ERRATA MATHEMATICS FOR THE INTERNATIONAL STUDENT MATHEMATICS HL (CORE) (2nd edition)

Transcription

1 ERRATA MATHEMATICS FOR THE INTERNATIONAL STUDENT MATHEMATICS HL (CORE) (nd edition) Second edition reprint page 95 TEXT last paragraph on the page should read: e is a special number in mathematics. It is irrational like ¼, and just as ¼ is the ratio of a circle s circumference to its diameter, e also has a physical meaning. We eplore this meaning in the following investigation. page 8 THE PEA PROBLEM With fertiliser (insert 7 before last 11) page 859 ANSWERS EXERCISE 1F. 1 a ], [ page 9 ANSWERS REVIEW SET 5B 6 b as! 1, f()! 0 (above) as! 1, f()! 0 (below) page 90 ANSWERS EXERCISE 0 7 Either A or B must occur, or A and B are disjoint.

2 ERRATA MATHEMATICS FOR THE INTERNATIONAL STUDENT MATHEMATICS HL (CORE) (nd edition) Second edition reprint page 55 OPENING PROBLEM change second sentence A circular stadium consists of sections as illustrated, with aisles in between. The diagram shows the 1 tiers of concrete steps for the final section, Section K. Seats are to be placed along every concrete step, with each seat being 0:5 m wide. AB, the arc at the front of the first row, is 1: m long, while CD, the arc at the back of the back row, is 0:5 m long. page 95 TEXT last paragraph on the page should read: e is a special number in mathematics. It is irrational like ¼, and just as ¼ is the ratio of a circle s circumference to its diameter, e also has a physical meaning. We eplore this meaning in the following investigation. page 96 INVESTIGATION 5 You should have discovered that for very large a values, µ a a ¼ : :::::: page 1 REVIEW SET A Without using a calculator, find: a log p 10 b log 1 p 10 c log(10 a 10 b+1 ) page REVIEW SET 8B Epand and simplify ( p +) 5 giving your answer in the form a+b p, a, b Z. page 6 REVIEW SET 9C 6 If u 1 = 5 and u n+1 = u n ( 1) n, then u n = ( n ) + ( 1) n, n Z +. page 90 EXAMPLE the speech bubble should read: As sin has half the period of sin, the first maimum is at -- not --. ¼ ¼ page 8 SUMMARY change second dot point: Summary: ² A B = (a ij ) (b ij ) = (a ij b ij ) page 5 NOTE Note: ² We can only add or subtract matrices of the same order. ² We add or subtract corresponding elements. ² The result of addition or subtraction is another matri of same order. should read: The product AB eists only if the number of columns of A equals the number of rows of B. page 5 TEXT following the third blue bo should read: For eample, suppose we replace the second equation by twice the second equation minus the first equation. In this case:

3 page 96 EXERCISE 1F.1 Ã! 1 15 If a = 1, b = Ã! 1 and c = Ã! find: d j a cj page 8 THE PEA PROBLEM With fertiliser (insert 7 before last 11) page 6 EXAMPLE 10 the third line from the bottom should read: Cuts the y-ais when = 0 page 78 TEXT the first line on the page should read: For eample, ² sin ( ¼ ) becomes 1 1 cos(6 ¼) page 90 ANSWERS EXERCISE 17F.1 10 a 0:809 b 0:150 page 907 ANSWERS REVIEW SET 18B 8 b i page 90 ANSWERS EXERCISE 0 a A = 1, B = 0, C = 1 1 b ln 7 ln 7 Either A or B must occur, or A and B are disjoint. 75 b ¼ :8 units page 91 ANSWERS EXERCISE b ¼ 0:001 7

4 ERRATA MATHEMATICS FOR THE INTERNATIONAL STUDENT MATHEMATICS HL (CORE) (nd edition) Second edition initial print run page 55 OPENING PROBLEM change second sentence A circular stadium consists of sections as illustrated, with aisles in between. The diagram shows the 1 tiers of concrete steps for the final section, Section K. Seats are to be placed along every concrete step, with each seat being 0:5 m wide. AB, the arc at the front of the first row, is 1: m long, while CD, the arc at the back of the back row, is 0:5 m long. page 80 EXERCISE B (note also correction to answer) 1 Simplify, then use a calculator to check your answer: k ( 5) page 95 TEXT last paragraph on the page should read: e is a special number in mathematics. It is irrational like ¼, and just as ¼ is the ratio of a circle s circumference to its diameter, e also has a physical meaning. We eplore this meaning in the following investigation. page 96 INVESTIGATION 5 You should have discovered that for very large a values, µ a a ¼ : :::::: page 119 EXAMPLE 6 b Using the same graphs as above, we seek values of for which f() g() > 0. page 1 REVIEW SET A Without using a calculator, find: a log p 10 b log 1 p 10 c log(10 a 10 b+1 ) page REVIEW SET 8B Epand and simplify ( p +) 5 giving your answer in the form a+b p, a, b Z. page EXERCISE 9B 1 Prove the following propositions to be true using the principle of mathematical induction: a n > 1 + n for all n Z, n > 0 page 6 REVIEW SET 9C 6 If u 1 = 5 and u n+1 = u n ( 1) n, then u n = ( n ) + ( 1) n, n Z +. page 90 EXAMPLE the speech bubble should read: As sin has half the period of sin, the first maimum is at -- not --. ¼ ¼

5 page 17 EXERCISE 1K diagram should be: 1 b A cm page 8 SUMMARY A cm change second dot point: Summary: ² A B = (a ij ) (b ij ) = (a ij b ij ) ² ² We can only add or subtract matrices of the same order. We add or subtract corresponding elements. ² The result of addition or subtraction is another matri of same order. page 5 NOTE should read: Note: The product AB eists only if the number of columns of A equals the number of rows of B. page 5 TEXT following the third blue bo should read: For eample, suppose we replace the second equation by twice the second equation minus the first equation. In this case: page 96 EXERCISE 1F.1 Ã! 1 15 If a = 1, b = Ã! 1 and c = Ã! find: c j b + c j d j a cj page 8 THE PEA PROBLEM With fertiliser (insert 7 before last 11) page 57 EXERCISE 19A 1 Evaluate the limits: o lim! page 578 EXERCISE 19C r diagram should be: page 619 REVIEW SET 0B 10 Use the product rule for differentiation to prove that: a if y = uv where u and v are functions of, then d µ y d d = u d v + du µ dv d d d + u v d

6 page 6 EXAMPLE 10 the third line from the bottom should read: Cuts the y-ais when = 0 page 68 EXERCISE D Consider the function f() = e ( + ). b Conjecture a formula for finding f (n) (), n Z +. page 71 EXERCISE D Z 10 1 Find: f p d 1 5 page 78 TEXT the first line on the page should read: For eample, ² sin ( ¼ ) becomes 1 1 cos(6 ¼) page 86 EXERCISE 0 17 a Show that for all positions of P, dá dµ = b cos Á a cos µ. page 856 EXERCISE 0 5 f Find the eact value of k if k > 0 and the region bounded by y = f (), the -ais, and the line = k has area equal to 1 (e 1) units. page 858 ANSWERS EXERCISE 1D n -+ o -+ r page 859 ANSWERS EXERCISE 1F. 1 a ], [ c [, ] page 861 ANSWERS REVIEW SET 1A 5 b page 86 ANSWERS REVIEW SET 1B 5 b page 86 ANSWERS EXERCISE D.1 7 c u n = ( p ) n 1 d u n = 10 ( p ) 1 n page 86 ANSWERS EXERCISE E.1 np 5 b (k + 1) (k + ) = n(n +6n+11) k=1 page 86 ANSWERS REVIEW SET A 9 u n = 1 6 n 1 or 1 6 ( )n 1 page 86 ANSWERS EXERCISE B 1 h i j 6 k 65 l 65 a b 01 c 15 d 15 e 6 1 f 6 1 g 6 1 h 90: i 90: j 90: a 0:1 b 0:1 c 0:07 d 0:07 e 0: f 0: g 1 h 1 page 86 ANSWERS EXERCISE B 5 7 page 868 ANSWERS EXERCISE H. 8:6 years

7 page 869 ANSWERS REVIEW SET D 9 b f 1 () = e 1, 0 < < ln page 87 ANSWERS EXERCISE 5B. diagrams should be: 6 y y -1 1 y = f ( ) y =+ f ( ) y = f () y = f ( ) y = 1 f ( ) y = f ( 1 ) y = h( ) y =+ h( ) 1 y = 1 h( ) y h( = ) y = h( ) page 87 ANSWERS REVIEW SET 5A 10 b i (1, )! (1, 6)! ( 1, 6)! (1, 6)! (1, ) page 878 ANSWERS EXERCISE 6G km h 1 page 878 ANSWERS EXERCISE 6H 1 f() = (a + b ) + (a b ), least value = a b page 88 ANSWERS EXERCISE 10D 1 c 8: cm page 88 ANSWERS REVIEW SET 10C diagram should be: y page 887 ANSWERS EXERCISE 1I d sin page 888 ANSWERS EXERCISE 1K 8 b p 7 page 888 ANSWERS REVIEW SET 1A 10 c 0:5 < t < :5 and 6:5 < t 6 8 page 890 ANSWERS EXERCISE 1C. c (A 1 ) 1 = A page 89 ANSWERS EXERCISE 1B. 1 b 9.9 o east of south page 895 ANSWERS EXERCISE 1I b 9:1 o page 897 ANSWERS REVIEW SET 1E µ 1 a t = b! 5 LM =,! KM = So, page 898 ANSWERS EXERCISE 15A. 5 a = 11, b = 7! LM ²! KM = 0 ) b M = 90 o µ 1

8 page 900 ANSWERS EXERCISE 16B. diagram should be: 1 a y b A(, ), line B(8, 0), line 1 C 5 C(, 6) A c BC = BA B = p 5 units 5 10 ) isosceles line page 90 ANSWERS REVIEW SET 16D 1 b 1 y z = 11, ¼ : units page 90 ANSWERS EXERCISE 17A 1 c The modal class is cm, as this occurred the most frequently. page 90 ANSWERS EXERCISE 17C b ¼ 87 students 5 b ¼ 69% page 90 ANSWERS EXERCISE 17F.1 1 a Sample A A B b 8 8 c s 1:06 a s b Andrew 5 Brad 0:5 Andrew.97 1:6 10 a 0:809 b 0:150 page 905 ANSWERS REVIEW SET 17A e ii 8:1 m page 906 ANSWERS EXERCISE 18D. a 7 b 7 page 907 ANSWERS EXERCISE 18J 6 Hint: Show P(A 0\ B 0 ) = P(A 0) P(B 0 ) using a Venn diagram and P(A \ B) page 907 ANSWERS REVIEW SET 18B 8 b i page 91 ANSWERS EXERCISE 1E d ii f 0 ( ) () = ( + 1) ( 1), local ma. at ( p, p ), local min. at ( p, p ), horizontal inflection at (0, 0) d iii -intercept is 0, y-int. is 0 page 918 ANSWERS EXERCISE D 7 ¼ 6: o page 919 ANSWERS EXERCISE E a ii Show that f 00 (t) = Abe bt (bt ) page 919 ANSWERS REVIEW SET A diagram should be: y =9 (0, ) y = e + (ln 5, 8) y = y =9-5e c f 0 () < 0 for < 1 and 1 < 6 and f 0 () > 0 for >. f 00 () > 0 for > 1, f 00 () < 0 for < 1. So, the gradient of the curve is negative for all defined values of 6 and positive for all >. The curve is concave down for < 1 and concave up for > 1.

9 page 90 ANSWERS REVIEW SET A 9 Tangent is y = ln, so never cuts -ais. page 90 ANSWERS REVIEW SET B (0, ln 1) page 91 ANSWERS EXERCISE C. 5 c dy = 1 p, ] a, a[ d a page 9 ANSWERS EXERCISE B b units page 9 ANSWERS REVIEW SET B 10 A = 1, B =, C = 1, D =, ( + 1) + ln j j + c page 9 ANSWERS REVIEW SET C 1 cos1 n n 1 + c, for n 6=, ln jcos j + c, for n = page 9 ANSWERS EXERCISE 5A 1 b 6 units page 9 ANSWERS EXERCISE 5B.1 b 16 km page 9 ANSWERS EXERCISE 5C 8 :800 units page 9 ANSWERS REVIEW SET 5A 11 ¼ units y 1 b i diagram should be: y = 1-1 p (p, 1) p p= p= page 9 ANSWERS REVIEW SET 5B 6 b as! 1, f()! 0 (above) as! 1, f()! 0 (below) page 95 ANSWERS EXERCISE 6A 1 h 0¼ units page 99 ANSWERS EXERCISE 9C. c k ¼ 1:088 a k ¼ 79:1 b k ¼ 1: page 90 ANSWERS EXERCISE 0 a A = 1, B = 0, C = 1 1 b ln 7 ln µ Á b cos( ), µ+á 7 Either A or B must occur, or A and B are disjoint. 75 b ¼ :8 units

10 page 91 ANSWERS EXERCISE b ¼ 0: diagram should be: c y a 1 A --1 C -1 B 1 d b 16 d = t, y = t, z = 1 + t, t R page 9 ANSWERS EXERCISE 0 8 a = 8 b = 5 c = 6 z > 9 b ¼ 0:571, t ¼ 0:76