Back to Baker Street... Lesson 6A Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /45 = % > Multiple-Choice Items 1. <> 2. <> 3. <> Numeric Response 1 < > 4. <> 5. <> 6. <> Numeric Response 2 < 7. <> > 8. <> Numeric Response 3 < 9. <> > Numeric Response 4 < Written Response 1. <> <> 2. <> <> 3. <> > <> <> 4. Back to Baker Street... Lesson 6B Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /19 = %> Multiple-Choice Items 1. <> 2. <> 3. <> Numeric Response 1 < > Numeric Response 2 < > Written Response 1. <> 2. Back to Baker Street... Lesson 7A Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /77 = % > Multiple-Choice Items 1. <> 2. <> Numeric Response 1 < 3. <> > 4. <> 5. <> Numeric Response 2 < > 6. <> 7. <> 8. <> 9. <> 10. <> Numeric Response 3 < > 11. <> 12. <> 13. <> Numeric Response 4 < 14. <> 15. <> > Numeric Response 5 < 16. <> 17. <> > 18. <> Numeric Response 6 < Written Response <> <> <> <> > <> <> <> <> <> <> <> <> Back to Baker Street... Lesson 7B Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /97 = % > Multiple-Choice Items 1. <> 2. <> Numeric Response 1 < 3. <> 4. <> > Numeric Response 2 < > 5. <> 6. <> Numeric Response 3 < > 7. <> 8. <> Numeric Response 4 < > 9. <> 10. <> 11. <> 12. <> Numeric Response 5 < 13. <> > 14. <> Numeric Response 6 < 15. <> > 16. <> 17. <> Numeric Response 7 < > 18. <> 19. <> 20. <> Numeric Response 8 < Written Response 1. <> <> <> > <> <> <> <> <> <> <> <> <> <> Back to Baker Street... Lesson 7C Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /67 = % > MultipleChoice Items 1. <> 2. <> 3. <> Numeric Response 1 < > 4. <> 5. <> 6. <> Numeric Response 2 < 7. <> 8. <> 9. <> > 10. <> 11. <> 12. <> Numeric Response 3 < > 13. <> 14. <> Numeric Response 4 < > 15. <> 16. <> 17. <> Numeric Response 5 < > Written Response <> <> <> <> <> <> <> <> <> <> <> <> <> <> <> Back to Baker Street... Lesson 7C Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /67 = % > Multiple-Choice Items 1. <> A g (x) = h(x)-f(x) 2. <> B F(x)-g(x) = -x2+3x-1 3. <> D Numeric Response 1 < X<0, f(x) = -(4x-1) = -4(-3) +1=13 > 4. <> Answer: C 5. <> Answer: A (X+3)>= 0 so x>= -3 and g(x) is defined for all values of x. 6. <> Answer: C ( a vertical astmptote at x=2) and a point of discontinuity Numeric Response 2 < > (f.g)(x)=f(X)g(x) = (2+ sqrt x)(4-3x) = 2 +3)(4-(3*9) = 5*(-23)= -115 7. <> Answer: A if h(x) = (fog)(x) then h(x)=f(g(x)) 8. <> Answer: C F(g(x))= 5 sqrt g(x) => g(x) = 1-2x 9. <> Answer: B g(f(x))= 1/(2x+1 + 3) domain is (0,infinity) so the range is 0 Answer: B (permutation is selecting and arranging) 11. <> Answerr: A (out of 7 letters 3 are S and 2 are C) 12. <> Answer: D Numeric Response 3 < > Answer: Females=4= 1 unit. + 1 other person n=2 == arrangements= 2! = 2 and females arraged among themselves by 4! = 24 Number of arrangements= 2 * 24 = 48 13. <> 4c2 * 4c2 * 4c1 = 144 14. <> Answer: D Numeric Response 4 < r=6 12!/6!6! = 924 > 15. <> Answer: B 16. <> Answer: C Fourth term = 5c3 (3y)2(-2x)3 = -720 y2x3 17. <> Answer: C 10c4 (3/x2)6(4x3)4 = 5 th term Numeric Response 5 < > Answer = n+1 =10 Written Response <> T(n)= c(n)+G(n)=80n - 275 <> n is number of lawns so it is always positive. domain:(n >0) range : earnings will exist only when lawns are cut, so, n=1 earnings= 80(1)-275= -195 range = (-195, infinity) earnings can be negative, that mean that extra money is due. <>80n - 275=2525 N= 35 yards <> (2x+1)/(4x2 -1) = (2x+1)/(2x-1)(2x+1)= 1/(2x-1) <> Discounted price E(x) = x ( 1-0.25) = 0.75x <>C(x)= x- 10 <> E(C(x)) = E(x-10) = 0.75(x-10) C(E(x)) = C(0.75x) = 0.75x -10 <> <> 10C3 =120 <> no. of ways to select 3 out of 10 without any restriction = 10C3 no. of ways to select 3 male out of 4 , not any female = 4C3 no. of ways to select 3 female out of 6, not any male = 6C3 total number of ways when at least one male and one female = 10C3 - 4C3 - 6C3 <>10C3 <> 10C3- 6C3 - 4C3 <> N+1 = 9 terms <> 8c4 (3/x)4(x2)4 = 5670x4 <> No,no constant term, Back to Baker Street... Lesson 7B Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /97 = % > Multiple-Choice Items 1. <> 2. Answer: A <> Answer: B Numeric Response 1 < Answer: 3. <> Answer: D 4. <> Answer: A > Numeric Response 2 < > Y= g(n-6) + 7 = g(5)+7 = 19 n=11 5. <> Answer: D 6. <> Answer:B Numeric Response 3 < > 7. <> Answer = C 3+4 8. <> Answer: A Numeric Response 4 < 4 4 0 1 > 9. <> Answer:D For astmptote y+5 = 0 and x-2=0 10. <> Answer: B X+2 not equals 0 11. <> Answer :A 12. <> Answer: A Numeric Response 5 < 23*2n = 25 N = 5/6 = 0.833 13. <> > Answer:A 14. <> Answer: B Numeric Response 6 < 15. <> Answer: A > 16. <> Answer: C Log( x3 * 23 / 2y) 17. <> Answer: B 2log3(4/12) = 2 * (-1) = -2 Numeric Response 7 < > Log2* (4)2*12 = log 249 / log 4 = log 249 / log 22 = 49/2=24.5 18. <> 10/x = x2 x3 = 10 Answer: D 19. <> (2x-3)log4 = (x+1)log7 (2x-3)0.7=(x+1) 1.4x -x= 2.1+1=3.1 0.4x=3.1 X=7.75 20. <> (x+3)/2 = x2 2X2 - x-3 =0 (2x-3)(x+1)=0 X=-1 or x= 3/2 Numeric Response 8 < > 1.18= 2.1 Thus, it takes 8 hours for population to double Written Response 1. <> Y=4x - 4 X=(y+4)/4 inverse of f(x) = (x+4)/4 <> Red line for inverse function. <> The invariant point y(x) = y(x)inverse 4(x-1) =(x+4)/4 X=4/3 y = 4/3 The point is (4/3,4/3) <> Y=aSin (bx +c) Amplitude=3 Period = (-/9 to 3/9) = 4/9 Range = (-1, 5) Y= 3 Sin(4.5 x) +2 <> Y = 3Cos(4.5x - /9) +2 <> Logb(14+2) = y = 2 2log44 = 2 so b=4 <>y = log4(x+2) 3 = log 4(n+2) 43 = n+2 64-2=62 = n <> m = log4(6+2) = 3/2 <> I1 / I2 = (eB1/eB2)1/10 I1 =0.0009 I2 I2 =1098 I1 which means intensity of threshold of pain is 1098 times louder than that of conversation. <> Tripled == I1 * 3 eB1-B2 = (I1/I2)1/10 = (3)1/10=1.116 B1-B2 = log(1.116) = 0.0477 B1=0.0477 + 60 = 60.0477 db <> A = P(1+ r/12/100)12*n A= 5000 (1+5/1200)12*6 =$6745.08 <> 3*5000=5000( 1+5/1200)12*n 264=12n N=22 years Back to Baker Street... Lesson 7C Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /67 = % > Multiple-Choice Items 1. <> A g (x) = h(x)-f(x) 2. <> B F(x)-g(x) = -x2+3x-1 3. <> D Numeric Response 1 < X<0, f(x) = -(4x-1) = -4(-3) +1=13 > 4. <> Answer: C 5. <> Answer: A (X+3)>= 0 so x>= -3 and g(x) is defined for all values of x. 6. <> Answer: C ( a vertical astmptote at x=2) and a point of discontinuity Numeric Response 2 < > (f.g)(x)=f(X)g(x) = (2+ sqrt x)(4-3x) = 2 +3)(4-(3*9) = 5*(-23)= -115 7. <> Answer: A if h(x) = (fog)(x) then h(x)=f(g(x)) 8. <> Answer: C F(g(x))= 5 sqrt g(x) => g(x) = 1-2x 9. <> Answer: B g(f(x))= 1/(2x+1 + 3) domain is (0,infinity) so the range is 0 Answer: B (permutation is selecting and arranging) 11. <> Answerr: A (out of 7 letters 3 are S and 2 are C) 12. <> Answer: D Numeric Response 3 < > Answer: Females=4= 1 unit. + 1 other person n=2 == arrangements= 2! = 2 and females arraged among themselves by 4! = 24 Number of arrangements= 2 * 24 = 48 13. <> 4c2 * 4c2 * 4c1 = 144 14. <> Answer: D Numeric Response 4 < r=6 12!/6!6! = 924 > 15. <> Answer: B 16. <> Answer: C Fourth term = 5c3 (3y)2(-2x)3 = -720 y2x3 17. <> Answer: C 10c4 (3/x2)6(4x3)4 = 5 th term Numeric Response 5 < > Answer = n+1 =10 Written Response <> T(n)= c(n)+G(n)=80n - 275 <> n is number of lawns so it is always positive. domain:(n >0) range : earnings will exist only when lawns are cut, so, n=1 earnings= 80(1)-275= -195 range = (-195, infinity) earnings can be negative, that mean that extra money is due. <>80n - 275=2525 N= 35 yards <> (2x+1)/(4x2 -1) = (2x+1)/(2x-1)(2x+1)= 1/(2x-1) <> Discounted price E(x) = x ( 1-0.25) = 0.75x <>C(x)= x- 10 <> E(C(x)) = E(x-10) = 0.75(x-10) C(E(x)) = C(0.75x) = 0.75x -10 <> <> 10C3 =120 <> no. of ways to select 3 out of 10 without any restriction = 10C3 no. of ways to select 3 male out of 4 , not any female = 4C3 no. of ways to select 3 female out of 6, not any male = 6C3 total number of ways when at least one male and one female = 10C3 - 4C3 - 6C3 <>10C3 <> 10C3- 6C3 - 4C3 <> N+1 = 9 terms <> 8c4 (3/x)4(x2)4 = 5670x4 <> No,no constant term, Back to Baker Street... Lesson 6A Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /45 = % > Multiple-Choice Items 1. <> 7!/4!2! = 105 2. <> 2 * 3* 4 * 2 = 48 3. <> Answer: C Numeric Response 1 7P2 = 42 7 different chairs. < > 4. <> 4C2 * 4C2 * 4C1 = 144 5. <> Answer: A Total possibilities - number of groups with 3 adults 6. <> 5C3 = 10 Numeric Response 2 < 126 paths > 7. <> 12C3 *12C5 * 7C7 = 15!/3!7!5! = 360360 8. <> Answer: 7C4 Out of available nine courses,two are compulsory.Hence the student is free to select 4 courses out of 7 remaining courses Numeric Response 3 < Answer : N=6 9. <> Answer = B 35! / 30!5! > Numeric Response 4 < > 6C2 = 15 Written Response 1. 4!/2! = 12 <> The word \"DATA\" has 4 letters. But A occurs 2 times and rest of them are different, Thus, 4!/2! =12 2. <> Number of arrangements of n different things taken at a time <> Number of ways in which none of the thing are taken is 1. 3. <> 4! = 24 <> 4!/(4-3)! =4! <> 4. n ! / (n-3)! = 2* n! / 4! (n-4)! n-3 =12 n= 15 Back to Baker Street... Lesson 6B Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /19 = %> Multiple-Choice Items 1. <> Answer: B 2. <> Answer: C 3. <> Answer: D 5C5 * 35 Numeric Response 1 < > 4320 Numeric Response 2 < 0.070 > Written Response 1. <> 2160 x4 2. No, there is no x3 term in the expansion. 1st term = x-2 2nd term = -x 3rd term = x6 Back to Baker Street... Lesson 7A Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /77 = % > Multiple-Choice Items 1. <> Answer: B When we equate 2 functions , the point we get is the point where the two functoions intersect. 2. <> Answer:A Number of bacteria can be greater than or equal to zero. - sqrt300x +200 >=0 300x>=0 0<=x<=200 and b(x) has whole numbers. Numeric Response 1 < 2 3x -5 >=0 Domain = So, range is so so minimum positive value is 0. 3. <> > Answer C Simplify the polynomial y=3x^4+6x^3-39x^2+30x The first coefficient is positive , so, the graph will go down and then rise up. From the graph, we can predict the answer. 4. <> Answer: B By hit and trial. Check for x= -6, -5,-3 , 0.5, 3 and produce the results. 5. <> Answer: A Vertical asymptote at x+2=0 and when x+2=0 you have discontinuity. Numeric Response 2 < Answer: A: c=1 B: c=0.5 C:c=2 D: c=5 > 6. <> 7. <> Answer:B S=r 210o = 210 * rad / 180 = 7 /6 rad 250 cm = r * 7 /6 r = 68.18 cm 8. <> Answer: D -310 * rad / 180 = -31 /18 and it lies in Quadrant 4 9. <> Answer D The line goes from the origin (0, 0) to the point Q located at (x, y) = (4,-1) r is the distance from the origin OR r = sqrt(x^2+y^2) = sqrt 17 Sin =y/r = -1/sqrt17 =-0.24 10. <> Answer: B Csc (pi/3) = sqrt 3 Numeric Response 3 < Circumference= 2r =39720 r = 6321.634 km arc angle = 66o =1.1519 rad > s=r arc length= 6321.634 * 1.1519=7281.89 = 7282 km 11. <> Answer:B Sec A negative in II and III Cot A negative in II and IV, 12. <> Answer:D Cos = Solution is 13. <> Simplify, we get sin 2x + cos x = 0 Ad domain is So , at n=0, the answer is D Numeric Response 4 < Answer:4 6 > 14. <> Answer D 15. <> Answer: A 4 sin2 -5sin +1=0 Factorize and we get Answer A. Numeric Response 5 < Answer: 2.553 > Tan = -2/3 = -33.7 degrees = 180-33.7 = 146.297 degrees = 146.297 * 0.01745=2.553 radians 1 degree =0.0174532925 radians 16. <> Answer: C The values which are not allowed will not give possible identical results. The identies lie in possible domain. 17. <> Answer: A Simplify it, (1-cos(x))(1+cos(x))/sin(x) 1-cos2x / sin x Sin x 18. <> Answer: D The expression is not defined at 2-sec = 0 Numeric Response 6 < > Solution between 0 and 90 is only one ie , at n=0 , x= 30o Written Response <> f(x) = 9x2 -2 Domain : Range : Plotting the graph , we can know the range. <> <> = tan- (12/5)=67.38o=1.17 rad When Tangent is 12/5, the angle is 67.38 degrees. Therefore, my reference angle is 67.38 degrees. Tangent is positive inI and III quadrant, Angle in III quadrant = 180 + 67.38 = 247.380 <> By Pythagoras theorem, hypotenuse = sqrt ( 122+52) = sqrt (169) = 13 <> = 0.675 +2n , 2.446 +2n At n=0, =0.675, 2.446 (considering the given restriction (0<<6.28) theta = 0.67513 radians= 38.68 degrees, round to 39 degrees. The 2nd solution (2nd quadrant) is 180-39=141 degrees. 39 degrees is still an acceptable solution, but the 2nd solution (2nd quadrant is now 141-360 = -219 degrees. (considering the restriction) <> =2n + -0.675 , = 2n + 0.675 =2n +2.446 , = 2n + 0.675 <> =2n +141o , = 2n + 39o <> Periodicity = /2 Thus, the restrictions on x will be defined by its domain <> <> Back to Baker Street... Lesson 7C Assignment Complete the Back to Baker Street assignment. Refer to the Tips From Scotland Yard by clicking on the link to assist you in completing the assignment. Call or e-mail your teacher if you would like additional help. Name: <> Date: <> Score: < /67 = % > Multiple-Choice Items 1. <> A Simple addition and subtraction g (x) = h(x)-f(x) 2. <> B F(x)-g(x) = -2x2+3x -1 +x2 = -x2+3x-1 3. <> B Sqrt (x2 -1) + x2 =h(x) x2 -1 greater or equal to zero for the square root to be defined. Thus, -1>x>1 , thus x2 value will bring f(x) always positive and the range will be y>= 1 Numeric Response 1 < X<0, f(x) = -(4x-1) = -4(-3) +1=13 > 4. <> Answer: C Simple identities , cannot be explained.(facts) 5. <> Answer: A (X+3)>= 0 so x>= -3 and g(x) is defined for all values of x. 6. <> Answer: C ( a vertical astmptote at x=2) and a point of discontinuity A point of discontinuity occurs when numerator and denominator have the same factor, x is common in both numerator and denominator , so a hole is created. And , taking the denominator, x(x-2) =o For the function to exist, x not equals 0 and 2, thus x=0 and x=2 are possible vertical asymptotes. But as we see, at x=0 a hole is created , thus the only vertical asymptote is x=2 Numeric Response 2 < > x>o, so |4-3x| will be 4-3x Fog(x) = f(g(x)) = 2+ sqrt (4-3*9) or (f.g)(x)=f(x)*g(x) = (2+ sqrt x)(4-3x) =( 2 +3)(4-(3*9) = 5*(-23)= -115 I am not able to understand if it is f.g or fog 7. <> Answer: A if h(x) = (fog)(x) then h(x)=f(g(x)) 8. <> Answer: C F(g(x))= 5 sqrt g(x) => g(x) = 1-2x 9. <> Answer: B g(f(x))= 1/(2x+1 + 3) domain is (0,infinity) so the range is 0 Answer: B (permutation is selecting and arranging) All the examples except B are about first selecting and then arranging. But in B, only selections are done, not the ordered arrangements. 11. <> Answerr: A (out of 7 letters 3 are S and 2 are C) 12. <> Answer: D I hope you understand the pascal triangle method As we assume that backtracking is not allowed so, we did not take in account the latter ways Numeric Response 3 < > Answer: Females=4= 1 unit. + 1 other person n=2 == arrangements= 2! = 2 and females arraged among themselves by 4! = 24 Number of arrangements= 2 * 24 = 48 13. <> 4c2 * 4c2 * 4c1 = 144 14. <> Answer: D (Total Ways of selecting 3 from 7 ) - ( ways in which there will be 3(out of 4) males in the group) Numeric Response 4 < r=6 12!/6!6! = 924 > 15. <> Answer: B The binomial expansion, nCr a(n-r) br In this, B fits in the equation. 16. <> Answer: C Fourth term = 5c3 (3y)2(-2x)3 = -720 y2x3 17. <> Answer: C 10c4 (3/x2)6(4x3)4 = 5 th term Numeric Response 5 < > Answer = n+1 =10 Number of terms in the expansion will be always (n+1) Written Response <> T(n)= c(n)+G(n)=80n - 275 <> n is number of lawns so it is always positive. domain:(n >0) range : earnings will exist only when lawns are cut, so, n=1 earnings= 80(1)-275= -195 range = (-195, infinity) earnings can be negative, that mean that extra money is due. <>80n - 275=2525 N= 35 yards <> (2x+1)/(4x2 -1) = (2x+1)/(2x-1)(2x+1)= 1/(2x-1) F(x)= 1/(2x -1) Denominator should not be zero 2x-1 not equals 0 X not euals So domain is And consequently, the range is <> Discounted price E(x) = x ( 1-0.25) = 0.75x <>C(x)= x- 10 <> E(C(x)) = E(x-10) = 0.75(x-10) C(E(x)) = C(0.75x) = 0.75x -10 <> <> 10C3 =120 <> no. of ways to select 3 out of 10 without any restriction = 10C3 no. of ways to select 3 male out of 4 , not any female = 4C3 no. of ways to select 3 female out of 6, not any male = 6C3 total number of ways when at least one male and one female = 10C3 - 4C3 - 6C3 <>10C3 <> 10C3- 6C3 - 4C3 <> N+1 = 9 terms <> 8c4 (3/x)4(x2)4 = 5670x4 No, there doesnot exist any constant term. For getting the constant term , the x must cancel out in one of the term. But it doesnot happen in any of the terms. Lets check : 1st term : (1/x)8(x2)0 2nd term : (1/x)7(x2)1 3rd term : (1/x)6(x2)2 4th term : (1/x)5(x2)3 5th term : (1/x)4(x2)4 6th term : (1/x)3(x2)5 7th term : (1/x)2(x2)6 8th term : (1/x)1(x2)7 9th term : (1/x)0(x2)8 X powers doesnot equate in any of the terms