HONORS PRE-CALCULAUS ACP Summer Math Packet

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Name Date Section HONORS PRE-CALCULAUS ACP Summer Math Packet For all incoming Honors Pre-Calculus ACP students, the summer math packet will be on the school website.

1 Name Date Section HONORS PRE-CALCULAUS ACP Summer Math Packet For all incoming Honors Pre-Calculus ACP students, the summer math packet will be on the school website. Students will need to print a cop of the packet and complete problems on the packet/notebook paper. HOW TO ACCESS SUMMER MATH PACKET HELP Go to Ms. Hampton s weebl page and navigate to the Honors Pre-Calculus ACP page. There ou will find the summer math packet again as well as videos to help with content. Videos will be labeled according to section headings. You ma also Ms. Hampton lhampton@iwacadem.org Once ou select the HONORS PRE-CALCULUS ACP page, scroll through to find the video ou need to help ou complete a section of the packet. SUMMER MATH PACKETS The purpose of the summer math packets is to review topics needed in the course ou are taking in the fall. The math department epects ou to review and know these topics as we start the new school ear. Ever summer math packet will be due on MONDAY, AUGUST 0 TH and worth 5 POINTS. A Summer Math Packet Summative Assessment will be due within the first two weeks of school worth 50 POINTS. Please the math department with an questions, iwamath@iwacadem.org or an of the math teachers.

2 Honors Pre-Calculus ACP _ rq0d1pv zkgu[tdaa ZSVoHfgtVwnafrLeR ELwLMCY.n H Aflel] Qr^iwgEhutosL erxemsnenrhvoehdy. 01 Summer Math Packet - Pre-Calculus CIRCLES: Graphing Identif the center and radius of each. Then sketch the graph. (HINT: Problem 3 & - Complete the square to put into General Form) 1) ( + 1) + ( - 3) = 9 ) ( - ) + ( + ) = ) = 0 ) = LINES: Writing equations Write the standard form of the equation of the LINE through the given points. 5) through: (-, ) and (-5, ) ) through: (1, -1) and (-5, -3) 7) through: (-, -1) and (0, -1) ) through: (-, -5) and (-, ) Worksheet b Kuta Software LLC

3 Write the standard form of the equation of each LINE. 9) 10) FUNCTIONS: Evaluating Evaluate each function. Problem evaluate with a numerical value. Problem evaluate with an epression. 11) g() = - 3; Find g(0) 1) p(a) = -3a ; Find p() 13) h(n) = 3 3n ; Find h(-1) 1) f (n) = n - 1; Find f (-5) 15) p() = ; Find p() 1) k() = -3 - ; Find k(n - 3) 17) h(n) = n 3 - n; Find h(-3n) 1) f (n) = n - 5; Find f (n + ) Worksheet b Kuta Software LLC

4 FUNCTIONS: Operations (Including Composition) Perform the indicated operation of functions. 19) h(n) = 3n + 3 g(n) = -n - Find (h + g)(n) 0) g(a) = a - 1 f (a) = a + a Find g(a) - f (a) 1) f () = g() = Find f () g() ) h(n) = n + g(n) = -3n Find ( h g) ( n) 3) h(n) = -n + 1 g(n) = n 3 - n Find (h g)(n) ) f () = - g() = - Find f (g()) 5) g(n) = 3n - 3 h(n) = n 3 - Find g(h(n)) ) f (n) = n - 3 g(n) = n + 1 Find f (g(n)) QUADRATICS: Graphing using transformations Identif the verte, ais of smmetr, -intercept, and -intercepts of each. Then sketch the graph using transformations. State the domain and range in interval notation. (HINT: Problem 9 & 30 - complete the square to put into verte form.) 7) = ( + 5) - 1 ) = - 1 ( - 3) Worksheet b Kuta Software LLC

5 9) = ) = RATIONAL FUNCTIONS: Graphing Characteristics Identif the holes, vertical asmptotes, -intercepts, -intercepts and horizontal asmptote of each. (HINT: Factor first!) 31) f () = ) f () = ) f () = 1-3 3) f () = RATIONAL EXPRESSIONS: Operations Simplif each epression. 35) 0-15r 3r - r - 3) ) 3 9r - 15r - 3 3r 3) Worksheet b Kuta Software LLC

6 POLYNOMIAL FUNCTIONS: Zeros Find all zeros using FACTORING. 39) f () = ) f () = ) f () = 3 - ) f () = LOGARITHMS/EXPONENTIAL: Rewriting Rewrite each equation in logarithmic form. 3) 11 b = a ) v = u Rewrite each equation in eponential form. 5) log 11 = n ) log 13 = LOG EQUATIONS: Solving Solve each equation. Remember to check for etraneous solutions. 7) 3 log 7 ( + ) = -3 ) 5 + log 9 = 9) ln ( + 3 ) = ln ( - 7) 50) log 0 (5a + 3) = log 0 (a - 1) 51) log 9 + log 9 3 = log ) log 7 - log 7 ( + 3) = log ) ln ( - 1) - ln 3 = 5) log 3 - log = 1 Worksheet b Kuta Software LLC

7 PROPERTIES OF EXPONENTS: Simplif. Your answer should contain onl positive eponents. 55) n m 3 n 5) m n - 57) ( -1 )0 5) ( 3-3 ) 59) 3 0) ) ) ( m -3 n ) m -3 n EXPONENTIAL EQUATIONS: Solving Solve each equation WITHOUT using Logs. (HINT: Rewrite each side as an epression using the same base.) 3) = 3 ) ( 1) 1 a = 3 5) 9 3k + = 3 3 ) k = 1 1 Solve each equation USING LOGS. Round our answers to the nearest ten-thousandth. 7) 5 n = 97 ) 5 = 9) e k =.5 70) 0. a - = 50 Worksheet b Kuta Software LLC

8 Answers to 01 Summer Math Packet - Pre-Calculus 1) Center: (-1, 3) Radius: 3 ) Center: (, ) Radius: 3 3) Center: (-, ) Radius: 3 ) Center: (3, 0) Radius: ) - = -1 ) - 3 = 7) = -1 ) = - 9) - 5 = 0 10) 3 + = 11) -3 1) 1 1) 15) ) -3n ) 7 17) -5n 3 + n 1) n + n ) -n + 1 0) -a + a - 1 1) ) -n - 3) -n 3 + n + 1, n ¹ 0 3n ) - + 5) -n 3-9 ) 1n + n - 7) Verte: (-5, -1) Ais of Sm: = -5 -int: (0, ) -int: (-, 0) (-, 0) Domain: (-, ) Range: [-1, ) - - ) Verte: (3, ) Ais of Sm: = 3 -int: ( 0, - 5 ) -int: (1, 0) (5, 0) Domain: (-, ) Range: ( -, ] Worksheet b Kuta Software LLC

9 9) Verte: (, -1) Ais of Sm: = -int: (0, -37) -int: No Real Domain: (-, ) Range: ( -, ] 30) Verte: (1, ) Ais of Sm: = 1 -int: (0, -) -int: (-1, 0) (3, 0) Domain: (-, ) Range: [, ) ) Vertical Asm.: =, = -1 Holes: None Horz. Asm.: = X-intercepts: 3, -3 3) Vertical Asm.: =, = Holes: = 0 Horz. Asm.: = 0 X-intercepts: None Y-intercept: 0 Y-intercept: ) Vertical Asm.: = 0, = 3 Holes: None Horz. Asm.: = 0 X-intercepts: None Y-intercept: None 3) Vertical Asm.: = -3 Holes: = Horz. Asm.: = X-intercepts: -1 35) - 5 r + 1 Y-intercept: 3 3) ( - r) ( - 7) 39) {3, -3, 1, -1} 37) 3) - 10 r(3r - 5) ( - )( - 1) 0) {0, -1, } 1) {, -1 + i 3, -1 - i 3 } ) {-5, i, i} 3) log 11 a = b ) log u = v 5) 11 n = ) = 13 7) { } ) { 3 9) {-1, } 50) {} } 51) { 17 5) No solution. 53) {3e } + 1} or ) {, -} 55) n 3 m 3 5) m 57) 1 n 5) ) 1 0) 3 3 1) 5 9 ) 1n10 3) m { } ) { - 3 } 5) { - 1 } ) { 1 3 } 70) ) ) ).703 Worksheet b Kuta Software LLC

WCCS Summer Math Packets School Year. Dear WCCS Students,

WCCS Summer Math Packets School Year. Dear WCCS Students, WS Summer Math Packets 0-07 School Year Dear WS Students, Please complete the summer math packet for the math class ou will be taking net school ear. Unless ou register within two weeks of the beginning