y- 12X 7 7 Find the midpoint of the line segment joining the points Pj and?2. 2) PI = (b, 9); P2 = (0, 1) 2) _ A)(y,5) B)(b,10) C)(b,5) D)(-y,8)

Transcription

1 Precalculus: Fall Final Review Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(pj,?2) between the points PI and?2. 1) PI = (-3, -7); P2 = (6,-4) 1) _ A) 72 B) C) 3^/10 D) 6 Find the midpoint of the line segment joining the points Pj and?2. 2) PI = (b, 9); P2 = (0, 1) 2) _ A)(y,5) B)(b,10) C)(b,5) D)(-y,8) Name the quadrant in which the point is located. 3) (-9,-7) 3) _ A) III B)IV C)l D)II Find the slope of the line containing the two points. 4) (-!,-!); (5,-3) 4) _ A)-- B)3 C) - D)-3 Solve the problem. 5) Find an equation of the vertical line containing the point (1, -10). 5) A)x = l B)y = -10 C)x = -10 D)y = l Find an equation for the line with the given properties. Express the answer using the slope-intercept form of the equation of a line. 6) horizontal; containing the point (7, -9) 6) A)x = -9 B)y = -9 C)y = 7 D) x = 7 7) Containing the points (-3,4) and (4,-8) 7) y- 12X 7 7 _, 12 8, 12 8 C)y = - x-y D)y = x-y 8) Parallel to the line x - 4y = 2; containing the point (0, 0) 8) A)y = - x B)y = -4- C)y = x D)y = x ) Perpendicular to the line y = -4x - 2; containing the point (-3, -4) 9)., _ ^ 1 13 A)y = -4x B)y = 4x C)y= x D)y = x Write the standard form of the equation of the circle with radius r and center (h, k). 10) r = 3; (h, k) = (-1,3) 10) A) (x - 1)2 + (y + 3)2 = 9 B) (x + 1)2 + (y - 3)2 = 3 C) (x + 1)2 + (y - 3)2 = 9 D) (x - 1)2 + (y + 3)2 = 3

2 Find the center (h, k) and radius r of the circle. 11) x2 + y2 + 14x + 12y + 21 = 0 A) (h, k) = (7,6); r = 64 C)(h,k) = (6,7); r = 64 B) (h, k) = (-7, -6); r = 8 D)(h,k) = (-6,-7); r = 8 H) Find the domain of the function, x 12) x/x-4 A){xlx>4) B){xlx*4) C)(xlx>4) D) all real numbers The graph of a function f is given. Use the graph to answer the question. 13) 12) 13) (-8,5) 10 x Find the numbers, if any, at which f has a local minimum. What are the local maxima? A) f has a local maximum at x = -2.5 and 5; the local maximum at -2.5 is -3.3; the local maximum at 5 is -2.5 B) f has a local maximum at x = -3.3 and -2.5; the local maximum at -3.3 is -2.5; the local maximum at -2.5 is 5 C) f has a local minimum at x = -3.3 and -2.5; the local minimum at -3.3 is -2.5; the local minimum at -2.5 is 5 D) f has a local minimum at x = -2.5 and 5; the local minimum at -2.5 is -3.3; the local minimum at 5 is -2.5 Find the average rate of change for the function between the given values. 14) f(x) = x2 + 7x; from 1 to 7 B)14 C)15 14) Match the graph to the function listed whose graph most resembles the one given. 15) 15) A) square function C) cube function B) cube root function D) square root function

3 The graph of a piecewise-defined function is given. Write a definition for the function. 16)..y 5- (3,4) (5,3) 16) (0, 1)< < I I I I I I -5 (3,2) I I I I I I 5 x -5- A) + l if 0 < x < 3 B) fx + 1 if 0 < x < 3 f(x) = I x + - if 3 < x < 5 f(x)= 1-x- 2 2 if3<x<5 C) + l if 0 < x < 3 D) fx + 1 if 0 < x < 3 f(x) = x + 2 if 3 < x < 5 l = l^x if3<x<5 Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 17) f(x) = -(x + 6)2-7 17) x

4 A) B)..y x C) D) x Find the function that is finally graphed after the following transformations are applied to the graph of y = -\/x. 18) i) Shift up 4 units 18) ii) Reflect about the y-axis iii) Shift right 2 units A) y = ~\/x B)y=<x/-x-2-4 C) y =-\/-x +2-4 D)y=^-x Convert the angle in degrees to radians. Express the answer as multiple of Jt. 19) 105 A) 1 OTT C^-rr 7-rr..y ID- B)- 11 D) _8_jt 13 19) Convert the angle in radians to degrees. 20, 20) A) 324 B) 160 C) 162 D) In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t., o Find cost. 21) B)- C)

5 22) (-^/M -1) Find cot t. 22) 7 7. > *\/33 % 4^33 _, *j33,-.> vss A) D) L.) u) Find the exact value. Do not use a calculator. 23) tan(39it) 23) _ A)-l B)0 C)l D) undefined 24) sec(-ji) 24) _ A) 1 B) -1 C) 0 D) undefined 25) cot 60 25) _ A)<y/3 B) C)^ D)l 26) sin ) _ A)^ B) O-^ D)-l A point on the terminal side of an angle 9 is given. Find the exact value of the indicated trigonometric function of 9. 27) (-4,-!) Find sec 9. 27) Solve the problem. 28) if sin 9 = 0.6, find sin (9 + :t). 28) A) 0.4 B)-0.4 Q0.6 D) ) What is the domain of the cosine function? 29) A) all real numbers from -1 to 1, inclusive B) all real numbers, except odd multiples of (90 ) C) all real numbers, except integral multiples of n (180 ) D) all real numbers 30) For what numbers 9 is f(9) = tan 9 not defined? 30) A) odd multiples of - (90 ) B) odd multiples of n (180 ) C) all real numbers D) integral multiples of n (180 )

6 31) What is the range of the secant function? 31) A) all real numbers from -1 to 1, inclusive B) all real numbers, except odd multiples of (90) C) all real numbers D) all real numbers greater than or equal to 1 or less than or equal to -1 32) If cos 9 = -0.9, find the value of cos 9 + cos (9 + 2it) + cos (9 + 4it). 32) A) -0.9 B)-0.7 Q-2.7 D) n 33) If tan 6 = 0.6, find the value of tan 9 + tan (9 + it) + tan (9 + 2ir). 33) A) 1.8 B)3.8 C) ji D) undefined Name the quadrant in which the angle 9 lies. 34) cos9<0, csc9<0 34) A) I B)II C)III D)IV 35) cot9>0, sin9<0 35) A) I B)II QIII D)IV In the problem, sin 9 and cos 9 are given. Find the exact value of the indicated trigonometric function. 36) sin 9 = \, cos 9 = find tan 8. 36) 4 4 A) 4 Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. 37) sin cos ) A) 1 B) -1 C) 0 D) 2 38) cos 50 sec 50 38) A)l B)-l C)50 D)0 Find the exact value of the indicated trigonometric function of 9. 39) esc 9 = -, 9 in quadrant III Find cot 9. 39) 2 Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 40) cos (-30 ) 40)

7 41) sin - 41) A)-- Use transformations to graph the function. 42) y = -3sin(x+- ) 42) H h A) H h H

8 43) y = -5 cos (x - ) 43) Jy ;t..y <H 1- H h \ a 2ji Without graphing the function, determine its amplitude or period as requested. 44) y = -3 sin 4x Find the amplitude.. ^ t B)3 c'f 44)

9 45) y = -5 cos x Find the period. J 45) A>f B)-5 D)6n Match the given function to its graph. 46) l)y = sin(x- ) 2)y = cos(x+ ) 46) 3) y = sin (x + ) 4) y = cos (x - ) D A) 1A, 2B, 3C, 4D B) 1A, 2D, 3C, 4B C) IB, 20,3C, 4A D) 1C, 2A, 3B, 4D

10 Find an equation for the graph. 47) 47) A) y = 2 cos (4x) B) y = 4 cos (2x) D) y = 2 cos x } ' 4 48) 48) A) y = -3 cos (2x) B) y = -3 sin x C) y = -3 sin (2x) D)y = -3cos x Graph the function. 49) y = -2tan[x-- 49) ^ y 2, y -4' -6 10

11 50)y={cot[x-f 50) H 1 h -\

12 A) B) 6- y 6- 'y 4- VI \ 3* \ ^5ji \ x -Jt T ^ ^ T_ 4-2- f I f>- :J n 2 JJ A 5n; /2n - /^ ~T~ 2 1 V / ' &n C) D) 6- y ) y Jn 4-2- ^-2- V., \ > V., M x ^T 1- \- :t V,^ V, V, V 6- v Write the equation of a sine function that has the given characteristics. 51) Amplitude: 2 Period: 4it 51) Phase Shift: - 4 A) y = 2 sin 4: <- l C) y = 2 sin -1x + - JTI D) y = 2 sin Find the phase shift of the function. 52) y = -4sin 4x--.. B)y = 2sin fl 1 ] 2X 8" M 52) A) 4n units down B) 4it units up 12

13 Solve the problem. 53) For the equation y = - cos(2x - 2ri), identify (i) the amplitude, (ii) the phase shift, and (iii) the 53) period. A) (i) 2 (ii) n (iii) TC (ii) 2:i (iii),' (ii) (iii) it (ii) it (iii) jc Graph the function. 54) y = 3csc x 54) 10- -y «I 1 1 h A) B) 10- H h -2,-t H h -2 r\ 1 h

14 C) D) 10- -y 10- -y H 1 1 h H 1 1 I > < I 1 1 h H 1 h -2u -n 2* -Z-i fii Find the exact value of the expression. 55) ^J^J) skr1-^ Mil 55) A)f B)f Find the exact value of the expression. Do not use a calculator. 56) cos [cos-1 ( )] A) B) C) D) ) 57)tan-ltanM I J A)f B)-f 57) Find the exact value of the expression. 58) sin (tan'1 2) 58) B) 2-x/S C) 5«j2 Simplify the expression as far as possible. r.^ COS sin 9 + tan 9 59) A) sec 9 B) cos 9 + sin 9 C) sin2 9 Complete the identity. 60) sin2 9 + sin2 9 cot2 9 =? A) 1 B) cot2 9-1 Find the exact value of the expression. 61) sin 25 cos 35 + cos 25 sin 35 C) cot D) sin ) 61) 14

15 ,,, f 2jt ] I n ]. (2n\ (x} 62)coS-coS-UsmU-Sm- 62),,,. _i. -, 63) sin cos i -sin"1-^ 63) A)0 B) 2-N/3 D)- Use the information given about the angle 0, 0 < 0 < 2jt, to find the exact value of the indicated trigonometric function. 64) cos9=-^, <9<2n -3, A) B) Find sin (28). 64) C) D) Solve the equation on the interval 0 < 6 < 2jt. 65) sin (49) = - 65) 4 4 C)0 ^^ 5jT T2'"6'l~/l2~'~6~'l2~/ 3 ' 66) 4 esc 9-3 = 1 A)2it B)f C)jt D)f 66) 67) sin2 9 + sin 9 = 0, 4n 5n; 00,*,-,- 67) Solve the equation. Give a general formula for all the solutions. 68) cos 9 = 1 A \ t C) 9 = * + D) 9 = 0 + 2kjr 68) 69) tan9 = -l B)9= 4 69) 15

16 Answer Key Testname: FALL FINAL REVIEW 1) C 2) A 3) A 4) A 5) A 6) B 7) C 8) C 9) C 10) C 11) B 12) C 13) D 14) C 15) D 16) A 17) C 18) D 19) C 20) C 21) D 22) A 23) B 24) B 25) C 26) A 27) D 28) D 29) D 30) A 31) D 32) C 33) A 34) C 35) C 36) B 37) A 38) A 39) C 40) C 41) A 42) D 43) A 44) B 45) D 46) D 47) C 48) B 49) B 50) C 16

17 Answer Key Testname: FALL FINAL REVIEW 51) C 52) D 53) D 54) C 55) D 56) C 57) B 58) A 59) A 60) A 61) B 62) B 63) A 64) C 65) D 66) B 67) D 68) D 69) B 17