 4 EOC Algebra II Review 0-0
SOL AII.7a The student will investigate and analze functions algebraicall and graphicall. Ke concepts include domain and range, including limited and discontinuous domains and ranges. Graphing calculators will be used as a tool to assist in investigation of functions. domain: values range: values Eliminate values in domain and range when: PRACTICE AII.7a. If the domain of is limited to {-, -,, }, what is the range? {-, -5, -, 5 {-, 5} {-, 5} {, 5, 5, }. State the domain and range of this graph: division b zero radicand (number under radical) is negative F. Domain:, Range: { } G. Domain: { }, Range: Domain: { > - and < }, Range: J. Domain:, Range: { }. Find the domain of. all real numbers ecept = and = - all real numbers ecept = and = all real numbers ecept = - and = all real numbers ecept = - and = - 4. Find the domain of. F. all real numbers ecept = G. all real numbers ecept = and = - all real numbers ecept = - J. all real numbers 5. Find the domain of f ( ) log( ). F. real : G. real : real : J. real : Henrico Count Public Schools 5 EOC Algebra II Review 0-0
SOL AII.7b. The student will investigate and analze functions algebraicall and graphicall. Ke concepts include zeros. Graphing calculators will be used as a tool to assist in investigation of functions. PRACTICE AII.7b Zeros when f() = 0 when graph crosses or touches the ais counting multiplicit, number of real and non-real zeros = n (degree of polnomial) number of real zeros < n (degree of polnomial) factor polnomial to find zeros graph to find real zeros. What are the zeros of? and and - and and. Which is a zero of the function f() = - - 6? F. 0 G. 6 J. -6. Find all the real zeros of the function. 0,, 6 0, 0,, 7, 6 7 56 84 4 Non-real zeros come in comple conjugate pairs (so there is alwas an EVEN number of non-real zeros) 4. Describe the zeros of the polnomial (counting 6 5 4 multiplicit.) p( ) 9 4 4 4 F. real, imaginar G. 6 real, 0 imaginar 4 real, imaginar J. real, 4 imaginar Henrico Count Public Schools 6 EOC Algebra II Review 0-0
SOL AII.7c The student will investigate and analze functions algebraicall and graphicall. Ke concepts include - and - intercepts. Graphing calculators will be used as a tool to assist in investigation of functions. and intercepts To find the -intercept, plug in zero for. To find the -intercept, plug in zero for. PRACTICE AII.7c. Determine the - and -intercepts of the function p ( ) -intercept (,0), -intercept (0, ) -intercept (,0), -intercept (0,) -intercept (,0), -intercept (0,) -intercept (,0), -intercept (0, ). Locate an - and -intercepts of the function p. ( ) 4 F. -intercepts ( 0.85,0), (.5,0), -intercept (0, 4) G. -intercepts ( 0.85,0), (.5,0), -intercept (0, 4) -intercepts (0.85,0), (.5,0), -intercept (0, 4) I. -intercepts ( 0.85,0), (.5,0), -intercept (0,4). Locate an - and -intercepts of the function p( ) log( ). (4,0) (9,0), (0,) (4,0), (0,) (0,) Henrico Count Public Schools 7 EOC Algebra II Review 0-0
SOL AII.7d The student will investigate and analze functions algebraicall and graphicall. Ke concepts include intervals in which a function is increasing or decreasing. Graphing calculators will be used as a tool to assist in investigation of functions. Practice AII.7d. For what values of is this function increasing? Increasing Function - -value increases as the -value increases (left to right) Decreasing Function -value decreases as the -value increases (left to right) 8 6 4 0 8 6 4 0 8 6 4 0 8 6 4 4 6 8 0 4 6 8 0 4 6 8 (-4, ) (, ) (-,-4) and (, ) (-, ). For what intervals is this function decreasing? 4 4 4 4 F. (0,) and (,) G. (-,0) and ((,) (-,0) and (, ) J. (,) and (, ) Henrico Count Public Schools 8 EOC Algebra II Review 0-0
SOL AII.7e The student will investigate and analze functions algebraicall and graphicall. Ke concepts include asmptotes. Graphing calculators will be used as a tool to assist in investigation of functions. Vertical Asmptotes Possible to have multiple vertical asmptotes Vertical asmptotes are when the denominator = 0 Factor denominator Practice AII.7e. What are the vertical asmptote(s) for the function? = -, = ½ = - ½, = = = -, = Horizontal Asmptotes One or no horizontal asmptote. What is the horizontal asmptote for the function? F. = 0 TEST Horiz As G. = 5 degree numerator < =0 degree denominator = J. none degree num = degree denom degree num > degree denom = leading coeff num leading coeff denom none (ma have slant asmptote). Which of the following functions will have a horizontal asmptote at =? Henrico Count Public Schools 9 EOC Algebra II Review 0-0
SOL AII.7f The student will investigate and analze functions algebraicall and graphicall. Ke concepts include end behavior. Graphing calculators will be used as a tool to assist in investigation of functions. End Behavior Use term with highest eponent + coefficient - coefficient Even degree Odd degree Leading coefficient: LC > 0: up to right LC < 0: down to right Degree: Even: same end behaviors Odd: opposite end behaviors PRACTICE AII.7f. Determine the end behavior of the graph of 4 f ( ). Down to the left, Up to the right Up to the left, Down to the right Up to the left, Up to the right Down to the left, Down to the right. Determine the end behavior of the graph of f. 5 ( ) 6 4 5 F. Down to the left, Up to the right G. Up to the left, Down to the right Up to the left, Up to the right J. Down to the left, Down to the right. Determine the end behavior of the graph of f. 6 ( ) 4 Down to the left, Up to the right Up to the left, Down to the right Up to the left, Up to the right Down to the left, Down to the right 4. Determine the end behavior of the graph of 5 f ( ) 7 4 5. F. As, f ( ), As, f ( ) G. As, f ( ), As, f ( ) As, f ( ), As, f ( ) J. As, f ( ), As, f ( ) Henrico Count Public Schools 0 EOC Algebra II Review 0-0
SOL AII.7g The student will investigate and analze functions algebraicall and graphicall. Ke concepts include inverse of a function. Graphing calculators will be used as a tool to assist in investigation of functions. To find an inverse ) Switch and ) Solve for Graph of inverse function f - () is reflection of f() across the graph =. PRACTICE AII.7g. If, find the inverse of f(). A.. Find the inverse given the function f ( ) 5 9. F. 5 9 G. 9 5 ( 9) 5 J. 5 9 Everthing switches for inverse (domain becomes range, - intercepts become -intercepts horizontal asmptotes become vertical asmptotes, etc.) Ordered pairs switch (,) to (,). Which graph represents a function and its inverse? 6 5 4 4 4 4 5 6 6 5 4 4 4 4 5 6 4 4 6 5 4 4 4 5 6 6 5 4 4 4 5 6 Henrico Count Public Schools EOC Algebra II Review 0-0
Logarithmic and Eponential Functions Eponential and logarithmic functions are inverses of each other. The inverse of is f ( ) a f ( ) log a Eponential functions h f ( ) a k horizontal asmptote k, domain all real numbers, range k PRACTICE AII.7g 4. The graph of f ( ) log Identif the point that corresponds to the point A and lies on the graph of the inverse function f ( ) (,0) (,0) (0, ) (0,) is shown. 5. Which statement below best describes the endbehavior for the function m ( ) 0. As, m( ) As, m( ) As, m( ) As, m( ) Logarithmic functions f ( ) log a h k vertical asmptote h domain h range all real numbers Henrico Count Public Schools EOC Algebra II Review 0-0
SOL AII.7h The student will investigate and analze functions algebraicall and graphicall. Ke concepts include composition of multiple functions. Graphing calculators will be used as a tool to assist in investigation of functions. Composite Functions f(g()) is equivalent to (f g)() To find f(g()): Substitute the entire epression for g() into all of the s in the epression for f(). Practice AII.7h. If and, which is correct?. If and, which is the value of? F. -5 G. 48-00 J. -50. Find and. = = = = 4. Find. F. G. = J. Henrico Count Public Schools EOC Algebra II Review 0-0
SOL AII.8 The student will investigate and describe the relationships among solutions of an equation, zeros of a function, -intercepts of a graph, and factors of a polnomial epression. PRACTICE AII.8 Equivalent statements: k is a real zero or root of the polnomial function (-k) is a factor of f() k is a solution of the polnomial equation f()=0 k is an -intercept for the graph = f() Note that a polnomial equation ma also have nonreal ( imaginar ) solutions. These roots come in comple conjugate pairs. If a root occurs an even number of times when a polnomial is factored, the graph will touch the -ais and turn around rather than crossing the -ais.. Which could be the graph of f() = ( )( )?. Which could the equation for the polnomial function whose graph is shown? F. ( )( ) G. ( )( ) J. 4 4 ( )( ) ( ) ( ) 4 4. What is a possible factored form of a polnomial whose roots are 0, i, /5, 4, -/ and -i? ( 4)( 4)( 5)( ) ( 4)( 4)( 5)( ) ( 4)( 4)(5 )( ) ( 4)( 4)( 5)( ) Henrico Count Public Schools 4 EOC Algebra II Review 0-0
Imaginar roots must be conjugate pairs (a + bi) (a bi PRACTICE AII.8 4. Give the possible number of imaginar roots for:. F. 5 G. 4 J. 5. Find all of the roots of 4 0, i, i,, i, i 6. Write a polnomial function with zeros at -5, - and. F. G. J. 7. Find all of the zeros of..6, -.6, - -.6, -, -.6, 8. A polnomial equation with rational coefficients has the roots. Find two additional roots. F G. J. Henrico Count Public Schools 5 EOC Algebra II Review 0-0
SOL AII.9 The student will collect and analze data, determine the equation of the curve of best fit, make predictions, and solve real-world problems, using mathematical models. Mathematical models will include polnomial, eponential, and logarithmic functions. Negative slope & correlation PRACTICE AII.9. Determine the correlation for the scatter plot. Strong positive correlation. Strong negative correlation. No correlation Not enough information given. Positive slope & correlation Curve of best fit: TI Calculator:. Put data into lists. Look at the given scatter plot. This data best fits what tpe of equation? F. Linear G. Eponential Logarithmic J. Quadratic Stat-edit-L -L. Turn Stat-plot on and zoomfit to view scatterplot. Stat-calc: Select tpe of curve 4. Scroll down to Store RegEq and insert Y (vars menu) 5. Equation for curve of best fit is. 6. To plug in value: in regular screen: Y(number). Which of the following equations represents the line of best fit for the following data? X 6 6 4 44 44 45 64 Y 5 5 6 8 9 9 5 4.8 0.5 0.4 0.4.4.4 Henrico Count Public Schools 6 EOC Algebra II Review 0-0
PRACTICE AII.9 4. The table shows the approimate number of microbes in a petri dish in the first 6 hours. Using an eponential curve of best fit, What is our best prediction for the number of microbes in the tenth hour? HOUR (X) Number of Microbes (Y) 0 60 490 4 00 5 050 6 400 F. 40,800 G.,00 5,000 J. 70,400 5. Which is most likel the equation for the curve of best fit for the scatterplot below? Henrico Count Public Schools 7 EOC Algebra II Review 0-0
SOL AII.0 The student will identif, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations. PRACTICE AII.0 Inverse Variation varies inversel with k k Direct Variation varies directl with k k Joint Variation z varies jointl with and z = k k = z. The area (A) of a circle varies directl as the square of the radius (r). If k is the constant of proportionalit, which is the formula for this relationship? k A r A kr A kr r ka. The frequenc of a radio signal varies inversel as the wave length. A signal of frequenc 00 kilohertz (khz), which might be the frequenc of an AM radio station, has a wave length 50 m. What frequenc has a signal wave length of 400m? F. 8 khz G. 750 khz 50 khz J. 90 khz. Suppose that varies jointl with w and and inversel with the cube of z. Write the equation that models the relationship. kz w k wz kw z kw z Henrico Count Public Schools 8 EOC Algebra II Review 0-0
SOL AII. The student will identif properties of a normal distribution and appl those properties to determine probabilities associated with areas under the standard curve. Normal Distribution PRACTICE AII.. Grades on an Algebra test follow a normal distribution with a mean of 74 and a standard deviation of. Approimatel what percentage of the students have scores below 50? 4% 4% 0% %. Grades on an Algebra test follow a normal distribution with a mean of 8 and a standard deviation of 8. How man of the 5 students scored above a 90%? Standard Normal Distribution Mean = μ = 0 Standard Deviation = σ = z-score 4 students 9 students students not enough information. Susan scored a 8 on the math portion of the ACT which had a μ=0 and σ =5. She scored a 60 on the math portion of the SAT which had a μ=500 and a σ =80. Which test score has the higher percentile and what was that percentile? ACT, 94.5% SAT, 94.5% ACT, 98.4% SAT, 98.4% z-score reflects how man standard deviations it is above or below the mean Henrico Count Public Schools 9 EOC Algebra II Review 0-0
SOL AII. The student will compute and distinguish between permutations and combinations and use technolog for applications. PRACTICE ALGII. Fundamental Counting Principle Event M can occur in m was and event N can occur in n was, then event M followed b event N can occur in m n was. Permutation Number of was to arrange items - order matters. Combination Number of was to arrange items - order does not matter. Permutation > Combination. Mama Mia s Pizza offers three crust choices, twelve topping choices, and five cheese choices. If a customer can choose one crust choice, one topping, and one cheese choice, how man different pizzas are available? 0 pizzas 60 pizzas 6 pizzas 80 pizzas. How man different basketball teams of five plaers can be chosen from a team of siteen plaers? F. 4,68 teams G. 54,60 teams 80 teams J. 6 teams. The Technolog Club is electing officers. If there are to be four officers elected out of the thirt members, how man different possible election results are there? A 7,405 outcomes 6,80 outcomes 657,70 outcomes 0 outcomes 4 How man different five card hands can be dealt from a standard deck of fift-two cards?,598,960 hands,875,00 hands 60 hands 70,75 hands 5. How man was can a committee with teachers and students be selected from a club of 5 teachers and students? 0 was 00 was 7900 was 60 was Henrico Count Public Schools 40 EOC Algebra II Review 0-0
Answer Ke and Comments AII.a Assignment:,,, 4, 6, 8. B. J. C 4. G 5. A 6. F 7. C 8. J 9. C AII.b Assignment:,, 4, 6, 8, 9, 0,, 4. C. F. C 4. J 5. C 6. G 7. D 8. J 9. D 0. H. C. G. B 4. G AII.c Assignment:, 4. C. G. B 4. F AII.d Assignment:,, 6, 8, 9. C. H. C 4. H 5. B 6. J 7. B 8. H 9. C 0. F (completing the square). B (completing the square) AII. Assignment:,,, 4, 6. B. H. C 4. G 5. C 6. H AII. Assignment:, 4, 7, 8, 0,,. A. F. D 4. J 5. C 6. G 7. D 8. G 9. A 0. H. D. H. B AII.4a Assignment:,,, 4. B. F. A 4. F Number line problems can be solved just b knowing whether interval or, open or closed intervals (filled in circles) AII.4b Assignment:,, 4, 6,7,8,0, (time-consuming). A. J. A 4. F 5. B 6. G 7. A 8. G 9. D 0. G. D. F AII.4c Assignment:,,, 4. C. F. D 4. G 5. C AII.4d Assignment,,. A. G. A AII.5 Assignment,?,. C. G. C 4. H Solve and 4 b plugging in and values. Henrico Count Public Schools 4 EOC Algebra II Review 0-0
AII.6 Assignment,,, 4. C. H. B 4. J 5. B 6. H Should be fast problems AII.7a Assignment,,, 4, 5. C. G. A 4. J 5. G AII.7b Assignment,,, 4. A. J. A 4. H AII.7c Assignment,,. D. G. B AII.7d Assignment,. C. J. B best answer. B 4. J 5. A 6. F 7. A 8. J AII.9 Assignment,,, 4, 5. B. G. B 4. J 5. C AII.0 Assignment,,. C. G. C AII. Assignment,,. D. A. A AII. Assignment,,, 4, 5. D. F. C 4. A 5. B AII.7e Assignment,,. B. F. B AII 7f Assignment,,, 4. C. F. D 4. G AII.7g Assignment,,, 4, 5. C. G. D 4. D 5. C AII.7h Assignment,,, 4. A. J. B 4. J AII.8 Assignment,, 6, 7. B Henrico Count Public Schools 4 EOC Algebra II Review 0-0
Henrico Count Public Schools 4 EOC Algebra II Review 0-0