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) 72-72 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 + 2 4 4 4 4 9) Perpendicular to the line y = -4x - 2; containing the point (-3, -4) 9).,. 13.. 13 _. 1 13 ^ 1 13 A)y = -4x B)y = 4x C)y= x D)y = x 4 4 44 44 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
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
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) 10-5- -10-5 10 x -5- -10-
A) B)..y 10-5-- -10-5 5 10 x -5-- -10- C) D) -10-5 5 10 x -5-- -10-- 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 -2 + 4 B)y=<x/-x-2-4 C) y =-\/-x +2-4 D)y=^-x + 2 + 4 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) 20031 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)
22) (-^/M -1) Find cot t. 22) 7 7. > *\/33 % 4^33 _, *j33,-.> vss A) D) L.) u) 4 33 4 7 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 405 26) _ A)^ B) O-^ D)-l 2 2 2 2 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)-0.6 29) 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 )
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) -2.7 + 6n 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)1.8 + 3ji 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) sin2 80 + cos2 80 37) 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)
41) sin - 41) A)-- Use transformations to graph the function. 42) y = -3sin(x+- ) 42) 6-- 4-- 2-- H 1 1 1 1 h -2-- -6-- A) 6-4- 2-- H h H 1 1 1- -4-- -6-
43) y = -5 cos (x - ) 43) Jy 4- -2-- 3;t..y 4-- 2-- <H 1- H h \ 1-2-- 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)
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
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) -2-- 371-5^ y 2, y -4' -6 10
50)y={cot[x-f 50) 4-- 2-- H 1 h -\ -4-- -6-- 11
A) B) 6- y 6- 'y 4- VI \ 3* \ ^5ji \ x -Jt T ^ ^ T_ 4-2- f I- -4- -6- 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, -4-4- -6- 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
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 8- - 6-4-- 2-- «I 1 1 h -4- -6- A) -8- -10-- 10-8 6 4 B) 10- H h -2,-t -2-4 -6-8 -10-- H h -2 r\ 1 h -4- -6-10-- 13
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 -4-- 6-- 8-- 10-0-- 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 (-0.9372)] A) -0.4686 B) 0.9372 C) -0.9372 D) 0.4686 56) 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 9 1 + 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) cot2 9 + 1 D) sin2 9 + 1 60) 61) 14
,,, 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) 527 625 B) 336 625 Find sin (28). 64) C)- 336 625 D)- 527 625 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
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
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