SUMMER ASSIGNMENT STUDY PACKET Calculus

Transcription

1 SUMMER ASSIGNMENT STUDY PACKET Calculus Dear Calculus student, This summer assignment will enable ou to be successful in knowing prerequisites for our net course. The content and philosoph of this summer assignment is consistent with our departmental goals for all high school students: The summer assignment will enable ou to: () value mathematics () become confident in our abilit to do mathematics () become a mathematical problem solver () communicate mathematicall () reason mathematicall This summer assignment will be reviewed the first week of school. You are responsible for knowing how to solve ever single problem. The problems should be done in chronological order. Each problem should include a summar of the problem statement, a complete step-b-step solution, and a boed final answer. You should not use a calculator to do the problems, but ou ma use our calculator to check our answer. Calculator ma onl be used in problems through, through, and 7 and 7. You will take a quiz on this summer packet stud material on Frida of the first week. The quiz will consist of approimatel twent (0) free-response questions (no multiple choice, matching, etc.); ou will not be able to use a calculator on the test. This will count as a quiz grade for the first quarter. If ou do not know how to solve a problem, ou are epected to use the sources available to ou (notes, handouts, books, Internet, etc.) to figure it out independentl. The best stud routine during the summer months is to constantl review topics and do a few problems each da, do not attempt to do the entire packet the da before school starts. You can also get help the week before school starts from :00 pm to :00 pm. If ou need eamples to help ou remember concepts or skills, ou can go to Khan Academ where ou will find similar problems to the ones in our summer assignment. If ou have questions, me at leticia.garcia@asfg.edu.m Enjo our summer and do our best! Sincerel, The ASFG Math Department

2 -- Calculus Summer Assignment Name Date Period Use the information provided to write the general conic form equation of each circle. ) ( + ) + ( 0) = Identif the center and radius of each. Then sketch the graph. ) + + = 0 ) + + = 0 Classif each conic section, write its equation in standard form, and sketch its graph. ) = 0

3 -- Identif the verte, focus, and directri of each. Then sketch the graph. ) = + Convert each degree measure into radians and each radian measure into degrees. ) 9π 7) 0 ) 7π 9) 7π Find a positive and a negative coterminal angle for each given angle. 0) ) Find the reference angle. ) π ) 0π 9 ) 7π ) π Simplif each and state the ecluded values. ) n n 0n + n n + 9 n + 7) p p + p 0 p p p p + 0 Solve each equation b completing the square. ) n 9n 79 = n + 7n 9) + =

4 -- Solve each equation b factoring. 0) 9r = 7r ) m + m = ) + = 7 ) n = n Factor each completel. ) 9 ) n m ) ) u v ) 9) + 0) 7u + v ) 00 + ) m m + m 0 ) n n n + ) 9k + k 0 ) 9a + 7a ) 9m 7m + 0m 7) p p

5 -- Using radians, find the amplitude and period of each function. Then graph. ) = + tan ( θ + π ) 9) = sin ( θ π ) + π π π π π π π π Graph each function using degrees. 0) = cos (θ + ) Solve each triangle. Round our answers to the nearest tenth. ) In ΔRPQ, p = 0 km, r = km, q = 7 km ) In ΔQRP, r = ft, p = 0 ft, m Q = 0 ) In ΔABC, m A =, m B = 0, c = ft ) In ΔBCA, m B = 7, m A =, c = 7 cm Solve each equation. ) log 0 + log ( ) = ) log ( ) log =

6 -- Find each product. 7) (m + n) ) ( ) 9) ( ) 0) (m + n)(m n) Evaluate each epression. ( ) ) ( ) + 7 ) 7 + (( )( 0))(( )( 9)) ) (( 7 9)(( )( )))(( 7 0) ( ) ) ) ( ( ))(( )( )) Simplif each epression. ) p p p ) ) m + m 7 m 7m ) 7 n 0n + n + 9) 9 0) a + In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest tenth. ) m B = 9., a =. in ) b =. cm, m A = ) m B = 0, a =. km ) m B =, a =. mi

7 -- Simplif. ) ) ) ) 0 9 Sketch the graph of each function. 9) = 70) = ( ) Identif the domain and range of each. Then sketch the graph. 7) = log ( ) +

8 -7- Sketch the graph of each function. State the number of real zeros. Approimate each zero to the nearest tenth. 7) f () = ) f () = + Sketch the graph of each line. 7) + 0 = 7) + = 0 0

9 -- Calculus Summer Assignment Name Date Period Use the information provided to write the general conic form equation of each circle. ) ( + ) + ( 0) = = 0 Identif the center and radius of each. Then sketch the graph. ) + + = 0 Center: (, 0) Radius: 7 ) + + = 0 Center: (0, ) Radius: Classif each conic section, write its equation in standard form, and sketch its graph. ) = 0 Ellipse ( + ) + ( ) 9 =

10 -- Identif the verte, focus, and directri of each. Then sketch the graph. ) = + Verte: (, ) Focus: (, 7 ) Directri: = Convert each degree measure into radians and each radian measure into degrees. ) 9π 7) 0 π ) 7π - 9) 7π -70 Find a positive and a negative coterminal angle for each given angle. 0) and 9 Find the reference angle. ) and 7 ) π π ) 0π 9 π 9 ) 7π π ) π π Simplif each and state the ecluded values. ) n n 0n + n n + 9 n + n n + ; {,, } 7) p p + p 0 p p p p + 0 p 0 p(p + 0) { ; 0,, 0 Solve each equation b completing the square. ) n 9n 79 = n + 7n { + 7, 7 } 9) + = {, }

11 -- Solve each equation b factoring. 0) 9r = 7r {, 7 } ) + = 7 {, 7 } Factor each completel. ) m + m = {, } ) n = n {, 7 } ) 9 ) n m ( + )( ) (n + m)(n m) ) ) u v ( + ) (u + v)(u v) ) 9) + ( )( 0 + ) ( + )(9 + ) 0) 7u + v (u + v )(9u u v + v ) ) 00 + ( + )( + ) ) m m + m 0 (m + )(m ) ) 9k + k 0 (k )(k + 0) ) 9m 7m + 0m m(m )(m ) ) n n n + (n )(n ) ) 9a + 7a (a )(a ) 7) p p p(p )

12 -- Using radians, find the amplitude and period of each function. Then graph. ) = + tan ( θ + π ) 9) = sin ( θ π ) + Amplitude: None Period: π Amplitude: Period: π π π π π π π π π Graph each function using degrees. 0) = cos (θ + ) Solve each triangle. Round our answers to the nearest tenth. ) In ΔRPQ, p = 0 km, r = km, q = 7 km m R =, m P =, m Q = 0 ) In ΔABC, m A =, m B = 0, c = ft m C =, a = 0 ft, b = 7 ft ) In ΔQRP, r = ft, p = 0 ft, m Q = 0 m R = 0, m P = 90, q = ft ) In ΔBCA, m B = 7, m A =, c = 7 cm m C = 0, a =.9 cm, b = 9.9 cm Solve each equation. ) log 0 + log ( ) = { 70, 70 } ) log ( ) log = {, }

13 -- Find each product. 7) (m + n) m + 9mn + n ) ( ) 9) ( ) + 0) (m + n)(m n) + 9m n Evaluate each epression. ( ) ) ( ) ) (( 7 9)(( )( )))(( 7 0) ( ) ) Simplif each epression. ) 7 + (( )( 0))(( )( 9)) 00 ( ) ( ) )(( )( )) 97 ) p p p p 7 p + (p )( p 7) 7) m + m 7 9) m 7m m + m (7m )(m 7) 9 + ) ) 0) ( + )( ) 7 n 0n + n + n + n + n(n + )(n + ) a + a + 00 In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest tenth. ) m B = 9., a =. in m A = 0., b = in, c =. in ) m B = 0, a =. km m A = 0, b = 7. km, c =. km ) b =. cm, m A = m B =, a =. cm, c =. cm ) m B =, a =. mi m A = 7, b = 7 mi, c =. mi

14 -- Simplif. ) ) ) ) Sketch the graph of each function. 9) = 0 70) = ( ) Identif the domain and range of each. Then sketch the graph. 7) = log ( ) + Domain: > Range: All reals

15 -7- Sketch the graph of each function. State the number of real zeros. Approimate each zero to the nearest tenth. 7) f () = # Real Zeros: Real Zeros:.,.,. 7) f () = + # Real Zeros: Real Zeros:. Sketch the graph of each line. 7) + 0 = 7) + = 0 0