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Complete Answer Book for ST(P) Maths 2A by Nelson Thornes.Note:- Scaned, OCRed version of Original.
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104 S1(P) Ma1hema11cs 2A
EXERCISE 26j
(p.409)
2. f\fethod (A) means that there is no way of checking who yon have aheady asked, or of checking son1eone's reply, or of reco1ding a reply glvcn in an unfa1nilia1 form that will need to be so11ed out la!eL
3. 1t is worth considering the dilficulty in categorizing eye colour.
3_ & 4. b) e.g. absentees, en1barrasstnen1, height not known,
nnn-co operation
1. This survey could be carried on! in the class rhe aim of this qnestionnai1e
should be discussed hefotehand so that !he results can be analysed and
presented. (~nestions (a) and {e} gather straightforward infonnation but notice that the individual answers to (a) and (b} will influence the answe1s In (c) nnd (d), so
analysis is not easy. lt nii~ht he helter to co111pose in class a questionnaire with a sin1pler oulco1ne if you wish to carry out a survey. It is ii11po11ant for the leache1 to be awa1e of the
p1oble1ns p1esented by a questionnaire of this type, if only to avnid them_
2. a) Boys and girls g1ow at different rales at different ages and the1efore fall into
two separate groups. h) A nume1ical scale i1eeds explanation
3. a) Scale needs an explanation. Words would he dearer h) Catq~ories needed c) Whal is incant by 'your fa1nily'? Do you include yourself?
ST(P) MATHEMATICS Teacher's Notes and Answers
l. Bostock, B.sc_
S. Chandler, B.Sc.
A. Shepherd, s_sc
E. Smith, M.Sc.
Stanley Thornes (Publishers) Ltd
fext (£! L. Bostock, S_ Chandler, A_ Shepherd and E. Srnith 1985, 1991 Original illustrations <f) Nelson fhornes Lid 1985, 1991
The right of L Bostock, s_ Chandler, A. Shepherd and E. S1nith lo be iderililied as authors of lhis work have been asserted by then1Jn accordance with the Copyright, Designs and Patents Act 1988.
All rights reserved. No par! of this public-~tion may be reproduced or transmitted in any form or by any n1eans. electronic or rnechanical, including photocopy, recording or any infounation storage and retlieval syste1n, without pennission in writing fron1 lf1e publisher or under licence fro1n the Copyright Licensing Agency tirniled, of 90 Tottenham Court Hoad, London Wt T 4LP.
Any person who co1nrnits any unauthorised act in relation to this publication may be liable to criminal prosecution and civil clai1ns tor dan1ages.
First published in 1985 by: S!anley Thornes (Publishers) l.td Second edition 1991
Reprinted in 2002 by: Nelson Thornes Lid Oella Place 27 Balh Road CllELTEN11AM Gl53 7TH United Kingdom
03 04 05 / 20 19 18 17 16 15
• A catalogue record for this book is available frorn the British Library
ISBN 0 7487 0543 O
Page rnake-up by Cotswold Typesetting Ltd
Printed and bound in Great Britain by Ashford Colour Press
3. a) 6 ~·
·a s ---0
g_ 4 ...._"'" --
0 3 ~··············
] E 0
z
ruache1 ·s Notes and Ans1+ers 1 03
--- --- --- - ('-- -·J
' ....
Number of rooms
b) Too much sca!ler to give an opinion
4_ a) 6 ---.-~---,-¥------ --·-- ----
-------·-
·.X:-~-- ---------- -----1-+-f- I
l f-·--- --- --- --*- - - -
I f- -- --t---
O'-~,'-«-'--',~~~IL0_Jl2~.~14~1L6~!L8.-J20~2~2~2L·l_J26
Pens and pencils
b) No -i.
EXERCISE 26h ()ne method of lo(:ating this !inc more accura!ely is lo find the 1nean values of the (p. 407) two quanlilies aud lo use lhesc values as the cootdinates of a point on the line
EXERCISE 26i (p.407)
1. S!roug. 1no<le1ate, weak, none
Although these exercises can he done 1nd1v1d11a!!y, the ideas do need rhorough
d1st:ussion aherwaids_
1. These answers are suggeslions only aud you may disag1ee wilh them
a) You would nonnally get enough categories by using whole nurnber sizes un!y
b) For half sizes agree to take the next whole number size up c) Take the larger srze (cons1sten! with (b)) (/u1k a nunihcr of people have one
foot larger 1han the other. d) Collecl the inforrnatton on paper auonymously c) You could gel idiotic answers, no answer or rnu!t1plc answers It is p1obably
best lo collect on paper but with the responden(s name attached f) fhere may he absenlees from the class
Pupils in another class n1igh1 1ef11se to co operate:
Should boys and girls Le consideied in separa1e groups'!
1 02 ST (P) MathenHitics 2A
EXERCISE 26e (p. 401)
EXERCISE 261 (p. 402)
EXERCISE 26g (p. 405)
2. Wcig.ht,w(inkg) 4~w<!I 8~w<l2
~H:qu:~;------~1-·-,---~·--r--~--,-,---1 12~w< 16
5. a) Suggested groups 50 ~ w < 55, 55 ~ w < 60, etc.
1. a)~ b) h c) £45 d) £15 e) £120 2. Bus, 144"; car, 84"; bicycle, 36"; walking, 6tr; other, 36° 3. Science, rnaths 90"; art, music, 60°; English 40"; languages 60~; others I Hr 4. Total viewing lirne 30 hours
Conwdy series 180"; news 12"; plays and fihns 60"; docu1nentaries 60";
other 48°
1. a) 90
85
80
" 70
65
!1 60 :ii
55
50
45
40
35
0
b) Yes
T - ->< x _,,_ x
x
- __,, x
x
40 45 50 55 60 65 70 75 80 85 f renrh
2. a) 75 ~ ·--·-~=~-! ~~ -·- _-,----- ____ _ t- --~-
--- ·----·-
-
70 -----·-- --- - -· -- --- ---- ---· {----- -··
o; >( ~ 6 5 1--+--+-·····• . - I'----'------ --···- .__ __ ---
"' ~ ; 60
---t-1----1----,/- "---- ---· '-- L__ -- -
--- l----- -- -·····- ----
55 ---- --'------ ---·-··
____ ; ..... ---~---
~
150 I 55 160 165 170 115 1110 !85
lle:igh! (cm}
h) Faitly likely
INTRODUCTION
Book 2A is the secoud of the A books in !he ST(P) graded sc1ics in nu1the1nalic A sc1ics auen1pts !o satisfy !he needs or pupils ptogressing lluough the Na Curricuhnn and ain1s to prcpa1c them to achieve about Level 7/8 al Key S and !he highest level at ( JCSE. A nu111hcr (>r lo pies have been introduced as a nf !he Na!innal C11rric11h1n1_ ()riginal!y kalured in the Supplcmcnlary Be !hey have now been incorporated into this new edilion and the chap1e1 on!
interest has been reniovcd.
The book builds on the work covered in Book I A and in many cases revist
work, completing coverage of !he attainmcnl targets al Level 5, n1ost of Level abou! half of Leve! 7_ Sonie of the wo1 k in Book 2A goes beyond Level 7 at oilers f-lexihi!ity in the use of !he b(lok For example, the inlroducti trigono1nctry is included for thn.se teachers who prefer lo slat I the 1opic at tbi~ and to develop it over a 1!11ee 01 four yea1 span and ror !hose pupils wl prog1essing t_piickly through the N<1!1ona! Cuniculurn The 1rigono1netry <
ornilled, howevet, as i1 is fully covered in Book 31\.
·1 he tex.! is brief and ai1ns to supply explanation for those pupils who wish tor themselves of the reasons for what they are doing but in most cases ii do
supply a con1plete introduction lo a new topic, thereby allowing lcachers
their own ideas
rhete are some !opics that can he done !alc1 or ornitted completely. [)c
suggestions on !his are given in the teacher's notes
' 1v1uch of the wotk tn the hook involves coordinates for which 5 mm squared p< best, though graph paper is needed for Chapter 22 and 24
There is a pkntiful supply of carefully graded exercises. Questions th; underlined, e.g.12, are extra, but not harder, queslions for extra practice o revision. <)1ws1ions !hat a1e double nndetlined, c_g_ 12, a1e for those pupil manage the straigh!lorward queslions easily and require n1ote stretching. chaplerscud with n1i:\cd exercises rhese can be used as and when 1he !cacher
lit.
A lot of the d1fficul!y that children have wilh mathematics cornes ho1
undc,standing the words Iha! we use_ Whenever a new word or pluase con1e
needs a lot of discussion to clarify its meaning and a re1ninder each time it reap
f\1ost children also need cons1ant ren1indcrs ol the ordinary processes of arilh
For exa1nple. each 1i111e 1nultiplica1ion of fractions is involved they shol
ren1inded of how !o do it
As is the case with Bo<'k I A, these noles are intended only as sngge~
[;>.:peiienced teachers will have their own ideas on approach and order of co
fbcy will also know their children we!! enough to know whal !hey can and c
tackle
EXERCISE 26b
(p. 396)
Teacl1er·s Notes and Answers 101
4. a) Number ol rooms
11
I ~1 l-l '111
6
-1·' 2244176) frcquem:y
c)S d)l40
s .• > ~""'""'-"'-"1""'"'J~j'L1\ ' j 'f •L1L'l-'-rrequeucy I o 1 I 2 _1 4 31 } ! 1 2
c) 14 d) 20
1. a) 3~- 'I b) No (As soon as data is g1oupcd, sorne info11nalion is lost)
2. a) 59
b) ~1ark ----~~~~--~-~i=:~ ~"'-~~!.~~- 7~180-89_ Frequency I 8 ] II !8 I !-1 I 8 I !1
3. a) 25
b) ~o ofwo1ds J_1-51-6-~~t1_~_1 __ s_t6 101!~.126 29
l·1equency I I J I 8 I 5 ] ) 1
EXERCISE 26c 1. Whole nurnbcr 4. ( 'ontinuous
(p. 397) 2. Continuous
EXERCISE 26d (p. 399)
3. Whole nun1be1
1. a) 8 b) 4 c) 140~h < 145
2. a) 47kg b) 5
d) 6 e) 81
3. a) I b) 7 c) 20
5. Continuous 6. ( 'ontinuous
d) l-le1gh1 Ill cm Frequency --------- ------!JO~h<!J5 8
--··--135:::,; h '-. 140 14 ---------- - ------· !40>i, h '-. ! 4) 18
14S~h< !Sll Jl
!50~h<!55
roial 57
c) Weigh! m hg
40~w~60 20
60~w<80 61
80~w< 100 J]
l<Xl~w~ll<l_ +-~
rota! l 100
d) No
100 ST(P) Mathernat1cs 2A
19. a) 7! hours
EXERCISE 25c 1. f:S I 50 (p. 389) 2. £68 32
3. f81J_J()
b) 37l- hours
4. f 112 29 5. £1()4 63 6. £116 21
c) £106_50 d) Ii hours e) f/1289
7. £74_09 10. £126 83 13.£9671
8. £150 37 11. £7(1 14. £133 84 9. £79 75 12. £74 81 15. Ul306
EXERCISE 25d Be careful with Nurnbe1s 13 10 20_ f)o no1 suggest 1ha1 they investigate the {p. 390) backs of elec11ical appliances such as cookers, fridges, TV se1s, etc., look111g
f111 1a1ing plates Ihe inforn1a1ion is usually in 1l1e i11struc1iun book and son1e1i111es in sales literalure and discount store lists, etc.
1. J 4. 0 06 7. (I 06 10. 7 2. 110 5. L2: 8. 0.02 11. 0_145
3. I~ 6. 0.25 9. 8 12. 2
21. 16 24. 3 27. 0 144 29. 2 22. I 25. 18 28. 0.56 30. 0 84
23. 12 26. 1.5
31. 4hours 34. 10 hou1s 37. 3 p 40. 1t p 32. !- hour 35. 2~ hours 38. 12 p 41. 18p 33. 2 SO hours 36. 6~ hou1s 39. 3 024 p
EXERCISE 25e 1. £35 6. il04 11.£7070 (p. 391) 2. £42 7. £140 12. £11080
3. £79 8. £48JO 13. £9.l 24 4. f!OO 9. £92_78 14. £85_44
5. fl 10 10. £82 90 15. £157 15
16. £1]5 19. £103 17. £98 20. £182-20 18. £95 '}0
CHAPTER 26 Statistics -=-=-_,~-~-'"'"".=.--...,"""'"---"-~-
Tluoughout !his chapter, data exlraclcd fron1 exisring databases within !he school can be used to supple1nent, or even replace, info:-nlaliou given in the exercises.
EXERCISE 26a 1. a) 3 and 4 b) 6 (p. 394) 2. o) 9 b)
c) fypc of pd
F1eq11cncy
d) 29 e) Rabbit, harnsler f) II is nol possible to answer this
3. a)
'o!"<>''--- -1 "l-w-f~ I 0
Frequency 10 9 6 7
c) 16 n1ales, 16 kn1ales d)
CHAPTER 1
EXERCISE la (p. 1)
EXERCISE 1b (p. 2)
EXERCISE le (p. 3)
NOTES AND ANSWERS
Working with Nu1nbers
Revises 1he wo1k 011 positive indices in Book IA Give a ren1inder of 1~
meaning ol 1hc wo1d nidex and point out tha1 1nd1ces IS lhe pluial of mdex
1. 9 4. 12.5 7. ! 28 10. 10000 2. 4 5. 1000 8. !O 11. 1000000 3. !00 6. 81 9. 6·1 12. 27
13. 7200 18. 537000 14. 893 19. 46 1 15. 65000 20. 503_2 16. \820 21. 709 17. 27 ') 22. 69 78
/'vl1Kh dass d1~cuss1on is necessaiy n~mg di!Tc1ent exainpks and 1ndud1n cases wluch do 11(1! snuph!y. such as ! 1 x f
4. )I l
5. b~
6. S8
7_ I!,,
8. pp
Discuss exan1pks wh1d1 do no! sn11p!dy. e g 31'--:- -2'. as well as those 1ha1 do
1. 4 2 4. HI-" 9. 9 1
2. Ji> 5. '/~ 10. p' 3. S' 6. I .':i~
11. 6 1 I 14. ()ll 17. 4 1
12. 3) 15. c 3 18. o' 13. 21 16. 29
EXERCISE ld The. meanmg ol ··reciprocal"· peeds to be lnade dca1 \\llh cxainplc:;, such a (p. 4) ··~is !he 1ec1procal of -1'" ··4 1:;, the rcup1ocal ul 1·· ··wha1 1s the 1cciproca
of JT' etc
Cons1tierable discussion is needed also 10 get over the idea 1ha1 a nega1iv1 sign Ht fron1 of 1he indell is shorlhand fo1 ··1he 1cciprocal of" and does no
mean that a 11ega11i:e 11ur11ber 1s involved, !f 11 1s 1hough; necessary. the pupil' could be !old 1ha1 a 0 =I is I rue only if /1 .f O
1.
2. "l~
3. 1!6
4. 5.
8_
9.
10.
11" i,!4
12. )'{;"
13. h 14_
15. }.,
16. ris 17. mo 18. i 19. lo 20. ' i:"4
2 ST(P) Mathematics 2 A
EXERCISE 1e (p. 5)
EXERCISE lf (p. 7)
EXERCISE 1g
(p. 7)
21. O.O<J34 26. 0.000 046 7 22. 0 26 27. 0 ]06] 23. 0.062 28. 0.028 05
24. 0_008 21 29. 0_()05 173
25. 0.000 538 30. .1.004
31. 5 - l 36. 10·· 3
32. r' 37. b "'
33. 6 ·-) 38. 4'
34. 2' 39. " 35. a l 40. 2~-h
1. 4 4. t 7. 81 10. ' n; 2. ' 5. l 8. l 11. ' 'f5 rooo 3. 64 6. 125 9. 4 12. 2
13. 2410 18. 0 1074 14. 0_7032 19. 783.4 15. 497.1 20. 1050 16. 0007805 21. 5 99 17. 59 200 22. 0.00018601
23. 2' 28. S' 33. ,,
38. a'" 24. 4' 29. J' 34. a" 39. 1- 1
25. J' 30. 6' 35. ]' 40. b' 26. a' 31. 4• 36. I' 41. 5 - 5
27. a' 32. 5 -- 6- 37. 4' 42. a'
Child1en with scienllfic calculato1s should be shown how numhe:rs in standard forin are displayed e g if 00000002) c- JOO is cakulated the display \~ill show
l 5 ~ 09 ·1 hey can be asked lo do simple cakulallons wl11ch resull in nmnhers given in s1andard fo1rn and 1hen be asked to wote down 1he answer as an ordinary number
1. 1780 6. OOOOOOJ67 2. 0 001 26 7. -10400 3. s -~00000 8. 00008SOJ 4. 740 000 000 000 000 9. 4 250000000000 5. 0.000 I J 10. {) 000 000 064 J
1. 2_5 x 10-1 6. 3907xJO-'- 11. 1 (i{)l x !()-'-
2. 6 l x 101 7. 4 s x 106 12. 547xlO' 3. J__5J x 104 8. 5.J x 108 13. ~-06 x 104
4. 1 6 x 10~ 9. 4 x 10-' 14. 4J)6 x 106
5. 9 9 x IO' 10. 8 x 101 0 15. 704xl0!
6. f 8.40
36AO 4_80
49_60
7. f 1_44
1_56
48
3.48
8.
9.
10.
£ 4_40
I 68
I 96
8 04
f ! 74
I 61 I 80
214 7 40
f
I 08 4.? 42
I 92
H.
12.
13.
14.
15.
f 61
2 08 96
76
4.41
f JJ)4 J_ so
44 71
s 70
f
I 26 !_86 ! 68 2_ 76
7 56
[
I 68 1 I 'i
LSJ
6 .16
£ ! 7 5 l 10
\4 !4
l 81
reacher ·s Nates and Ansivers 9 9
16.
17.
18.
19.
£ 3710
6 __ ')0
I J_80
IS 60
7 3.40
f ')I 7S J7_60 32.95 4 50
126 80
f
J 18 2 79
I 84 4 40
16 41
[
J 12 I 0 ]_)
I 5? ))
46
16 01
EXERCISE 25b lhscuss gJoss and !Kl wages a1:d ,kdt1c!HlllS [)1sn1ss also d1flerenl way~ of
(p. 384} cak11lat1ng pay are they Ian. why a1e they use(f'
1. r 1 ·,o 3. [91 48 5. t 1,tx 61 7. £120.41 2. fl22.50 4. 1!7618 6. f 196 :!4
8. a) ?hours 40rn1n bl '8hours 201n1n. flOl 97
9. 4'ihours_ fl4! 75 10. a) lJ h) 3X~, £87.57~
11. a) £11780 h) £164.10 c) £17160 15, £171 4J 12. £20.194 16.£18837 13. £15715 17. f 144 80 14. £201_76 18. £176_88
98 57 (P} Marhernatics 2A
EXERCISE 24h (p. 375)
7. a) Reily, Chris, A11drey e) al 2.JOpm, af1er 25 01iles
g) 2t km
b)JOkrn/h c}lSkm/h d)20k1n/h f) Audrey 10 kin. fk11y 9 kni. Chris 15 kin
8. a) at 3.23 pm, 9! miles frorn Jane's homC b) 3 8 rniles
9. a) al J_l4pm, 601niles f101n A b) 61niles flonl B
c) 26 01iles fron1 A
1. a) 20 kru b) 2! hours c) 8 km/h
2. a) 1"i km b) Ii-hours
3. a) !4hours b) 57 hours
4. 80 kn1/h 5. 70mph
6. 5 kru/h 7. a) 15 krn b) It hours c) \01nin d) I 0 k1n/h e) 45 km/h
EXERCISE 24i 1. a) 175kln h) !}hours c) the train stopped d) 120kn1/h
(p. 377) 2. l E
' . 'fl T
_500
400 1 5 : Jill
" 200
J " lOO
0
Time m lwui~
3. a)900m b) 1575rn. 54k1n/h 4. a) } hours b) ii hours 5. 200 km/h by )_6 m/s or 20 kn1/h
6. 11 kni/h 7. a) i) 125 kin ii)760kln b)l~hou1s c)l7J~kmjh d)no
8. a) 35 n1iles d) at 1330_
9. <18 1nph
b) Nina. 2~ h; Fa1hcr, I~ hours c) f'athcr. by 51nph
15 1niks froln Farley
CffAPTER 25 Bills and Wages
EXERCISE 25a Check son1e aclual supennarkel bills and go into lhe meaning of all cnl11es on
(p. 380) 1he1n
1. £11 32, £8_68 4. £15 72. f4 28
2. fj)_J6, £4 64 5. £ 15 04, £4_96
3. £ 12, £8
EXERCISE 1h
(p. 9)
EX~RCISE 1i (p. 10)
7eacherS Noces and Answers
16. 26xl0- 2 21. 79x!()-I 26. 9_07x 10- 1
17. 48xi0- 3 22. 6_9 x 10·:; 27. 8.05 x 10-i
18. 5 3 x 10·- l 23. 7 5 x 10 • 28. 8 808 x 10- 1
19. 18x10-~ 24. 4 x 10 '" 29. 7044x 10·•
20. 5 2 x 10·-l 25. 684x 10- 30. 7_3x 10- 11
31. 79]x!01 36. 6 O'i x 101 41. 53xl012
32. 5 27 x !O ' 37. )_005 x 10· _, 42. 5_02xl0- 8
33. 8_06x!04 38. 6_0005 x lO 43. 7.00809x 10 ' 34. 9.906x 10-- 1 39. 7 08 x HJ" 44. 708xi03
35. 7_05 x JO'" i 40. 5608x105 45. 4_05 x 101
46. 8892xl0' 51. 8-4 x 10' 56. 5_09xl0J
47. 506x 10·~ 52. J s 1 x 1 o' 57. 268x10 5
48. 5_ 7 x lO • 53. 9 x 10 ' 58. 3 07 x 10'
49. 503x 108 54. 7 05 x l 0 ' 59. S.05x 10- 3
50. 9 9 x 10 1 55. .~ 6 x 10 1 60. 8_8x!l)-- 6
Revises the woik done in Book!/\_ Nunibns 11 to 15 are useful for discussio
with everyollt: hut only !he abtc chdd1en should work tluough these llll 1hc1
own
1. 1550 l.'100_ 2000 7. ,-HJ 10. 4100. 4000
2. 8740. 8700. 9000 8. 7\111. 7500 8000
3. -1750_ 2800_ HJOO 9. 'l J 800. 5J 800. 5,1 000 .. 16 840_ 16 800. -17 000 10. 6010. 6000, 6000
5. 68 ,11 o_ tiR ,100, 68 ooo 11. -1980< ')(100. 5000
6. 5730. 5700. 6000 12. 8100_ 8700, 9000
13. '14, ·15 16. i 1 ){)() ooo 14. 4) 499 44 ){)() 17. !YSO
15. ! S-19 1,1)0
Revises the wo1 k done in Book I A l'!!pds do not always realise thal a nuinbe
correct 10, '>ay, two dcci1na! phu:s inay end 1n Le10, e g. 2.596 = 2 6-0 conec
to 2 (Lp
1. 276. 28. J 6. 390.39.4 2. 7_17_74,7 7. 894,89_9
3. i6 99_ ]} 0, JI 8. 71 65, 7J.6, 14
•• 23 76_ 23 8, 24 9. 6 90_ 6 9. 7
5. 9 86. 9 9, '" 10. )5 )8, 55 6, 56
11. 5.1 16. 0 9 /)
12. 0 009 11. ) )"JI
13. 1 90 18. 281 6
14. J4 8 19. 6 I 15. () 0078 20. lO_OO
4 Sr( P) Mathematics 2A
EXERCISE 1j (p. 12)
This exercise is particulaily i1nponant wilh fullHe work in mind
1. 3 2. 8
•- 8 5_ 7
3. 6 6. 8
7. 0 9. 0
8. 0 10. 8
EXERCISE 1k Particulally i1npor1ant with fu111re work in mind_ N1unbers 41 to 50 a1e not
(p. 12) intended for use with a cak11la1or
EXERCISE 11 (p. 14)
1. 60000 5. 80000 9. 700 000 2. 4000 6. 500 10. 900 3. 4 OOOl~Xl 7. 50000 11. 30 4. 600000 8. 4000 12. !Orn!
13. 4700 17. 7000 21. 50000 14. 57000 18. 10000 22. 54000 15. 60000 19. 7JOOO 23. 480 16. 890000 20. 440 24. 600
25. 0_008 46 30. 000785 26. 0.876 31. 7.51 27. 5_84 32. 370 28. 78_) 33. 0.990 29. 46_8 34. 54_0
35. 47 40. "iOOO
36. 0 006845 41. 37_9 37. 600000 42. 7000 38. 500 43. 0 0709 39. 7 82 44. 0 07
45. 1 __ , so. 29 46_ 1.7 51. 24 47. I J 52. 0.23 48_ 13 53. 0.0~6 49. 14 54. 0.0004 l
Revise n1111fiplicatinn and divi:;ion hy deci1nals hefore working through this exercise. Allow sorue discretion in the nun1ber of sJ. accepted for the answer.
1 _ 100 11. 600 2_ ]6 12. 4 5 3. 0 35 13. 2 4. 10 14. 0_7 5_ 180000 15. 17
6. 08 16. 0 001
7. 0-48 17. 0 0056 8. J 6 18. 80 9. I J 19. 90000
10. J 500000 20. !_)
Teacher's Nores <Jnd Ans1-<vers 91
13_ 80 kmih 17 12 km/h 21 _ Sci rnph
14. 90 km/h 18. 8 k 111/h 22. )4 mph
15. 64 km/h 19_ !8 km/h 23. 601nph
16. I JO k1n/h 20. "i m;s or 18 kllllh 24. I OS 1nph
25. "i!ikrn,'h 27. 80 km/h 29. 80 kin/h 31. 50 k mfh
26. 4_, kn1/h 28. 42~ k111/h 30. QO kin/h
EXERCISE 24e lnlended fm the above average only bu! can be U'ied for discussion \vith
(Jl- 356} everyone
1. 9km/h 2. I01nph
3_ 7 1nph
4. 7 1nph
5. 75 km/h 7. J knols
6. ! 25~ kn1/h
EXERCISE 24f Use Numhcrs 7 to !() for discussion wilh all hut lhe above average_ In
(p.356) ques11on 10 a ruler can be used lo see how !he g1adien1s change
1. <1) i) 1215 ii) jJ,18 iii) 1445 b) 1~ hours c) i) 11h111ns1i) H hours
d) 64 kni/h 2. a) 40k111 b) 21 hours c) 17~k1n/h d) 21~ kin e) no 3. a) Xkni b) JOJO c) 11-houts d) 6.4 krn/h e) 6 4 km
4. a) ii 125m1les i1) 17\miles 111) 60miles h) 1) 4l hours 1i) Zho11rs 121nin c) 80111ph d) 200 1niles frum A e) noon
f) no
n yes
5. a) i) 90k1n ii) )Olnn b) )hours c) 28km/h d) ?8krn e) i) 42kn1 i1) 48 kin
6. a) i) 1309 ii) f'i09 b) 40rni!cs c) 20mph d) Hln1in e) 13niiles
f)ll\4 7. a) 45 krn h) l ~hour"> c) JOrnph d) I hour el 4'.i 1nph f) 31 mph
8. a) 801n b) !Osec c) 8m/s d) 801n e/ 40s.ec f) ?m/s g) J\m/s 9. a) 1) B ii) B h) i) 80 k1n/h ii) 64 krn/h c) j hnut d) 1/ hour
e) 58 1 kn1/h (co111111ng !he stop) 10. a) Rrniks b) 1 c) lhour d) !!hours e) 2~ ho111s f) J_l n1ph
g) the last one h) the firs! and second
EXERCISE 24g Numbers J to 10 are infended for the above ave1age; they can be 11scd for discussion
(P- 368) with the f!:Vcrage.
1. ;:i) ISO miles b) ~hours c) 75111ph d) I hour e) 1110: ]~hours f) 60 n1ph
2. a) ]J)6p1n ii) 3 48pm iu) 4_06pn1 iv) 4_J6pn1 h) SS miles
c) i) 50 mph ii) 40 rnph d) I 8 nun e) 16~ n1ph 3. a) First 141nph; second 40111ph b) at II 15_ 40 nllks frorn Lond()n
c) 601n1lcs
4. a) 561niles b) 45minult's 5.a)i)08l0 ii)l~JO b)5h
6. a) 80km/h. 1430 b) IOOkrn/h. d) 51 n11les
c) 'i6 mph d) .}61nph c)l!hours d)4km/h e)7hou1s
I 154 c) al 1410_ 153 miles fron1 A
96 SJ (P) Mathematics 2A leacher·s Nores and Ans~vers
14. 21. lU 26. t:? 22. () ]6 27. ! 5 23. 10 28. ll .?5 24. ? 29. 0 I! 25. 32 30. !:HJ
EXERCISE 1rn Pupils rnay need re<1ss111ance 1ha1 1he cakula101 11lus11a1ed Hl lhc P11p11"s Bo
a) 2 miles b) 141n1les (p. 16) on page 15 is only an c;>;ampk and that 1hcic are many dif!e1en1 designs
'- 7 08 6. 7 71 11. 3 80 16. 11JO 2. 1 55 7. 7 49 12. I 10 17. 8170 3. ! 02 8. 9 I\ 13. 2 94 18. 6580 4. 8 S4 9. J 61 14. l S4 19. 15 5
Tim~ rn hours 5. 9 !9 10. I )6 15. I 44 20. 6.65
21. 172 26. J6 8 31. 2 70 36. 0 0481 22. !4 7 27. 19)0 32. 0 0196 37. I 79
15. a) 800 k111 b) I IOOkm 23. ! 1 2 28. J8 0 33. 0 0549 38. 0 0051 ~
16. a) 48 krn b) 84 km t:) S4 kin 24. ! I 70 29. I lSO 34. 526 39. -197
17. a) I ?00 rniks b) 1650 1niks 25. ! :: 600 30. 14400 35. 4 6.~ 40. 0 548
18. a) 90 kin b) 135 kn1
19. a) 9 n1iles b) !Soules 41. o_ 1 ·21 46. 1)4 51" 49 0 56. 9 83
20. 4) 52.5 m b)8915m 42. () 0825 47. \\ 8 52. 11100 57. () 691
21. a) 32 miles b) 38 1niks 43. 0 -~9 J 48. 9 ! 7 53. 8 J.6 58. 0 742
22. a) 4 krn b) lj- kin c) !Okin 44. 0 103 49. 186 54. 2 28 59. 0 1?8
23. a) J7 mites b) /85rni!es 45. 0 !39 50. 957 55. 0 671 60. 10 300
24. a) 500 m b) 850n1
25. a) 17551niles b) 4185miks 61. 6.3·10 65. 0 l6J 69. 0 000 000 096 I 72. 16 7
26. a) 30 b) 11 62 0 006 08 66. 0.0201 70. '1YJO 73. 0 000 14 63. 34. 8 67. 0000123 71. 0 !74 74. I J 4
64. 484 000 68. 611
EXERCISE 24c 1. a) 2 hours b) 3 hou1s
EXERCISE 1n 1. ' 4. \ 6·l x !04 7. 0 0614 j(,
(p. 17) 2. l/h) 5. ) 07 x 10 ,
8. 3 71 3 6. 60000 9. 2 88
(p. 351) 2. a) 5 hours b) J! hours
3. a) ~hour b) 11 hours
4. a) 2} hours b) 'i} houis
5. a) I~ hou1 s h) '}hou1s
6. a) I! i101lfS b) 4~ hours
7. al 25 sec b) 200sec
8. a) 24 min b) 54 min
EXERCISE 1p 1. 216 4. " ,
7. 2! 'iOO 9. ;i) ?J6ho11rs = 9days b) 5l days
10. ") 11 ho1J!S b) 21 hours (p. 18) 2. ' , s. 6 s x 1 o~ 8. !JSO
11. a) 2} hours b) 5 hours 20 rmn 3. 6. 46000 9. 0 699 12. a)~ hour b) J! huuis
EXERCISE 24d 1. XO kin/h 4. 120 n1ph 7. 50 krn/h 10. 8 mph EXERCISE lq 1. 4. S108xl0 ,
7. 9 (p. 18) 2. la 5. 10000 8. 9 89
3. 6. 0 0508 9. 4 JO (p. 352) 2. 60 kmlh 5. 201n!s 8. 65 k111/h 11. l6 lll,'S
3. 60mph 6. 45m/s 9. } ') tt)ph 12. I 7 1n/s
6 ST(P) A1alhernarics 2A
CHAPTER 2
EXERCISE 2a (p. 19}
EXERCISE 2b (p. 20}
EXERCISE 2c
(p. 22)
Prnbability
The language 11secl to describe rhis !opic often leads 10 111is11nde1s!:u1ding the words ··exper1rnen1·· -·even1· "outconte" etc all have fai1ly precise meanings and plenty ol discussion is needed 10 n1ake their 1ncan1ng:s dear. 11 1s also
importan1 lo discuss the ohjec!s used for expenn1cn1s: fo1 exa111pk not all
children a1e familiar will1 an 01dinary p,1ck of playing ca1ds_ especially those
frorn rvfuslint hackg101J1His II is a gnod Hka to have sorne packs of cuds available and so1ne dice (We have used the plural fonn. dice. for one die
lhis is deliberate as ii is the word lhal 111ost people use fhese days. b1Jt ii is a good ide<i lo 1ell the ch1ld1en thal !he singu\a1 is die )
ln several questions 1e!'erence is made lo sets of integers or whole numbers these do not include zero.
Can he used for discussion
1. 2. ill. T) 2. 1. (R. B. Y) 3_ 10. 11. 2, 3. 4. 5. 6. 7. 8. 9, 10) 4. 6. { R, Y. H. Rrown. Black. Ci) 5. l. {chewing gum. boiled sweets. har or c!Hx·olate!
6. 4. (Ip. IOp. 20p. \Opi 7. !J. {A.?.. J_ 4. '.'_ 6. 7. 8. 9. 10. J, Q. K] 8. 5, {a. c. I. o. u/ 9. S. (1. ]_ ~- 7. 11}
10. 10. !?. 4_ 6_ R. !O 12. 14. 16. !R_ ?O}
Discuss !he phrase ··,n r::indn1n-· and intlude exa1nples whe1e ob1ects are no1 chosen at 1andorn: e g. a boy taking a piece of cake from a plate-- ii he likes 11 he will try lo take the largest slice. The quesllons !fl this exercise c;in he
used for d1scuss1on (ahei the coruhtions)
1. 4. 7. ' ~-!
2. ' s. 8. t 10
3. 6. 1io 9. 1'1
Nurnbers 9 10 15 rcq11tre an above average unde1s1anding of language_ Use
1he1n for discussion w1!h everyone bu! allow only the ahove average to try then1 on their own
1. 5 6. 4) b) ~- c) d) ib 2. 7. a) ls h) ~ c) d) ' " 3. !6 8. a) ~ b)\ c) d) ~
4. 1 9. a) ! b) ! c)
5. 10
11.
12.
13.
0
a) 7~ km
-~ 160
s: 120 u c
6 80
40
()
lune !>l ho11rs
b) 111 km
h) 12~ kn1
l c
I une 10 1-ioms
I eacher·s Notes and Answers
J ,J
:!_:
b} 44 rnilcs
95
94 S f(P) Mat11ernat1cs 2A
5. 8.
]{llJ j
,; J e l
I OU
'l u· +
" .!! e " 100 " 50
g " ~ g 0
1 l lime in hmHS Jim<' Ill homs
6.
9.
I 11lle in ~cc
lime"' hours
., .
l 1m« •n hour~
EXERCISE 2d (p.24)
Teacher ·s Nares and AnsH'ers
10. ' ,, 14. " l6
11. al b) ~ c) l 15. ' 4\
12. ' 46 16. a) j~ b) ! c) i ' 13. a) " b) t:} 1 36
CrHl be used for d1sn1ss1Dn
1. o_ 1mpnss1bk 2. O l, t111like!y to be this heavy
3. alrnos1 ce11a1r1
4. () 001. possible b1Jt unlikely
5. ()_ 1nost unllkdy~
6. 0. unposs1bk 7. CCI lau1
8. 0. vutually 1n1pr>ss1bk
9. !. I! !llU~l be
10. 0 aim PSI 1rnpnss1b!e 11. L 1ld} you will wa!d1 IV ll11s wn:\,. you will get 1na1hs humcwofl.;
week \ 1nlikdy vnu will he ;i 111ill1unanc !l will snow Ill Brna1n on nut! Slln
da:
EXERCISE 2e Nu1nbers lO lo !4 can be used Im '11sn1ss1011 with evnyon.:
1 4. 7. ~~ 9. ~JI •O
(p. 25)
2. " 5. 8. 10. .!_Q
" 10 " 3. ~A 6. i
11. a I ' tiJ rU cl di tli " 12. a} ' b) 1 c) i d) " i"l n 13. o) !_} b) i1 c) /-J d) r1 !!
14. a) h) " <) ' d) () Hi -ro
EXERCISE 2f Can ht> OllHIH:d
(p. 27) 1. () I l () • •
--~·----
(J (C) (l) (( ) (_)) i("J \_)) 10. . , ((). • (! t Cl Cl) ((_) ( l) (() UI {() . , 10 • () i (_) ()) IU ()) (()_ {_)) ( () ., {(__). • • le ()) 1• (_)) 1• OI 1• •1 1• • • ,. {_)) ,. (J) 1•. ()) llil ., 1• •
8 ST(P) Mathematics 2A
EXERCISE 2g (p. 29)
2. [)ice
2 3 4 5 6
------------ ·-~·- --~·-~------
H (II. 1) (H. 2) (H, J) (11. 4) (11. 5) (ll. 6)
\Op
T (T. 1) er. 21 (T. 3) (T. 4) (T, 5) (T. 6)
3. Isl bag
R R y B
------------- ------------R (R. R) (R. R) (R. Y) (R. B)
y (Y. R) (Y. R) (Y. Y) (Y. B)
2nd hag y (Y, R) (Y. R) (Y. Yi (Y. ll)
B (B. R) (9. R) (B. Y) (B. B)
4. IS! spin
' 3
------------------( l. 1) (1. 2) ( 1. ll
2nd spin 2 (2. II (2. 2) {2. J)
3 (3. 1) (l. 2) (l. 3)
5. Penc-~I
Red Green Yellow
-------------------- -------· ---------.. ------·-Round Round. Red Roun<l. Green Round, Yellow
0 n Square Square. Red Square Clreen Square. Yellow n " "'
f"riangular rriangular. Red Triangular (lreen Triangular. Yellow
()1ni1 this exercise if Exercise 2f was no1 covered
1. a) ~
J eache1 ·s Nor es and Answers
CHAPTER 24 Travel Graphs
Al! ahihly groups find this 111teresllng
EXERCISE 24a 1. a) 90km b) ) hours r) 4) km
(p. 345) 2. o) 146rniles h) ) 2 hours c) 28 ni1ks
3. a) 10 krn h) 3 hours c) !Okm
4. a) !6111 h) 6sec C) 24 Ill
5. <) j() Ill b) 8 sec c) ! 2Sm
6. •1 107km h) 11 ho111s c) 1 J 4 kn1
7. <) l'iOmiles h) l hnu1s c) 7'i miles
8. ') 50 nnks bl ?hours c) 2 n11les
9. a1 20 rn b) 'i ~ec c) 4 Ill
10. 'I \Jm hi I I sec d lm
EXERCISE 24b !"he scales 111 some of these answers have been halved
(p. 349) 1. 3.
Ml ]00
E
' 40 < 0 -"
20 " !00
c_';:
0 5
l nnl' rn hu"" JOU
l HH~ !!l hnnt\
2. 4.
' :no
0 150
0 0
>00 6
50
0
l ulw 111 hn11<> Tim<' in houis
97 ST(P} Mathe1narics 21\
23. 183'/ rniles 27. 114 24. 2583 kin 28. £I 10
25. 72 nun 29. 92
26. 131 6hours 30. 9
31. 61, 21 35. 68; reduces it to 67
32. 23J. 193 36. 158cin; ii;:icreases it to 159cm
33. 106, 238 37. 6-1610, 12 722. 8294
34. 10_5 hours, ]~ hours 38. I 364 kg
39. 160_6crn 42. 285 Clll
40. 55_6 kg 43. 2652
41. 26
EXERCISE 23b 1. 12 5. 5.9
(p.340) 2. 9 6. 26-4
3. I 8 7. I
4. 56 8. 8
EXERCISE 23c 1. 5 4. 16
(p. 342) Z. 41 5. 3_2
3. 17 6. 12
EXERCISE 23d 1. i) 10 ii) 7; iii) 0_7 iv) 10 v) 0.3 vi) 06 (p. 342) 2. a) Sandra (I l conipared wilh 12 on average)
b) Karen (range 5 compared with l 2).
3. ~v1ean weight for hoth ba1ches was 20 g
9. 10. 11.
7. 8. 9.
155 cm
ll. J 36. 6
98 36 I 885
Range fo1 Mr Bullon·s balch was I Jg and for tvtrs Bunon's was 5 g lng1cdients were lhc same fen each ba1ch: tv1f Burton was not so experl al
dividing the 1nixture into 20 equal portions
EXERCISE 23e At Ibis point ii would he useful 10 discuss the advantages and disadvantages of each (p. 343) type of ave1age_ For exa1nple: If five people arc en1ployed by a sn1a!I flnn and their
weekly earnings a1e £400, £90, 180, £80, £60 whal is the !Jest foru1 of ave1 age to use
for these llgurcs and why?
1. a) 23 b) 21 c) Zl d) 16
2. a) 71 b) 66, 67 c) 69 d) 16
3. a) 45 b) 43 c) 45 d) 7
4. a) ·1 _1 b) ll c) J2 dJ 80
5. a) 28 b) 27 c) 27 d) 6
6. 77, 77, 73 7. a) I 57 Cfll b) 157 Clll c) IY7cn1 cl) 10
8. a) 54 b) \1 c) 12 d) 54
9. 83. 84, 81 5 10. a) 0 b) 0 c) 1.5
leck:her ·s Notes and Answers
z. a) n b) )~
3. ' ' •• ol i!t: h) ~ c) r~ d) i
5. 5 p coin
I! r
I! (ll, II) (11. n Ip coin
r er. HJ (f, I)
6.
• 4 • - ---
(L I) (I. •l (I JJ (I. 4) (I. •I (I. 6)
l (211 U.•I I' Ji (14) (1. •I ('. 6)
?od (1 I) (l. •J (J. 1) (1. 4) (1. ii) (1. 6)
dice ·I 14 I) (4. el (4, 3) (4 ·1) (4. •> (4 6)
( \ I) (5_.) { ~- i I n. 4) (5. •> (\ 6)
6 (6, I) (6. •l (6. 1) {6. 4) (6. •> (6. 6)
a) A h) ' c) ' cl) l'l' jli ,,
"
1. Fusi bag
10 p 10 p 10 p 50 p 50 p
JO p (I Op, I Op) (!Op. I Op) {!Op, !Op) (!Op.50p) (!Op. 50p
2nd hag
50 p (50p, !Op) {'>Op, I Op) (50p, !Op) (SOp, SOp) (50p.SOp
JO ST(P) Mathernatics 2A
EXERCISE 2h (p. 31)
8. First shelf
Story Story Tex I rext Te:» I
·-~·----·-- ··---·- ------~···
St or) (S, S) (S, S) (S, n 15. I') (S. T)
S!ory (S. SJ (S, S) (S. T) (S, T) (S. n 211d shelf
S1ory (S, SJ (S, S) IS. T) (S, 1) (S, n
rexl (T. S) (T. S) (T, T) (f. T) IT. l)
o) i~ b) fa 9. o) b) ' c) i d) 1 n,-
Can be done earl!e1 111 the chapter. e.g. afl<'r Exercise le. At this ~tage It 1s
nnt wise 10 plau:- too niuch en1phasis on !he difference be1ween !heorelica\
and experimenla\ probability
4. ' 16. 50 ' 5. ' 17. About 500 heads It is unlikely, ,
6. ; hnl possihle, that you will get 8. ~ 1000 heads or JOO() lails
10. JO 18. Any nu1nber of heads from 0 lo 12. Roughly rectang11lar JO_ 13. Ten throws is too few 19. Very unlikely 15, No. All the same. number.
CHAPTER 3 Constntctions
Revision nf the facts learned in Book lA is nece:<>sary
EXERCISE 3a Revises the geonietry covered in Book IA. (p. 36)
EXERCISE 3b
(p. 38)
1. 60" 6. 70° 2. 75" 7. p ~ I JO", q = 5ft'
3. JOO" 8. J = 70", I= I Ill° 4. I JO" 9, I~ 60". 111 = 100°, "= 20~ 5. d= 60", e~ 120" 10. d = 30", e = 75'', 1~ 105"'
l)iscuss the space needetl for constructions (a 101 more is nt><"ded than pupils realise). Discuss also wha1 1adius is a sensible chou:e (pupils iend lrJ choose too sniall a radius. 1naking in:cu1acy dilficul1)_ Stress again lhe need to use a sharp pencil and poml ou1 that !he co1npasses are much easier 10 use if 1he pencil is p111 into 1he con1passes so that the po1n1eJ ann is almos1 vertical. rather 1han al an appreciable angle 10 !he venical h 1~ also worth mentioning
that if an angle of 90' is to be cons1ructed al !he end ol a line. lhe line must
first be produced beyond that end
Teacher ·s Nores and Answers ~) I
EXERCISE 22a J"he answe1s given are p1obably more accura1e 1ha11 !hose found fio1n n1os1 (p. 325) pupils· graphs This could be used to en1pha.si!.e !he need for sharp pencils,
e!c
EXERCISE 22b
(p, 329)
1. a) 16;C bl 78·c c) 77cr d) l 16"F
2.a)f!l2 b)£.67 c)$!74 d)$109
3.a)496F b)/02-1F c)l42fHv1 d)ll6Dtvf 4. constant speed a) 12 km bl 11 kn1 c) I hour 40 mtnules
d) 3~ hours 5. constant speed a) 825 km b) ?475 kn1 c) ! hour 49 minutes
d) 4 hours J.1 minutes
6. a) )4''.~. 77~,~ b) _12~ . .S2 7. a) £43 75 bl f84 c) f! !7 2) d) £! 14 \0 e) £2)1_4_)
8. a) J4 mpg b) 22 km/{ c) 64 1npg d) 8 kn1// (lo nearest unit) 9. a) 19m/s b) 166kin/h c) 6)kn1,lli d) 4iJm/s (to nearest unit)
10. 9 5cm. 5 Bern, 6 5crn. 9 2cm
1. a) !190g h) ?mm
z. a) 1) B~s i1) l"i~s b) 1) lJ4 kn1/h i1) !91 kn1/h 3. a) i) '05g 1i) 9\0g b) t) 6'idays ti) !"iOdays c) 240g d) 10g 4. a) 84111/s when t = 4)'i b) i) Rlm/s 11) 6! 5111/s
c) 2.2)s and 6 6s
5. a) 19 knots. i !6 40 b) 14 5 knots and 2,1 2 knots c) i) £ 17.57
ii) f 17 0.1 6. a) t) jl\6g 1i) l ~40 g bl i) 3 82 crn iil 5 Scm
7. a) 9? ·c. 74 c bi J!.?5'11TL 9 10 pin
8. a) ! 612 bl ! 1 November 9. a) 2108 bl 14 Augus1
10. i!) t) I 7cm ii) !Ocn1 b) i) I Jcin ii} 8 6nn
{)o 1101 progress 100 quickly; thlC IS a frequently !l\ISlllldCfSIO()d IO{llC. rry IO
keep dose lo the pupils· experience
EXERCISE 23a I Jse 1he restihs of Nurnbers I! lo ?.O lo d1sn1>-s the interpre!ation of the n1ean (p. 334) in each case
1. 8 4. 29 7. 10. ls 2. 7 5. 16 8. 40 11. \0 3. II 6. 28 .. 6 2 12. 0 61
13. 63 16. 6.\ 19. 0 8'l'i 21. 2 rn1n
14. 96 17. 74 20. \ 8 22. 86 kg, 81 kg
15. 16.5 18. I .l'J
90 ST(P) Mart1e1natics 2A
22. 8 64cm
23. 17-4n1
EXERCISE 21c 1. JOnn 3. (p. 312) 2. !8-4c1n 4.
EXERCISE 21d 1. J!cn1 2. (p. 313)
5. 4_90C!ll 8. 6. 2.65nn 9.
7. l.73rn 10.
EXERCISE 21 e 1. 6.71 cm
(p. 315) 2. 8_67 CTTI
3. )_'j CIT\
7. 146nn 8. 8 15 Ill
9. 88_5 cm
EXERCISE 21f 1. ll.5cm
(p. 317)
•• 4_25 cm
EXERCISE 21g 1. l 71 cm
(p. 319) 2. 4.69cm
EXERCISE 21h 1. 2 60n1
(p. 320) 2. 781nn
3. 14 I cm 4. 105 IH
5. 7 55111
24. 2-6lcn1
25. 35_0cn1
I JO min 7.Scrn
48cm
4 ':18 cm
7.48 m
7.94 cm
4. )_66011
5. II 5un
•• 9 Clli
10. 265cm 11. 9 )J cm
12. } 'J CHI
2. !Onn
5. 11.J CUI
3. J0.4cu1
4. I0.2 C!ll
5. 6.
3.
11. 12.
26. IJ On1
27. 11 Ocm
26 m 7. 2~ CUI
31 Ocni 8. I] 8 CHl
14 Clll 4. 10111
6 24 CHI 13.671011 14_ 117nn 16nn
13- 6 8111 14. 89 6crn 15. J51rn
3. 150crn. JOcrn
5. 12 7crn
6. 743111
7. 83 I rn
8. I 6Jm 9. 14._I nn
10. 6_22 kni
EXERCISE 21i ()roil if lligonomelry has no! been taughl
(p. 322) 1. 71 14nn~ 4) 6". 4)6°,888c 6. a) 27_2k1n b) 54~. 306", 126~
2. 265111,414" 7. !79cm. 20cin
3. 18 9 kin, 058" 8. 7.81
•• 164crn, 66_6-', 11 -1 4'" 9. 7 07
5. ,O 6rn, 12 601 10. 12.6
CHAPTER 22 Pr-actical Applications of Graphs
P!cnly of discussion usu1g dif!c1enl examples 1s ne~:essary on cho1ee of sens1hte
scales and ou whteh qu<intily lo put on which axis the honzonial axis sh111tld
he used loi the quau1i1y which changes steadily (1i1ne_ age. ) or tbe
quan111y that we slilll wilh (e g £ it conve11111g f lo$)
l&dcher·s No1es and Ans~vers
EXERCISE Jc 11. 90~ (p. 40) 12. 45"
14. they are parallel
EXERCISE 3d N11mbe1s 1 lo 9 can be uscJ !01 d1scus$ion (p. 41)
EXERCISE 3e (p. 43)
EXERCISE 31 (p.45)
CHAPTER 4
EXERCISE 4a (p. 49)
2. they are equal 6. " the 1n1dpm111 of AB 3. AB and Cl) 7. " the nudpmni of CD
4. coincidcn! 8. 90"
5. co1nc1den1 9. each is 9()C
Bisecting lines and dropping perpendiculars: !he radit1s fo1 lhc arcs bdt the line can be smalk1 1han tha1 used frn the first a1cs---w11h able clu!dren 11 worth explaming 1lus, but discuss !he diagonals \If a kJ!e <ll 1hc sarne lune Poi ou1 that !he p!uase ·,hop1i1m-f· a pe1pend1n1!d1 applies also when the prnn! below 1he hnc
Numbers 8 to 14 invohe co11s!fuc11ng urcumnrcles and 1nc11ck:. !'hey a suaightforwa1d bul kngthy and. Im inn1ck~ 111 parucular. 1he construc111 works only if ihe drawing 1s accu1ale Ahle duldren can cope. bu! u d1sne1ion w11h !he others fhe foima! consl!1JClion of a nrcumcirde is Book JA and of the incirdc in Book 4A
4. I he pnpend1cular biset.:101 ol I l'VI pas~cs through N
5. The perpendicular biseclor of PR does not pass through Q 6. fhe pnpendiuda1 b1secior ol ihe cho1d AB which passes through ll
centre C
Use firrn cartodge papei If used lor C!111strnas decorauons. ellhtr colou1 wn felt lips bdoic culling out 01 use ~pray 1n11nl when cornplelcd_ ;ind ren1ernb<
to rncorporale a 1/11cad w11h a kHul a! one end wluk 1he solid is being st1K
Jogethcr
J ntroducing Percentages
CalculaLors are not necessa1y but 1he weakt1 pupils 1nay benefit front usir lhe111_
Emphasise 1he conunon result~- c_g _)()"ti"--'-~
farmhar aillL 1f necessary, karncd
1. 8. 15. ' 1"0
2. ' 9. " 16. l
"' Hi • 3. 10. " 17. ~ i n 4. \ ~ 11. " 18. " j{i{j 1{i\i
5. 12. 19.
6. 13. 20. . f)
7. ' 14. 21. ' '" 40
0 5 These should be niad
22. " :iO
23. lb 24. }~ 25. rA 26.
27. ' " 28.
12 S r(P) Mathen1at1cs }A
29. 0 47
30. O I 1
31. 0 05-5
32. I 45
33. 0 58_1
EXERCISE 4b 1. 50 ~;, (p. 50) 2. 70 /~
3. 6S';-~
4. JJ! ·;;,
5. 52.5 ~~
21. 50~~
22. 22 ''.<,
23. 8 .J ·;;
24. 172 /;,
25. 62.5 /~
34. 0 18
35. 0}
36. 062J
37. J 5
38. 0 <187
6. !'";"! - "
7. IS';{,
8. 16''-~
9. J7.S'%,
10. 18t '.'{,
26. 90~-~
27. 4~-~
28. '15 ·;~,
29. 264 °',,
30. 84 5 ·;~
39. 0 92 44. () 08
40. 0 6'1 45. n 01
41. I 1 46. I 8
42. ! JI 47. 0053
43. 0 857 48. 0 5,~ I
11. 75~-~ 16. 60~~ 12. 45·;~ 17. 35~-~
13. 140~{, 18. 124 ';~
14. 62~/~ 19. 87~ ·:-~
15. 266t% 20. 160~~
31. 15''.~ 36. 16 ~ ..
32. 74~,, 37. 16".;,
33. 125'\, 38. IJ9~,,
34. J41 ''.,, 39. 615/;,
35. I I'\ 40. IX 25 ""
EXERCISE 4c Questions _) to 10 provide a very convenient way of confirn1ing !he
(p. 51) relationships between fractions, percent<1ges and decimals
1. a) i~ 2. a) 0-44
3. a) 40~~
4. a) ?0~-0
b) ~~ b) 0_68
b) 85'";,
b) 61 ~-~
Fraclion
5.
6.
7.
8.
9.
10.
c) 12~ ".,
d) -No d}0.165
d) 11 J!, "0
d) I JR",
Percentage
75 ~~
80".,,
60~,,
70"-~
55 ~~
44'\
32 '/~
Decimal
0 75
OK
06
0_7
0 'IS
0 44
0 32
EXERCISE 4d r-.1ay he used for class discussion Numbers 9 to 14 are inlended for !he above
(p. 52) average child.
1. 52 ~~ 4. 92·;;, 7. 4J '.:~
2. I J j~ 5. 88 '.\ 8. 68 /~
3. J6~{ 6. I:?~~
9. 10~-~ 12. 252
10. J8 ~; 13. 14()()
11. ] ~~ 14.a)l~.:_ h)IO/~ c)66~~ d)22~.:_
leacher s Noles aod Answers 89
EXERCISE 20h Ihe 1nore ahk cl1ildren may be 1111en.·s1ed 111 manual rneihods for fin(hng
(p. 305) square 1001s lle1e ts a !n1d tkscrip11011 ot one such 1ne:!hod
EXERCISE 20i (p. 306)
EXERCISE 20j (p. 306)
To find -,/]{i_ first app1ox11na1e. i c_ J70 """ 4, 1hen proceed as follows
)()-'- 4 =- 'i tvlean of 4 and 5 ts 4 5 20 4 S -"" 4 44 tvlean ul ,~ 'i and 4 44 is 4 47 (wndung to '~I )
20-'-441 = 4474 = JiO--"" 447 CO!!CC! tu l sf
1. 6 10 8. } 19
2. 4 45 9. 25_ 5
3. 20 7 10. 8 06
4. 6'i 0 11. Ll\ 5. 'J f-i6 12. 7 62
6. 1. 11 13. 4 90
7. 8 19 14. 4 36
15. I 0 I 16. fA.!
17. 11 0
18. 8\ l 19 .. , 81
20. 1700 21. I 0 1
22. 374. 250_ 250. 8'19 268. 118 )71_ 2(M 6•1 'i_ 12?. 6?9 199. 27 )_ 275
2750. 64.2. 27 0. J 9L I 92. 6 28. 19 'J
1 _ o lOS 2. 0 h48
3. () 110 4. 0 748 5.00IH:I
6. 0 701 7. 0 775
1. 9.]2 CITI
2. 11 Onn 3. 22 4 Ill
4. 5h6rn
8. 0 )-77
9. 0 167 10.00)21 11. O'i48 12. 0 4!6
13. 0417 14. {) 811
5. 0 _1 4)111
6. J 89cm J. )7 4 !JHll
8. 290 kin
15. 0 208 16. 0 0980
17. 0 9!2 18_ 0 )66 19_ 0 _1_28
20. 0 866 21. 000854
9. O 09.~2 kn1
10.768nn
11. I 5 S n1
12_ 7R!cm
EXERCISE 21a So1ne histoiical backg1ound would in1erest most child1en (p. 307)
1. !Ocm 4. \Jcrn
2. 11.7c1n 5. I! 4nn 3. 9.4Jc1n 6. IJ 9crn 7. l he sq11are of !he thi1d side is equal lo the sum of !he squares of the
other two
EXERCISE 21b 1. !Ocm (p. 308) 2. I 3 CUI
3. 20un
11. J_6lnn
16. 5_40c1n 17. 121 cn1
4. 9.85 cm 7. I I 7cm 9. 12_1 CIH
5. !08cm 8. !26cn1 10. I0-4rm 6. 10_6nn
12. ll.4cn1 13. 6_40m 14. !l-4m 15. 12.2cn;
18. ] 11 crn 20. 44 7 HI
19. 9.57cn1 21. 0_361cin
BB SJ (P) Mathernarics 2A
17. 51 98 21. 07726 18. I 34 6 22. 0001110 19. 58080 23. 5242 20. I) 6790 24. 1419
33. c) 4 8, 3.2, 9.6, 7_3
EXERCISE 20c (p. 301)
1. 55696 2. 212521 3. 27 667 600
4. 17 305600 5. 1049_76 6. 103041
4. Ll2 rn 1
5. 296cin 2
25. 0 0601 29. 0 020 16 26. 0 005 184 30. 94 67 27. 201 6 31. 1912 28. 20160 32. 0 005 285
34. c) 30. 70. 164. 185
7. 628 849 10. 4078 56
8. 38937600 11. 152881 9. 2 044 900 12. 21996100
7. 0_003 84 rn 1
8. I05000km 2 EXERCISE 20d 1. 5 76cn1 2
(p. 302) 2. 92.2 Hli
3. IOSOnn2 6. 2700nun 1 9. 00961crn"
EXERCISE 20e Po nol use cak11la1ors_
(p. 302} 1. 2. 3.
10. 90
11. 0. 9 12. 0 8
19. ()_] 20. () 4
EXERCISE 20f Do not use calculators (p. 303}
1. 4 2. J 3. 6 -
4. 6 5.
EXERCISE 20g no nol USC calcuh1101s
(p.304} 1. 30 2. :100 3. )() 4. 80 5. 20
16. 60 17. 20
18. 20 19. 6
4. 9 5. 10 6. 6
13. 70
14. JOU 15. 0.2
21. 0_02 22. 500
6. l --7. 9.----8. 4. - --9. 2_
10. 0.2- -
6. JOO 7. 50 8. 200 9. 60
10. JOO
20. 3 21. 22. JO 23. 60
7. 7 8. 8 9. I
16. 20
17. lO 18. JOO
23. 2000 24. 0_004
11. 0 4-12. 9. -
13. l 14. 0.7---15. 2.
11. 600 12. 10 13. 20 14. 200 15 . .?000
24. 6 25. 10
26. J 27. 200
!edcher·s Notes and An.,;vvers 13
EXERCISE 4e Although rtearly all the ques!Jons give nuinheis wllli units, none of the
(p. 53) answers involve unHs D1st:uss1on ol ·-wha1 has happened 10 lhe un11.;· rs
wo11hw!11k In ;,orne ques1ions 11 1;. necessary to make the u1u1s c:o1npa1ible
1. :is~ 0
2. 60 ~-~
9. 10 Go
10. ?0°,:
17. :Z5 '.'.~
18. l7f 0.,,
19. 20''.-0
Z7. ,10'.'-~
28. 65 °; 29. 1 )~ ''.~
37.046''.,, 38. ')00 ~~ 39. 65 ~/;,
EXERCISE 4f 1. 48
(p. 55} 2. 96g
EXERCISE 4g (p. 56)
EXERCISE 4h (p. 57)
3. 55 5cn1
11.25?m 12. 14-'1 in 1
13. 3_13
21. 90 _i;
22. 1.94 min
23. 18crn 24. 9m1
1. 40 ~~ 2. 70 ~--~ 3. 20 ~-~ 4. 1\J'_'.-~
11.a)46~~-~ 12. a) )2
13. a) I 2 14. a) _\6
1. a) ~ 2. a) 60~1~
3. 8 ~~
3. Ll~ ~-~ 4. JJ~ ~~
11. )0 ""
12. 50"-~
20. 40 ~G 21. 60'.'-;, 22. 2:5 "-~
30. b()~ ~-~
31_ 1~~" 32. J6'_'.;,
40. !5 ''.., 41. 400~;.
42. !O",~
4. 286 krn 5. 16p 6. ] 08 kg
14. 198 kg
15. I 44 1n 16. £1 ){)
25. 320ni2 26_ 45 knl
27. 5 kin 28. 149un~
5. 30'\ 6. 75 "-~
b) 53~ ~< b) ?8
b) 18
h) ?04
b) ~~ b) 78 ~~
c-) 1b c)!lt~-~
5. 7) '.::, 6_ 60~-;;
13_ ?tHl~u
14_ 62~ ''.~
23. 1 ! u"
24_ } l_I\ ~;,
33. ) l)'
3-4. ·I'.'-;,
43~
44. 2) •;;
7. 252
B. 989 g
17. 0 34km
18. I 61!tres
2:9_ !4 p 30. f 5 \ 'l]
31. ·18p
32. 6g
7' 75 '.'.~ 8. 66{- '>~ 9. 65 ~--;,
10. !960
15. 5760
16. 78 1'7.£6240 18. l ! l
4. ! 2J ~~ 5. )4 Ill
6. 97 ~--~
7. 15 °,, 8. 25 ·:~
15. IO":,
16. 66j ~~
25. 12·;~
26. 41 ';.--~
35. 36.
I 3 ~ ~., )! "' ~i _,,,
45. 666~ ;;, 46. 8 ~'~
9. '~ 7] Ill
10 . .206un 2
19. I. 75
20. 198111
33.2Jrn 34. i 10
35. 2 kg
36. 14 llHTl
14 ST (P) Marhema11cs 2A
EXERCISE 4i (p. 58)
EXERCISE 4j (p. 58)
EXERCISE Sa (p. 59)
EXERCISE Sb (p. 63)
EXERCISE Sc (p. 65)
A vulgar haclion is referred lo in N11n1ber I 11 needs explaining II IS worthwhik also 10 point out 1ha1 ·-,1ecin1al f1ac1ion .. is the lull descr1plion of
what we normally rele1 lo as a tlecirnal
1. a) 195
2. a) 62~~-~ 3. 12}~-~ 4. 289 rn' 5. £840
1. a) 12~ 0 0 2. a) 28.6~~' 3.
a) ' 4. 90p
5. 54
h) 0 }6
b) I l 3 '/~
bl 17~ ,,~
b) 27_9/~
b) 0 125
c) 250~~
c) 50~~
c) 122/~
Answers given fo1 1neas11re1nen1s are calculated and lhis accuracy is not anainable fro1n d1a\vings, so allow for this when deciding on acceptable accuracy
Mosl questions have- the scale given bul Nun1hcrs 6 10 10 do 1101 fhere is a
short no1e n1 the C;>.:e1cisc <ihout choos1ng: srn1able scales. bul much 1no1e
d1scuss1on is necessary. Ii can be profi1oble 10 begin 1h1s topic by asking the pupil:. 10 draw a simple reclang!e, 55111 by JOrn say. <:hoos1ng their own
scales_ onrl 1hcn con1pare 1csuhs
11. 5001n 12. 1_29 Ill
Li11k !he words elev;ition and depre%ion to 1he11 eve1 yda y IJ5t' and inducte wo1ds hmn the saint rooL l"..g ekvalor, elevah:_ depr.:ss depressed eic
1. ?1m 3_ 50m
2. ?: ?: Ill 4. -~X rn
5_ 70m 7. S'lm 9. 9m 11. IK01n
6. J2 Ill 8. "iH rn 10. '9lm 12. _91 rn
1. 86111 2. 77 Ill 3. 71 m 4. Xl m
5. _119m 7. I I~ rn 8. 9::'.~ rn 9. :'i::'.8m
6. 8_1 4 rn
10. '14 rn 12. X660m 14. I J4 n1 16. "'80111
11. I I 70m 13. <IJ> HI 15. sx_:i rn
EXERCISE 19g C<1n be used for discussion (p. 294)
1. 48_6"
2. 5_}j COl
3. 51 l~
4. 53_ 1~
5. I 69 m
6. 7 45 Clll
l"eache1 ·s Noles and Answers
7. 48.2", 8"L6"
8. A= 65-4", 65-4", 49.2'' 9. l !R''
10. 9.59"
11.574• 12. 2 87"
81
EXERCISE 19h Only for able children: 1111endt>d to !!ive the ulea. in an 1nfo11nal way. nf !he
(p. 297) rela11onsh1ps between the SlllCS and rosines of con1pkme111ary angles
1. ,, 0 64) b) 0.64_1; equal 4. () 8
2.a)08 b)08;90" 5. 45'', isosceles,
3. O.J
EXERCISE 19i 1.09925 3. 0 8829 5. 6 25 cm 7. 6.75 cm (p. 297} 2. 585° 4. JO_{)" 6. 5.i /"
EXERCISE 19j 1. 0906 2. 68.6'' 3. I 00 4. 21 4"
(p. 298)
5. 12.J crn 6. lll O' 7. 7 14 cn1
CHAPTER 20 Squares and Squares Roots
EXERCISE 20a Do noi use calculators (p. 299}
1. 9 6. 2500 11. 0 09
2. 25 7. 90000 12. 4 000000 J_ 81 8. 0 0004 13_ 0 000016
4. 900 9. 250000 14. 5. {) 16 10. JOO 15. 0 0009
16. 900 20. 64 24. 0 0009 17. 10000 21. 1600 25. 8100
18. 16 22. I 000000 26. 0 0064 19. 0 09 23. 4900 27. 40000
EXERCISE 20b \Vi1h very able children_ Nurnbcr 28 can be expanded and much more made
(p. 300) of ii
1. 60 84 5. 0 0256 9. 16_11 13. I 040
2. 1444 6. 0001024 10. 96 {),j 14. 185 0
3. 62 7 J 7. ?J1J 11. 146 4 15_ ?:89
4. 0 1681 8. 117 7 12. 8 644 16. 1.232
86 ST(P) Matheniatics 2A
EXERCISE 19c 1. () 515 5. 0 498 9. 0.954 (p. 285} 2. 0 669 6. 0391 10. 0 904
3. 0 998 7. 0.139 11. 0_070 4. 0_708 8. -0.971 12. 0.985
13. 642" 18. 194° 23. 89.3° 14. 24 6° 19. 34 9° 24. 424° 15. 44.4" 20. 55.5° 25. 51. J" 16. 45.6° 21. 76.1" 26. 818° 17. 75.J" 22. 20.3° 27. 32 5°
EXERCISE 19d 1. 8.48 cm 6. 7 nn (p. 286} 2. 2 68 Clll 7. 3.08 Cill
3. 5.07 cin 8. 3.22 cm
4. 3.75crn 9. 2. 78 cm
5. 10.2cm 10. 0.799crn
11. 53 I" 14. 38 9° 17. 41.4" 19. 66.4" 12. 41.4" 15. 329°. 18. 63.J" 20. 56.9" 13. 38 7" 16. 600°
EXERCISE 19e Many children have difficulty in decidin~ which ratio lo use Discuss several (p. 289) differe111 examples_ The following mne1nonic for S()llCAllT(lA rnay be
EXERCISE 19f (p. 292)
useful: Some old hands can always have tickels on application!
1. tan A 4. sin p 7. 1an A 10. Siil N 2. cos A 5. tan X 8. "" E 11. tan x 3. Sin Q 6. cos M 9. cos p 12. cos F
13. 81 9~. 31-0~, 48_6°, 33_1", 59.fJ", 68 O" 2.44 CO\, 4.90 Clll, 6-43 Clll, 0_647 Cnl, 30.9 Clll, J 3_9 COl
14. 36 9° 17. 610° 15. 49 5" 18. 41.4'
16. 41.8° 19. 32 6°
1. 44-4". 45.6° 4. 7.61 cm 2. 4_50crn 5. 35_3 cm
3. 71.9'', 18_ I~ 6. 59". l66cn1
11. 45 6'' 12. BC ·- l 69cm
13. BC 1.95 Cfll, c ~ 72
14. 66.4'' 15. ;; '"" 52.I~, f -· 17 9Q
20. 3 06cn1 21. 32 7nn 22. ()_282 Clll
7. 12.2cn1 8. 15_9m
16. 5 56 crn 17. S2 .tl" 18. 5 5 2'"
19. ;; ~ 54·' (~ -20. AB= 17.0cn1,
23. I 09cm 24. 2_37cn1 25 . .320c1n
•• I J 4 rn
10. 41.8''
36"
RC ~ I0 6cn1
Teac·her·s Noles and AnSl-Vers 1 h
EXERCISE Sd Explain lhe meaning of con1pass pornls (can be confused wirh the point uf ;; (p. 68) pair of con1passes)
1.
JY' •• N
r
JO() 2 .
.f~ 7. N
... /\
~) 3. N 320~ /
~- a. N
1 rn· A
M 10 ](>()" /
•• N
r .) !R0° 9.
ty s
(;
5. N 10. N
H ') ""' 270:') ----
1 fi ST(P) IV1alhernatics 2A
11. N 16. N
A ~0 A
II
12. N
17. N
r 140•
13. 18.
14. 19.
t:J" ,v~ rn·
20.
15.
l"ear.·/1er ·s Notes and AnSJNers 8 ~)
9. 2'100nn 3 11. ll 5nn·1 13. 690 nn3 15. 864 cm 1
10. 2880 CJTI) 12. 450cm 1 14. 614 Cll\J 16. 720cn1 3
17. 'l_ 184 ml 18. 11.6 ml 19. I J44 nn 1 20. 624n1 1
EXERCISE 18c Ask for aciual nb1ects !hat are cylinde1s An interes11ng discussion point. why
(p. 279) arc cylinders. ra! her than ct1bo1ds, used for canned soup. baked beans etc_?
1. 126cm' 6. 15_ J 1nl 11. _l22cm 1 16. 2810cm 3
2. 11 3 cn1·1 7. 37.7 nn-1 12. 407 Ull1 17. 941 rnrn 3
3. }14 CJTil 8. 50. 9 crnJ 13. J_Hlcrnl 18. 82S cm 3
4. 59 4 cm-1 9. 4520cni 1 14. 652 cm' 19. i.60rnJ
S. 1 !4cm 3 10. !J90nn 1 15. 70800cn1 1 20. 44 Ocn1·1
EXERCIS.E 18d The pupils c;in be asked to dcsuibe wtlill lhese C"ould be sections of
(p. 280) 1. IOIOcrn _1 3. 34 S crn·1 5. 628 crn 1
2. 402cm 3 4. 204crn 1 6. ll60cn1 1
CHAPTER 19 Sine and Cosine of an Angle =""-~"'~..=====
()p1ional at this stage and omit if Chapler 16 was not covered. This work is
repeated in Book JA.
Re-vise !he ratios of !he sides of similar triangles hdo1e starting this work. As an 1n1rod11ct1on. pan ol Exercise 16a can be repeated, asking for the 1atio of
1he opposite side to !he hypotenuse to be ca!cula1ed
EXERCISE 19a Sorne of these can he done 01ally lo de1nonsfrate the use of a calculator.
(p. 281) 1. 0 4 38 6. 0.951 11. 56 5" 16. 4Jr 2. 0 995 7. 0 289 12. 24 4" 17. 40.3"
3. 0 419 8. 0 07) 13. ]9_ 1" 18. 20 9"
4. 0 601 9. 0 886 14. 44 7'' 19. 25.3"
S. 0 981 10. 0 946 15. 69 6'' 20. 15 I"
EXERCISE 19b 1. 8_8J Clll 6. 1 68 Clll 11. 44_4'' 16. 33-4"
(p. 282) 2. 6 11 crn 7. 2-61cnl 12. 236° 17. 220"
3. I 95cn1 8. 2 51 cm 13. _36_9" 18. 30"
4. 1.0'/ cm 9. 9.54 cni 14. 51 1" 19. 42.1° 5. 6 02cm 10. 4 85 Cfll 15. 23.6~ 20. 45.6°
21. 2.06cin
22. 6_64cn1 2J. /\ ~ 36 9". f 53. I" 24. 28.2" 25. J 72 CTII
84 ST(P} A,ta1hema1ics 2A
4. Stall
numhcr/
'/ Yes
...• -]-Write dnwn e value ol l
-f~
(Sior)
No
ClfAPTER 18 Volumes: Constant Cross-section
EXERCISE 18n Revises the work in Hook IA on volumes of cuhoids_ C1ive a re1ninder nf the (p. 273) n1eanin~ of "units of voh11ne" ;ind why they are c1n 3, m' e!c
1. 216crn 3 2. 432ni 3 3. 180000cm 1 4. 105 4cm'
5. 1600 1nn1J 9. 0_000008cn1 3 13. 129 6cmJ
6. 58 'i c1n3 10. 39 680cm 1 14. I _1}_28 ITIJ
7. 403 2 mm 3 11. 112_5c1n-3 15. J44_6cin 3
8. A9.68 n1 3 12. 189cn1' 16. 2304 nn·1
EXERCISE 18b f>iscnss ac1ual objects with unifonn cross-sections, e g_ a hexagonal pencil, a (p. 275) nJler etc_ Pupils may need help lo ··sec" that the volutne of a triangular pris1n
is half Iha! tir a rec!angular one_ They need a d1awing or 1he cross-section lo find the area hut discourage thcn1 fron1 1-hawing the solid: it is tin1e
consu1ning, somelirnes difficult and does not help
1. 720cm3 3. I 120cni 3 5. 1242cm 3 7. 660nn-1 2. ) 16{) CITI
3 4. 7 )0 CITI 3 6. 12Rcn1 1 8. 19?c111 1
EXERCISE 5e 1. 87 in
(p. 70)
EXERCISE 51 (p. 71)
1. 860crn
2. 161 In
2.
~ 17°
I )0 m
EXERCISE Sg (p. 72)
tower
3.
1. 94 m
4.
sn rn
N
N 5.
2.
Teacl1er's Nares ar1<f AnsH--ers
4. SI m
••
)0!)
3.
N
n ~~·~-o-·~~~~~,o-,-,o-,-,,~~~-+~..::.i101;~ --·
rfiA TAB so /\TA is isosceles
Ar= Bf
ST(P) l'v1a1llemat1cs 2A
EXERCISE 5h (p. 72)
CHAPTER 6
EXERCISE 60 (p. 73)
1. 154 In
2. 32°
4. "
45 m
I Om
3. N 5. N
A 210"
SOm
x l
B is nearer to T 1han A is
Equntions and For-n1ulae ~----~-~~-~---
Much of lhis chapter repeals wo1k that is in Book IA, but with shorter exercises.
Repeats 1he work on equations in Book IA. The equations are grouped according to cornple~ily and d' any of these types are being 1ne1 fo1 the first ti1ne, Sl'pplemenlary questions will probably be necessary All will need 1en11nding aboul the meaning of 5x, like 1errns, unhke teons, etc, and lhe order in which it is sensible to reanange equa11ons
1. 4 4. 2 7. I 9. 2 2. 4 5. J 8. J 10. J 3. 12 6. 4
11. 4 14. 4 17. J 19. -2 12. 5 15. 18. 8 20. I 13. J 16. I
2.
3.
" x>4
7, 9, 11, I J
leache1 s Nou:s and Ans1vers
No
b) The mnc lrn< .eplacc 0 by (>
~----~ l '""''' J ---::::i:::=_
Write down !he value ol n 1 +2
3, 6. 11, 18, 27, 38
BJ
82 ST(P) Matfletnatics 2A
5.
6.
EXERCISE 17d 1. (p. 271)
_star1
(\V;~do.wn lhe ~mber
Is it divisihle
by ]
' No
I is nol
sihle by 3
Yes ls il divisible
by 8
' No
It is not divisible by 8
t.._ ... _--_~ _ _,f-~ _L
S1ar1
fl is not~ divisihle ~~---}
Yes
/,~ / Is 1he Yes ls the ~e•
first angle ~ second angle (ill~ // ~ 60" __,/
' ~'/
No G ... ±o f) c·. -o·· {The lnanglc 1s The triangle is The lri<1ngle-~~~mbte1al net equila __ ~e~ is_--=quil~-l~al
a) To give no 1nore than the first four tenns. h)60 c)
0
EXERCISE 6b (p. 75)
EXERCISE Ge (p. 77)
Teachers Nores and Answers 19
21. 2 24. 27. 4 29. 4j 22. 4 25. 28. I 30. I!
' 23. 26.
31. 34. 2 37. Sl 39. 32. 35. 1 38. • 40. 2 1 33. 36. 2
Repeats the work done on brackets in Rook 1 A. All will need reniinding abou! the rneaning of a lf'P7t of an expression II doing this work for the firsl llOlC
1nore e:r.:arnples may be necessary
1. 6\ + 2'1 4. 6t- 10 1. 6-9x 9. J(J_, 14
2. 6-t + 3 5. 12 - 8 \ 8. 35 - 2~h- 10. 47. + I 2-\ 3. " 12 6. 2{h t IO
11. 8' 1 18 14. 8 \ -l 4 17. 28x + 27 19. 4 ,- I 25 12. 26> )l 15. 2 I\+ 5 18. 18,.- -4'1 20. JO, I 47 13. ,4_l ll 16. JJ, + 19
21. !Or+_) 24. 4 \ I 14 27. 7 \ -+ 32 29. 2 I."\ 19
22. d I) 25. f(h I 14 28. x+ 21 30. 6.> +1 23. 17, - }3 26. 36~ -! 26
31. ' 35. 39. 43.
32. Ii 36. 40. -4 44. 33. I 37. !l 41. )!
' 45.
34. 2 38. 42. l 46.
Revision ()f 1nuhiplication and division of ordinary number haclions (with
exercises for practice) is advisable before working !hrough !his exercise Equations of this type occur in the work on ratio anti 111gono1ne1ry
h 1. 4.
2 3 7. h 9. 6.1
io
' 4, 2. 5.
6 5
h " •- 10. 2 6
3. Jx
6. 2x
5x x 11. 14. '·' 17. 19. 9x
8
12. 15. 4,
IR 5 2_.,-1
18. 9, 20. .1
13. '·' h
16. 10
20 ST( P) Matfle1natics 2A Teacher ·s /Vores and Ans;vers 81
EXERCISE 6d Plenty of class discussion " nccc:-.sary at e,ich stage of 1his exercise N111nbcrs 3. (p. 78) II 10 20 can be done by firs! 1n11l1 iplying by 1he LCJ\.-1 of the .-le1101nn1;l101 as
shown for 1he 1ema1ndcr ol the excrnse ,, " probably advisahk '" use ibis
n1elhod 101 ch1ld1cn othe1 1ha11 the 111051 able; 1he la11e1 can have both
1nethods prnnlcd Olli
1. I 5 4. 11 7_ 14 9_ 8
2. 8 5. 3~ 8. 31 '
10. 8
3. 48 6. 2")1 -l
11. ' -14_ • 17_ '- 19. .li ' " 12. 11' 15. 1 • 18. ' 20. I !J
' .. " 13. 16. I 11u
21. " -· 24. 1!.!.
" 27. ,,~ ., 29. - lk
22. 1 lf 25. 6! 28. 20 30. 1 l 23. Ji~ 26. 31
' 31. 1 36. ~~ 41. I' 46. • ' 32. I\ 37. " 42. 51 47. )!~
l) ' - " 33. II 38. ' 43_ !ff 48_ 2 ' 34. _!_ 39. I; 44_ 1!.l 49_ ' .. " "'4
35. I~ 40. Ii 45. I 50. ~~ }0
EXERCISE 6a Use for discussion Even 1hc mosl abk children are likely "' find lhese (p. 82) d1fficul1_
1. £150 4. 12 7. 9 9. 12
4_
~ w~~lowi~h~
11umbc1 _)
2. 40 5. 1•1 COl 8. 3 10. £1000 3. 30c1n 6. 5 crn
EXERCISE 6f Ntunbers I lo 10 revise 1nuhiplic11ion of directed n1J111bers N111nhers II '° 16 h>. 83) use these results for sinlp\ify1ng brackets and solvmg cquauons: again a good
deal of class discussion " necessary and ponll (>Ill 1hat (1 \ -- 4) can '" written as . I (2.\ - 4)
1. -8 4_ -] 1. 2 9. -9 2. 15 5. 12 8. 10. -45 3. --24 6. 28
11. --2:t+ 17 16. -9x-t-6 21. 26. !1
" 12. 17x- 10 17. 2 22. 3 27. 10 13. --15x -- 30 18. 25' 46 23. 2 28. 7
14. 15~ 14x 19. 5t - 17 24. ll 29. -4 15. I 5x ·- 20 zo_ 21-.,., --- 29 25. !_} 30. L
" "
80 ST(P) Mathematics 2A
EXERCISE 17c (p. 268)
4.
5.
6.
Put in value for :t
a) 1 b) 0
Put in value for ;i;
a) 6 b) J
from 12
(·-,r1~~,m - sqnare~--rc·, vaueor:t --- - - ~---- --
a) 29 b) 4
a) 12 h) 75
.--·· .. 0··· Get oul
~alue for ~-~·-t 4
·rhere are alternative arrangements.
1.
2.
·Does she want
'" ' / No
@~;-i~·er ~;c·
Sta11
Does ~he wan!
sqn:1sh
'
Yes
Slop
No Does she wanl
No
\'Ola
'/
[ (iive her le·;::~~Je]
·--:--.....::::::.:r-
EXERCISE 6g (p. 85)
EXERCISE 6h (p. 87)
EXERCISE 6i (p. 90)
Teacher's Noces and An.s»'ets 2
These exr11nples on constructing formulae are not very dillicull, bnt a go< 1nany examples should he used for dass discussion before children are allowe 10 hy any on their own Note !hat capital le!lers and small let1e1s a1e us(
for different quantilies so a is no! the same as A. To son1e children 1his is II(
obvious
1. 21+ lw 5. 2/+s+d 2. JI
3. ll+d 4_ 51 6. IV= x-f-y
7. p = 21 ~ 2h 21. d = b--a y
8. T- N-!- Al
9. T- N I. 10. A = 1' ' 11. N - !On
12. C= nx 13. I. •.. I- d
14. p - 61 15. A = ll' 16. N .. S·
\_)
22. 1
q = 5
17. IV T+S 18. s -· N-l R
23. L ny
JOO
19. ' .. p--q, 24. A 100/h
orr-,,,qp
20. IV Kn 25. T- It 60
rhis e:o;crcise covers an nnpo1lan1 topic with the fuhue
11nportance ol putltng nega!lve nun1bers "' hrackels "' the
canno! he stressed loo much
1. 10 4. 2 7. 24 9.
2. 100 5. 20 8. 15 10.
3. JO 6. 200
11. -I 14. 1) 17. 16 19.
12. . 12 15. 50 18. 20.
13. 5 16. 19
21. 15 24. 27. " 29. 22. 200 25. il 28. '.!~ 30.
23. J~ 26. 21
1. a) 48 b) 18 c) 6 di
2. ') 4 h) .?O c) 8 d) . I l 3. a) 52 h) 20 c) 96 d) 4 .. a) h) 1 c) 18 d) "' 5. a) H h) 4l " I 2t di ' '1"4
• 6. a) I 'i h) I 'I -15 9 d) 0 J8
" 600p 01 7. c"""' ~On_ £:6 8. I ·- 15 ,.
"' rnind ·11:
fi1s1 1nstanL
25 )! '
!OS
.ll
11 1
12 ST(P) Ma1hematics 2A
EXERCISE 6j (p. 93)
EXERCISE 6k (p. 94)
EXERCISE 61 (J>. 96}
EXERCISE 6m
(I'· 97)
9. V = /bd. I 200cm 3
10. /' = la -t 2b. 70crn 11. P""'6:1:,6cn1
12. P= L Nr. 5m
13. P = ]a. 24c111
14. JV= Ng+p, 45 15. A=2lw+2lh t-lhw, 6200cn1 1
Changing lhe subjec1 of a fonnula runs throughout 1he series of books in increasing co1nple:xi1y: this is a firs! in1roduc1ion and involvi::s JUSI one
operation, except for qut:slions 21 to 24.
1. r ~ N- G 6. " .. 11--(
7. d ... S-1-r 8. ' . p ·- 2y 2. x ~
y
3. J ~ 5, 9. r
c 4. x ~ I. t y R 5. a . s lb 10. " ~ L-b-L·
11. " . P--b 16. )' . x+z 21. r=q .. p
12. T = N R 17. ' . /' --ab 22. a= s ---b- ' 13. c . b· " d
14. u ~ !' - r/
18. m ~ Ln 19. u = 1·-at " y
23. ' =1-
15. N
" ~ 20. v ;;;; s-at PR
24. L ~ 10
1. 6_3, 6-4 (6.l2) 4. 14.1, 14.2 (14 14)
2. 94, 9 5 (9 49) 5. 89,90 (894) 3. 5.2, 5.3 (5.29) 6. 11.9, 12.0 (11.92)
7. 6.3, 6 4 (6 32) 9. 4.0, 4 I (4 08) 8. 14.1, 14 2 ( 14.14} 10. 17.8, l '1_9 (17_89)
11. 2, J; 2.8, 2 9 (2 83) 14. 2, ]; 25, 2.6 (2 54) 12. 3, 4; J.2, 3.3 (l 27) 15. 3. 4; J_S, J_6 (l.56) 13. 3, 4; .J.6, J_-, (l 65) 16. 3, 4; 3.8, J 9 (l 89)
17. 282,283; 117,328; 3 64, 1_65;
2.54, 2 55; J.56, 3 57; l 77, J.78
1. " -! 5. " 8. /'-.oc:tl/1/l·q
2. J~ 6. l 9. ..)
3. 6> 14 7. " 8 10. N~ R1D 4. 6x
1. ' 5. I~ 9. N =11 t-b t-c ' 2. l 6. x, 1 10 10. N = t1 t <1b
3. 6, 7. 'i-i~ 11. b) _1_45
I ST 4.
]
8. I 5
7eacher·s Nores a1Hi Ans1-vers I !l
EXERCISE 17b 1. ----·--) ~tin Ge! out (p.267) e fo1 va~~~~~~.
") 22 b) 57
2. ~Q-Pu1 in 1
Gel out value fo1 + value fo1 8-~0
a) 9 bl 41
18 ST(P) fvlathen1ar1cs 2A
8. rl1cse are suggestions only EXERCISE 6n (p. 98)
CHAPTER 1
EXERCISE 7a (p. 101)
EXERCISE 7b (p. 103)
1. Is~
5. 4
2. ' l 6. 3. 2 7.
4. llx
12
8.
x
4 x -f 6
' . "' 10
Teacher·s Noles and An~vers
9. P = 6a
I p ~ ..
)q 10.
11. b) 32. J .1 c) ]_2
it is for the leachcr to decide how nHKh, if any, of this wo1k is covered this stage It is repeated in Book JA However we recornrnend 11
Exercises 7a and 7b a1e coveJed by eve1ybody: 1hey give an introduction the idea of an equation of a sflaighl line and provide practic:e in 11s1
coordinates ·1 his section of work is necessary also if transforrna!ions covered lron1 this book (Cha piers 8, 9 and I J)
In a!! cases 1evision nf the use of coordinates is desirable_
Everyone can 1ry Numbers I to 8 lJse the 1e1nainder of this exercise I tliscu.ssion except fo1 the able who can tly so1ne on their own
1. a) 2 b) 3 c) 7 d) ! 2 2. a) b) 6 c) 8 d) -20 3. a) 3} b) 4} c) -6 I d) 8}
4. a) - 7 b) 2 c) -_<i} d) 4 l
5. a) IO b) ···8 c) 7 d) 5 2 6. a) I b) J c) ,.. 2 d) j 7. a) 3 b) -6 c)} d) 4.1
8. a) -2 b) 4 c) ' d) 1 -, 9. a= -- 5. b = 3, c= .. 4
10. a= -2,b~s. c ~ 18
11. y = 3x
12. )' = 2"' 13. y '·""' - ~:.:
14. y = -~x 15. ( ·2, -4). (6, 12)
16. ( ·2, 6). (I. -.1), (8, -24) 17. a) above (2, 2), (-1, I), ( 4.2, -2) b) below (3, 0)
Discuss, with exa1nples. which value!> of "( ate sensible lo choose and whi, are not In !he introduction to this e;w;ercise we have chosen the ex1reme valw of x: this ensures thlll the f111l 1ange nf y values is known before the axis scaled. When the giaphs a1e d1awn they can be usr-d to find y values f( given x values and vice-versa. Use lhese graphs lo discuss ''slope" and ''ang made wilh the x-axis". Point out !he need to use a more specific wonl lha
slope and so introduce "gradient".
ST(P) Marhernaocs 2A 1eacf!er s Notes and Answers 77 1-6 4_ 5_
S;op
7-12
6. 7.
76 SJ (P) Mathemaf/cs 2-J\
B
4
9. 75.6", 104_4°, 75.6°, 104.4"'
10. CAB~ 2H0, 1108"
CHAPTER 17 Flovv charts
EXERCISE 17a 1. (p. 265)
a) 7+5= 12 or 5+7-= 12
b) 12-~-3=4 or 12""-4=3
c) 2x3---2=4 or 2x3-4=2
26 6'
11. 15Acm
d) 3x3+4= 11 or 4+3x3=- 13
2. 3.
EXERCISE 7c (p. 105)
reacfler·s No1es and Answers
Discuss inany el\amples and include all possible co1nbinations of _t y/J.
keep away fro1n a decrease n1 x unless you wanl to use ibis to inlto< division by negative nu1nbers \Jse the g1aphs already drawn lo dis1 poq1Jve and negalive grad1en1 and k;:id to 1he conclusion that in !he equa )"=mt, mis !IK g.radienl
l his is a good place lo introdw:e division by zero - one of !he children 1
we!! <lsk wha! happens when the line is vnt1o::al A way lo show that divi~
by ?Clo is 1n1possihk 1s lo intopre1 !2-'- 2, say. as ''how 1nany ?s a1e thn•
1r· and 10 find out by repeatedly s11h1rauing 2 fio1n 12. fhen interp1et 12
m lhe sanw w;iy and conclude tha1 d1visio11 hy zero is irnpossibk {ur concep! nl cin infiniie answc1 can be introduced)
L ;1) 2 2. al - ·•
5. ' )
6. ~05
7. e)
d)
b) 1 b) 4
h)
"
«)
c) -- 4
c) + f)
3. a)
4. a) 4
h) 3
b) -4
EXERCISE 7d Explain 1hc nwamn_g ol steep and sleeper in !his context Rcfe1 10 olhet t
(p. 108) of the words. e g wnh rclc1en('e lo hills. 11se m p1ice. clc. En1phas1se tliai
aJJgle be1ween the posiu~e 'l'-axis and a hnc is always measu1ed a11!idockw1
1. = ), 4. '
I = 5 \
'-=----· ()
Z. ."i\
0
J. I o=,- ~-t 5. ! -= l{h
10,
,,
0 ()
ST(P) l\Aathernaf!cs 2A
::XERCISE 7e p, 110)
6_ }'-'-" -~_\;
7_ y = -6x y = - 6r
9. acute 13. a cu le 17. obtuse
10. obtuse 14. acute 18. obtuse
11. obi use 15. acu1e 19. ob1use
12. acute 16. ac111e 20. obtuse
21. approx1matdy ' 1. ' 0 "
--- )",
Introduces y-in1e1cepl F1cqlieru 1en111Hkrs of us meaning are necessary
1. g1adienl J. y rn1eicep1 I. ') 5. bl 7
2. gradient J. r 1n1e1cept 4. a) 7, b)
3. gradient ' y 1ntern~pl 4. a) 3, b) 4 2·
4. g1ad1ent I. _I' 1nlercep1 3. a) 7. b) . ' 5. g1adienl ' y 111tercep1 l. a) 4, b) ' •· 6. gradient 2, r 1n1en:ept ·-1 11. g1 adient '· y mlcrcepl
7. gradicn1 2. _v 1111<:1n::ri1 4 12. gradient -- 2, 1· 1nlercep1
8. g1adicnt J. F 1nte1cep1 4 13. gradient -. J v 1111ercept -t 2
9. grad1en1 ! r rnte1ccp1 J 14. grad1en1 l 1· ullcrcept 6 ' ' 10. grad1en1 ' _,, 1u1ercep1 15. gradient ' ,. u11ercepl ~I -- 1· !·
In Ntunhers 6 10 15 the value for {a) is the .sa1ne as the gradicnl and the value
for (b) is the sanie as they une1ccpt.
EXERCISE 7f Discuss what you expect in 1he way of a sketch We fed 1ha1 pupils should
(p. 112) develop 1he ab1l11y 10 draw co1nple1ely freehand sketches. v.-iihoul even using a
1ulct. but app1ena1e 1ha1 !ahcll1ng 1he ske1ch is necessa1y
reacher ·s Nor es and AnS\IVers
EXERCISE 16i Answers given correct-to
(p. 258) ,_ 23_0"
2. 34_4''
3. 383" 4. 42.8" 5_ 31.7"
6. J 1.2°
deci1nal place
1. 64_ Ja
8. 6 7 _4"
9. 62.1" 10. 177" 11. 8 4"
12. J6_ 3"
EXERCISE 16j (p. 258)
Answers given conect to I deci1nal place.
EXERCISE 16k (p. 259)
1. 31 0° 2. 387" 3_ 26 6°
13. 18 4" 14. 8 I" 15. 95"
1. 42 O"
4. Jil.7°
5. 36 9" 6. _'jl) }__~
11. Hr 12. HF' 13. 5 7_ 5"
17. 26 6"'
18. _11_8"
19. 29_7°
20. 59 o~
21. 33.7°
27. 425" 28. 41.2"
29. S6_J"
30. 52 I"
4. 21 8" 7. 5. 35.0'' 8. 6. 8 5" 9.
16. 39 8" 19.
17. 49 ,r' 20. 18. 59 O" 21.
2. lJ_ 7''
7.
8. 9.
10.
14. 15. 16.
22. 23. 24. 25. 26.
13. 18-4° 14. 16_5"
15. 48.4" 16. 50.7" 17. .5! O" 18. 45.0"
5 L3° 10. 16 J" 20_6" 11. 68" 66.()'' 12. 67 4"
21 2° 22. 66 8" 12_5" 23. 24_0"'
3S Y' 24. 53 I"
3. 55 O"
12 8"
26 6" 59 OQ
8 8°
_l6 9'' ]J 7''
24 ·1"
51 '.\''
18 7" 41 7°
30.Y' 51 3~
75
EXERCISE 161 Discussion 15 uecessary HJ remind p11pds of ihe 1ne,_in1ng ol ·be;urng· '"angle
{p. 262) of ekva11011·· etc
1. 310" 5. 10_2 krn
2. 266" 6. 26 6", -t)_O", 18 4°
3. 59 tr. 59 O'', 62-0" 7. 108111 4. S6_J"
74 ST(P) Mathen1atics 2A
13. 4_ 50 Clll 17. 16.9c1n
14. 7_0)cni 18. 1 44c1n
15. 6_43 nn 19. 9.33 cm
16. 6.24 Clll 20. JO 2 COl
21. 5_22 cm
22. .l001n.
23. l7_8cm
24. 9_23 cm
EXERCISE 16f 1. 5 17 C!ll 4. S 60 nn
(p. 253) 2. 4_60on 5. 8.96cin
3. ]_68 CIH 6. 6 64 cni
7. 9.99cm 10. J SOnn
8. 14 I Clll 11. 17 9crn
9. .34 5 cm 12. J 26cn1
EXERCISE 16g 1. 14 3 cm 3. 8 l6cn1 5. 5_10rn
(p. 255) 2. 179cm 4. 10.1 cm
6. 69 9m 8. 30 8c1n 10. 1_40nt
7. 3.23 cm 9. S.66rn 11. a) 16" h) 17.2rn
EXERCISE 16h Poinl OU! that if 1he langcnl (1f an acute angle is greater !ban I, the angle is
(p. 257) greater lhan 45" Use the enrlier discussion about Ian 90" 10 show tlrnt there is no 11ppe1 li1nit for the value of the tangenl of an angle (but keep It sin1ple)
Answers given (;onecl to I decimal place
1. 65_6" 4. 76 J" 7. 9 I"
2. 19_8" 5. )4 5'' 8. 31.8"
3. 12. 3° 6. 17.2" 9. 39 O''
10. 34.l)0 13. 29 J" 16. 64 4"
11. 44 8' 14. 59_7° 17. 69 4'
12. 20_6'" 15. 74_4" 18. 18_4~
19. 2) , .. 25. 20 9"' 31. 51 6"
20. 1<1 4" 26. 29 9c 32. 41_7''
21. 37 6" 27. J4 9" 33. 48_ I"
22. ,10_0" 28. lQ ll° 34. 59 ._,.
23. 44 1" 29. 487° 35. 45 _r'
24. 4_, 6~ 30. 74. ·1" 36. 50 4'
Teacher's Nares ancf Answers
1. "' ~ 4 ' - 6. "' ~ ' ' -· -3 " 2. "' ~
!
' ~ 4 ,, 7. m ~ ' ' ~ 7
" 3. "' 3, ' ~ 2 8. "' ~ -3, ' - 4
•• m -4, ' -- 5 9. m ~ ' ' - 6 -;.
5. m 7' ' ~ 6 10. m -· 7. ' ~ .. J
11. 15. y
grn<lknt -
-+----'>.,.,->- ' 0
16.
12. gf3dieul 4
0
17. t
13.
0 grndi~nl - 5
18. gra<li~n! 1
14.
()
78 S F{P) Mathematics 2A
19. 20. y
gradient I
0 0
gradient \ -j
21. y 25.
' gradierH :
- I
, I)
()
22. 26.
0 grJdiem -1
23.
27.
24. 28.
0
_,
25.
EXERCISE 16c 1.
(p. 248) 2. 3.
4.
5. 6.
EXERCISE 16d 1. (p. 249)
4.
Angle
))" () 62)
27" O :i!O
37" 0 7 )-l
JI" 0 601 50~ I 19
0 217 7. 0 )')!
0 S68 8. 0 18)
0 202 9. 0 180
L74 10. 0 0664
186 11. I I\
I 05 12. () 642
. "'"~ ~opp
hyp
leacJier s Notes and Ans;vers
13. () 9 ! 1 19. 0 J78
14. ? 9~ 20. 0 0122
15. I 11 21. 2 75
16. I 6S 22. 0_279
17. -! I 7 23. 0 836
18. ! ()8 24. () 969
2.
OP!'
hyp
EXERCISE 16e In the worked example we chose lo loun 1h1~ equation wi1h lhe ratio of the
(p. 250) _\ opp sides on !he kft, Le. -
4- -"" ---:- =tan l2° Some 1eache1s, however, may plefe1
adJ
lo stan with the trig 1atio, i c_ lan -~2" = ~£~ = _: adj 4
1. 5 64cm 5. I 4Jcin
2. 5.81 cm 6. S 38cm 3. 0975crn 7. l·Llun
4. 4.55 cm 8. 5.40cn1
9. 7.77cm 11. 7 _00nn
10. ~-12cm 12. 5 40c1n
72 S F(P) MatfJemat1cs 2A
EXERCISE 16a (p. 244)
In Question 14 we expect
nearest ~", e_g_ 26!"
angles measured by a protractor lo be given lo !he
(Angles given to neatest half degree)
1. h) 26tc c) 0.5 4. b) 26t" c) 0.5
2. h) 2w c) 0.5 5. b) 26t" c) 0.5
3. b) 2#" c) 0.5 6. yes
7. h) 37~ c) 0.75 10. h) 11" c) 0.6
8. h) Jr c) 0.7.'i 11. b) 10° c) 1.2
9. b)W c) 0 6 12. b) 50" c) 1.2
13. B,C, B,C, B3C3
AB 1 AB~ AB,
14. BC Angle A AB
---·----· 26!~ 0.5
2 26f" 0_5
3 26j~ 0_5
4 16~" () 5 5 7.&!'' 05
6 3T' 0 75
7 17" 0 7)
8 31" 06
9 JI" () 6
JO 50" I 7
II 50'' I 2
EXERCISE 16b Ciive a rrmintkr ahonl si~ni!\cJnt ligures One of !he dass wdl probably ;i~k
(p. 247) aboul 1.10 9\)' C 1nnrnen1 on it ;ind use 11 ;1,; another npporluni1y 10 disc11ss
division by lero: see the notes for r_:,e1n~e 7c.
1. 0 Jf>4 9. 0 J!M 17. :?8
2. 0 5.l::' 10. I Oil 18. 0 700
3. _1 Ol:i 11. I 80 19. 0 0875 .. I lJ 12. 2 75 20. I 2J
5. I 66 13. 0 0699 21. ? 61
6. 0 1)8 14. 0 754 22. I II
7. 0 _14'1 15. 0_966 23. 3A9 8. 0 :i l_l 16. 57_3 24. 0 306
EXERCISE 7g (p. 115)
EXERCISE 7h (p. 116)
leacher ·s Notes and Anstvers 2'
29.
6
f.rMhcn!
Numbers 11 to 16 require changing lhc form of the e-quation
1. "I hey are pinalkl Then 111 values are equal 2. J hey are paia!lel Their m \;Jines ;ne equal
3. Yes 7. Ye~
•• Yes 8 . Yes
5. No 9. No 6. No 10. Yes
11. Yes 14. Yes 12. Yes 15. No 13. No 16. Yes
IT can he useful !(l ask pupils fl'f !he equation nf a line 6 umts lo 1he rig.ht o
the r-a;o;is and pa1allel lo it Sin1ilady f11r lines parallel to the x-axis lndud1
negauve values f()r both
I' -o-j
' ' 0 - ) --4 2
I
:io ST(P) Mathen1a11cs 2A
2. y
6
4
x ..,, -- J
" 0 .
-6 4
-1
4
-6
3. JO
8
6
- 6
y ~ ~5
4.
6
y = 5 5
4
y = - 5
y "' lx
4
y
6
4
-4
-6
x"" 6
6
,.- "' 5
6
x=4
y=J
6 '
( s. JO). (5. -5). ( 2.5. -5)
A r1gh1-angled 11ianglc
(4. l). (4. -2). ( -6. l)
A right angled triangle
Teacher·s Noles and A11s1·vers 71
29. _§_Q_ 30. u_ 31. 1%2-0 32. H
'°" !00 <OU
33. 140 38. 849 J 34. 310 39. 104
35. 493 40. 185
36. 748 41. J 19
37. 2768 42. 2415
43. 70 48. 3312
44. 170 49. 62
45. 189 50. 91
46. 652 5 51. 26 47. 2448 52. 15'i
EXERCISE 15b 1. 6'l_2Skg 12. !98 kg
(p. 240) 2. £226.80 13. 414
3. 84 14. £1 !O
4. 18\l Clll 15. a) £J6 b) f76.SO
5. J3 16. 61
6. £747_50 17. 94 ] kg
7. £8-40 18. a) f)4·10 b} £4624
8. £9.20 19. ll 4\8
9. f8;~ 20. 27mpg
10. fl05 21. a) )6 p b) 6161iues c) LS 04 less
11. £7SO
EXERCISE 15c 1. a} 16% b) () 16 6. 12 5 ~~
(p. 242) 2. a) 45 'j~ h) to 7. .!_.'.!j
'"° 3. a) 0.85 h) 16 8. a) 98cm b) 960 sheep
4. 20 ~-~ 9. £43 _)()
5. 42 rn 1
EXERCISE 15d 1.a)45~'~ b) 0 4) 6. 'i8 ~;,
(p. 243) 2. a) 85 'j~ b) ~J 7. 0 82
3.a)064 b) ~ 8. a) 94_5 b) 8.81niles
4. 42~ % 9. a) Ul 05 b) £14"760
5. 2 ! 7 rn
Ct-IAPTER 16 Tr-igonometry: Tangent: of an Angle
The 1rigonon1erry sec1ion (Chapters 16 and 19) is optional al this slage. ll is repeated fro1n the beginning in Book JA. Discuss the 1neaning of tbe wo1J •·1rigonorue1ry"
70 ST(P) Mathernat1cs 2A
EXERCISE 14d 1. yes, 2.5 cm 3. no
(p. 223) 2. yes, 7.2c1n 4. yes, 6.3cm
5. 7-5 cn1 7. 8-lcm 6. 7_5 CIU 8. 4} cm
9. 4cm 10. Cl)= 9nn, DE= I0.5nn 11. Sctn 12. l)E = Pinn, AE = 13 Snn, CE= 4_5cm
EXERCISE 140 1. 8cm 4. 30cm
(p. 227) 2. 6nn 5. 24c1n
3. IOcin 6. 6cm
EXERCISE 14f 1. yes. P 5. no
(p. 229) 2. yes, Q 6. yes, P 3. no 7. yes, B 6.f E, !hey are parallel
4. yes, p
EXERCISE 14g 1" yes, CR = ]_6ctn 4. yes. HQ~ 7_2 crn 7. 5 I cm
(p. 232) 2. no 5. yes. AC~ JO~cm 8. Jcrn
3. yes. RQ - 35cn1 6. no
EXERCISE 14h 1. yes, 4 CITI 9. yes, J~ cni
(p. 235) 2. yes. 2-4 crn 10. yes, l8cm
3. yes, 5 12 cn1 11. AC= 3 !SCin, CF I 05 cn1
4. yes, 56~ 12. 14-1nn
5. no 13. yes 6. no 14. !0 HI
7. yes, 14° 15. 19.2 rn
8. yes, 32" 16. 60cm
CJfAP-TER 15 Percentage Increase and Decrease -"'-~~··="'""-«'-~====·-~"'-""-""==
EXERCISE 15a (I'- 238)
Revise earlier- work on percentages_ Explain the nieaning of the words "percentage increase" and "percentage decrease".
1" 150~-~ •• 160~-~ 7. 148 % 10. 112_5 '% 2. 125 ~-~ 5. 175 ~~ 8. 400% 11. 157 ~~
3. I ?O ~~ 6. 115 '.'~ 9. 275 ~-~ 12. 115 /~
13. "' 14. '"' 15. '" 16. BO i(Hj H>ii HH'.i 11'0
17. so/~ 20. I 5 ~~ 23. 96~~ 26. 66i ~-~ 18. 71 /~ 21. 6" ~i 24. ]4 /~ 27. 41 /~ 19. 10 ~-~ 22. 58 ".~ 25. 37~/-~ 28. oo~~
EXERCISE 7i (p.117)
EXERCISE 7j
h>- 118)
5.
1" a) 1 b) 4
2. 0 = - 4. h - ' ' 3. o) l b)
••
0
y
- ' -6
c) i ' - I
l) +
~r~<hr.nl _1
. '
leaclw :, Nor es and Answecs :J I
)' ~ - 5
F,, 4- J,: {(( 4), (4_5, 5). ( ---4.5. - 5)
An isosceles hiangle
5. a) ob111se b) an!le c) obtuse d) ob!use
6. (- L --6}
1. a) Ill b) " ') ? 2. (1 = ~5. & - J. ' •I
3. ') I b) " •• ;1) gradien! 4. I' mtern·pi
b) gradit"nl ' " ' 1ntncep1
<) gradient l. r 1nten·er1 2 d) .i;radient ' - i· ' rn!e1cep! -4
5. a) Yes b) NP
:J 2 S l (P) J\.1arf1ernatics 2A
EXERCISE 7k (p. 118)
6. y
·----4
--- ]
. -4
1.a)ll h) 10 c)-JI
2. a= 4. b ""' 11, = 5 3.
-. I
yo h
4. H1 -
11 " = -''
-J. 4). (8. 4). ( J, I I)
gradienl 5 1- 1nte1cep1
_ ,
ti '.l
enla1gernen1s and scak fdnor~ F<)r e;>,arnpk_ in ExctcJse 14b_ you could refer
10 !he UbjC:Cl lr1ang\e and !\5 !mJ.gc. I lus app1nach leads nalurally lo llnd1ng
rrnrt':>ponding vertict~ <ind apprcua11ng that co11espondu1g s1de-s arc in the
saint ra!lo
EXERCISE 14a <;ive 01 ex1uicl itD!H ihc class iu11lici txampl,;s before lhcy begin the
(p. 217) e:o.c1usc
1. yes 7. yes
2. 110 8. no
3. yes 9. !l\'!
4. no 10. no 5. yes 11. A ;ind I>
6. yes
EXERCISE 14b Number l can be 1epeated wh<.'.n 1he pupih have h<Hi experience ol duing It
(p. 218) once_ 1'he values for (c) should improve
1. a) yes b) AC = 'l I cm. CB 6 4 Clll
c) each 1s 2 d) all are equal 10 .[
2. a) yes b)AC = 86cm CB= 71un A-C )_7cnl. ·s· )_!cm
c) Ct1ch 1s O 67 or~ d) all equal 0 67
3. a)ycs b)AC l9cn1 LB,,--6.lcm ,\(. ~9cin_ C"B" ]2cn1
c) each is 0 5 ~)r j- d} all equal 0 S 4_ a) )"CS b) AC 10 I cm_ CH =.c 6 6nn. ;\ c 7 6nn. c·n 4.9nn
c) each is 0 75 01 ~ d) at\ equal 0 7_)
5. :i) yes b) AC=- 6 ! cm. CB= 9 lcrn AC '""9 2c1n_ c·tr = IJ 8cm
c) each lS ! 5 ur ! d) all equal ! )
6. 80°, 52°, yes
7. Tl'', Tl", yes
8. 70", 70", yes 9. 93"', s2~, no
EXERCISE-14c. Children need lo be shown hnw to pick oil\ che co11esponding sides. either
(p. 221) use the fan 1ha1 cor1espondrng sHks are oppos11c equal dngks. Of t:o111pilre
1he sho11es1 sides !hen lhc m1Jdk knglh s1dt•s_ !ht:n the largest s1rks
AB BC AC AB BC AC 1. yes 5. yes
PQ QR PR PQ QR PR
AB BC AC AB BC AC 2. yes. RQ P<)
6. yes. PR RP PQ RQ
3. no All BC AC 7. yes
:\C CB AB IU) ()P RP 4. yes _
PR <)R QP 8. no
68 ST(P} Mathernatics 2A
CHAPTER 14
12. y
6
-6 -·-4 ·-· 2 0 ,.
_, I I
---4 c
---6
13.
ll
14.
., . -.,-------,
- JO - 8
Sirnilar Fiuures
-4 /
/ c
, 4 6
,.
---,/~ ll
0 / )\
rh1S !(>ptc is l"t)\TfCJ wilhl'll! llllKh rdi'-rt."fl\T !O <:'11!<11).'ClllC!!tS bCC\!J)(' W('
tt'n)gnise 1ha1 snn1e 1e;1chcrs m;iy n.11 do a1n Hanslo1niat1nn "111" I! {"haple1 I~ ha_~ heen dDne. lh('n similar 11iangk~ can bf" approached 1hro11gh
5. a} r """' 2x ----4 b)2v=xl-10 c) y = -..'..4::r -3
6.
-- 3
y
()
li:!acher·s Notes and Answers 33
y=4
(I. 4). (I. 4). (-). 4)
CHAPTER 8 Reflections and Translations
EXERCISE Sa (p. 120)
1 his topic, together with the wo1 k in ( 'hap1er,; 9 and J _1_ can be dnne laler or
no! al all. l'vJuch discussion is necessary at every St(!ge
Ri:::vises I he wo1 k on line sy1nrnct r y n1 flook I
1. a) and c)
2.
3.
4. 6.
-B-&X' s. I
~ I I
34 ST(P) Mathematics 2A
EXERCISE 8b (p. 121)
Revises the wo1k on line syn11netry in Book I
' - I
-~ I
2. \ I
None
4. \ I I
I
- ',~\ I,,-- v / 0::--
/ I\" / \
I I
5. I
~
6.
7.
8.
/ /
/
/ /
/
/ /
" .__,__.L-__j___l '
9. I
-~--\
10.
9.
"
b - 4 - ]
10. )
- 4 0
' t' [)"
-4
'
' A
()
6
h~crci1er·s Nores and Ans•vers 67
,,
IJ
b
Ccn11e: (2, 3), S..:ak factor -- J
a) (~euhe (0,0). Scale factor -I
b} f{ota1ion about 0 through 180"
66 ST(P) Marhen1atics 2A Teacher·s Nares and Answer~ 3!)
6. 11. 12.
" ,.
'1~ ~
--~ ~
---- ~ --" -------' Cenue (I. 'i). ., " I Scak !annr
I Noni'.
0 --,-
- " -6 -·4 1 ,, c 13. 16.
" /
I 7_ I
" B
I \ --+--\ I
c \ I / " ,,· I
----- - ----"\ Cen!ie- ( l. 0)_ 17_
0 Scale lannr _)
I -6 -4 - . - \J/' I
14. I --+--
' I I - ' -~-- j I
I 8. I
- b
c o· 18.
Li\ 4
I 15. I
o· A'~o-c:: "
C~ntre I -- 1. 1;)_ I \' A Scak lac101 I I ___ L __
' I --6 - 4 -- ) 0
---L--6
\ "'- I I - '--. I I I
D -4
36 ST(P) fv1atflernatics 2A
EXERCISE Be The words ··ob1ec1"' ··unage .. ··minor line" are 1n1roduced A good deal llf
(p. 123) d1scuss1on 1s nct:cssary to make 1he1r 111ean1ngs dear
Nu1nbc1s 21 10 1·1 can he dune on the sd1ne diag.1am. Ill wluch case scale bn1h
axes fronl ---5 10 5
1. 4.
2. 5.
~ ~ 3.
I 6.
" D " -=-r=- ' " I
D " \...j...J " " " 7. c B B' c 9.
---A' ·A·---
0 A
8. ('
A~B
c
l'edcher -s Notes anJ Ans1vers
EXERCISE 13e ()n11t 1h1s w!!h .ii! bu! the 1no~1 ,ibk
(p. 212) 1. ( )_ 6) ' 3.
4. H
5.
2. iO I) ·.l
/';;/ I / / . .. /
I .. · '///
.... --- .. ·
(
,,
. "
I
{
Ce11lle (0_ !). Sco~k fano1
64 ST(P) M athemarics 2A
10.
Teache1 ·s Nares and Ansive
15_ rs f" E
8
I 6 I
c B [)' cl I) 8'
I I I :_~ I
c I I c
A B A I A"
11 /\I A'
0 4 6 16. A I A' I
I EXERCISE 13d 1. (6 (J•. 2101
1). l 2. I ·· I. 01.
3. Cl!. 4l. '
l ' 4. (!, 2), l
I
B ll I o'
5. y I I
( c (
12 . B ,,
c ./
. / /~~:~ ,- -----
.
A'
0 "'
6 ' 8 10
A
rzr A'
qc
/ 17. A I A.
0
I
' //n· f.
I
,/c B
I B c c ••
B
10
6. 13. A' A 18.
--BB-><-8
6
c c 4
B
~t=7 c
14.
,\
0 8 10
:rn ST(P) f\..1atheu1atics ZA
19. <)9: A and A'. QI!: Band l!". Q12: A. A'; B. B'; C, C'. <Jll A. A' and I), LY. Q14: A. A' and n. f)', QIS: A. A. and r. f ·. Qi6_ A. A·. C. c·; l), lY; F, F', Q17: C, C'; E, E'.
They all Ile on the axis of syn1rr1e1ry.
20. Equal distances; perpendicular Jines.
21. Equal distances; perpendicular lines
22.
23.
c
B"
- J - l
' -
p
-]
l--~~-~-'
y-,--
4
A' A
I
- I ? l_. .. ---l~-
H
-·~-
Q
5.
6.
9.
leache1-'.<; Notes and Ans~vers 63
10 (
6
I l •---~-------~"
\ B
)I)
!O
c
(
,. A IJ A' "
0 -.---+ 6 8 IJ)
y
>O
('
"
4
l " ()
6 '"
li 2 ST(P) Mathen1at)cs 2A Teacher·s Nores and AnS\vers
2. 24.
-4 - i
_,
0 W' + -3-
ll'
3. )'
'" C'
fl 5 -y' 7
8 25.
y ··--- ·---
-1 6 - 8 - -----("
4 6
26.
A' 4
c
' 0 _, 6 0 8 A B
--0
4. c 4 &
Ill
I 6 I
A' 4 I
,-/
Ir_ /
B
, 0 6 8 Ill
40 A1a1hemat1cs 2A ST(P) "
EXERCISE Bd (p. 128)
oints is of inv;uianl p The iu1ioduct1011 of the inirror line
1.
I- I the equauon lo UH J.
2. y
0
-2---
5.
y
·o: ! .d o I
- 5 --4
Fii I I I
{) 4
D
A
-2
4.
6.
--4
optional
c
B
0
y
7
y~l
l'
can be asked Abk ch1id1en
I I COD I B' A
I
/ /
/ /
/
6
y
----y·
X, X' . 3' poHllS are inva1rn1
3.
4.
., ·-;
EXERCISE 13c 1. s· (p. 208)
Hl ·
0
B
I
- 2 A
c/·
·«1 B
6
and Answers Teachers Notes 61
Cenue o c I b. ( ), 2) f ·11largcn1en
Ill
I- eulargemenl Centre o
IS ( \, ])
!l' j()
'----7-; 6 B
' B -·
:~-----···· / ---/_/,,. (
------- -
o~--.----:---~--~.~--;1~11--;,\, .
60 ST(P) AJ!athernatics 2A
7.
EXERCISE 13b 1.
(p. 206)
10
()
- ]
z
()
..
4
~ Cenlrt" of enla1gement is (10_ 2)
"" " " ~~ x· x
6 8 10
Cen!re of enlar!!emen! is(:!_ 4)
6
Cenlre of enhH!-'-eflle!ll is (.?. ::0)
7.
-4 • 1
/ /
/
The1c are none
9.
/
/
/
/ /
/
r 4
·4~() R
(
8.
I)
6
Teacher~'> Notes and Ansi-vers
y
5
4
0 -\
--1 A
41
II
If there is a mirror line it has to he the perpendicula1 hiseclor ol AP_ Bui lhis line does not pass through the n1idpoinl of <.lB, su P(~ is no! !he 1ef1ection of AB
R
I'
()
I'
R'
~2 ST(P) Marflerna11cs 2A
10. y ll
'-.. '-..
" '-.. '\] 4 c' - '
11.
• A
/ /
4 / /
-4
EXERCISE Be (p.131)
1. Yes 2.
') -l " -4
/ /
,( Q
0
r
A
' "
A
•
" ~---r---1-0~,..,,----.,-,-.. x
• A
'-..
" '-....
12.
-3
N
3.
\ 8
6 \ \
4 \
B
0 -\
4. Gradient Equa1io11 1·
Teac/1e1·s No1es and Ansn/ers 59
3. l
' X~Y ' ' ' "
' cl- /'- --
0 '
" 4
M
" " l)
( "cntrc of enlargn11cu1 1s (8, 4)
Q'
- l " -4 0
4. In I PQllPV. PR!IP'R'. RVllWQ In 1 P()!IP'Q'. PKi!P'R'. RVllRQ In J PQ!IP'Q. PRllP'Jl". RV!IRV
5. y
c
Ct':nllc of cnla1ge1ncn1 is (1. I)
0 ~----------~--·--t- . 6
6. y
9 .. ' --
\ .. 6
\ \ Ccntn: of t:nlargemenl is {9. 5)
\ ~'
\ 4 6 8 \ c' \
r 1nfefcept 7 0
- ~l +- 7 DC _l~·+7x--21 =0 6 10
58 ST(P) Mathematics 2A
EXERCISE 12j 1. ; 5. 8i (p. 201) 2. 5. 8 6. IOOnt
3. £40. £52' £8 7. I I 4. a) 2 : l h) 8 • 27 8. £13.IZ~
EXERCISE 12k 1. 10 3. 2· 5 5. : 500000 7. fl). f6, £8 (p. 202) 2. 7. 6 4. 9. 7 6. 5} 8. 510
EXERCISE 121 1. 257 . 144 3. IOkg 5. 6: J ' 7. 91 . 20 (p. 202) 2. 32 - 24 4. 33m 6. 3.2 krn 8. £154
CttAPTER 13 Enlargements
Omit if Chaplers 8 and 9 we1e no! covered
The teacher can introduce !his 10pic by producing an enlargen1enl on the hoa1d (e.g. one sin1i!ar to Question 7 in Exercise 13c) The chihhen need to see the process in action before they do ii lhen1selves
EXERCISE 13a 1. Y
(p. 204) 8·
6
Cen11e of enla1gernent is (6.0)
()
6
2. y
s· R
/ /
R / 6
-h,~ /
~.~ () ·-.......__
Centre of en!argenlt'nl i~ ( 1. il)
Q.
~-()
4 6
EXERCISE Hf (p. 132)
EXERCISE 8g (p. 133)
1.aandc
2. Translation e and b
Reflection a and c Neither d
Teacher ·s Nor es and Ans1vers 43
3. Translalion 2: 1dlcc1ion ! , neilher 3 and 4
1.
2. ' A H A' fl'
DD 0 o· c
0 6
3. N 5.
6J 6
4. N
~ Wt!' [7 , .. '>'
v
6 8
44 ST(P} Mathematics· 2A
EXERCISE Bh Revise the work on vecto1s in Book IA before Joing this exercise_
(p. 134) 1. (7. J) 4. 11. 5) 7. ( ~2. 2)
2. (6. 9) 5. (I. 1) 8. ( 4. -2)
3. (2. 7) 6. (6. - 7)
11. G) 14. G) 17. ( ~:)
12. ( :) 15 (;) 18. ( :)
13. G) 16. (~)
21. (5. 6) 23. { --<L 3) 25. (9. I)
22. (2. 2) 24. (1. 5)
1 AA ~ (-;) RB ~ (-:) ('(' ~ ( :) EXERCISE Bi
(p. 135)
Yes. Yes
2. Lr· = (~)- ~·t~r = (~)- NN· = (·~)- No. Nn
3. (:) 4 C~) (_:) 5 a) ( :) b) ( ~) c) (:)
c '
l z
l A B
x y R
6.
_, 0 '
r •J
.,
<>l ( :) b1C) d( ~) d) (::)
9. (9. 6)
10. (2. 0)
19. ( ~)
20. (:)
26. (-4. -5)
lI. 2 13. 14.
24. 5J l
25. 7l , 26. _11 •
EXERCISE 12f Use many
(p. 195) d1su1ss1on
1. 21~-p 2. 18cm
3. 98 cm
Teacher 5 Noles and Ans-.vers
15. 6~ 18.
16. Ii 19.
17. o' ' 20.
27. l 30. ZB. 1\ 31.
29. ,, '
1no1e examples for chscuss1on with eve1 yone bu1 only the fllOS!
4. lOjcm 5.!0~CHl
6. '27cm
I! 21. j , I~ 22. 10
7 ~ 23. I;
16~ 32. Jl • l} 33. J~
These questions can b' abk ~hould work on their
1. lOcrn 8. llm
57
used for
own
EXERCISE 12g Much class d1su1ss1on usrng d1lle1cu1 examples_ 15 advisable
(p. 196) 1. 48 p. J] p 6. 16
2. I 2 un ~Ocm 7. [_~ ){) f 17 )0
3. f20. £2S 8. "I 2S2 rn' b) lO'i rn 1 .. Dick " fom 2) 9. L!
5. JOp --15 p
10. rn f !O, f8 12. --1! rn ! l-l1n' Im'
11. 6cm. 8 Clll. IOcm
EXERCISE 12h Not essen1ia! at tlus s1agr- but an 1n1crc~11ng u~c: nl ra110
(p. 198)
EXERCISE 12i (p. 199)
1. 2.
soooo 500000
3. !00000
7. ) km 8. 70m 9. 200m
•• 5_ 6.
10. 11.
':>00000
100000 ~ noo ooo
~000000(fll !Onu I 8 crn
f'len1y of d1~cuss111n 1s n.ccessa1y Ratio JS 1cv1~nl ,iml p1opo111nn 1s done more
tho1oughly 111 Bol)k Ji\ so !lus exern~c r.:an he 1)0H1!cd Ano1hc1 rnclhod lor propml!on p1obk1ns 1~ to 111ull1ply by ,; scak LJ,:101 e g 111 the wo1k.el1
example 111 ihis exeichc. 1hr- ~cak lanoi is H« {cnn1pa1rng jMgc ru1rnbe1s).
thu::k•1ess of 1he !a1ger bnok = I ) x y~g (we wan! the !a1ger book_ S{) !he
hnger nun1b.:1 goes ou !op 01 the scak factor)
1. 12 m
2. l6 3. IR nn 1. 7'
6. I hou1 s
7. 9 hou1s
8. fl I 90
9. fX400 10. )til 1111nutcs 5\ 1-.rn
4. J6un 5. 105
11. S4nunuks
1 Z. f I__! (must buy Lolllpk1c kngths) 13. 1-LHtlly a11y 1 (no 1oom to wn1I-}
14 . . q k;ISpoous
56 ST(P) Mathematics 2A
1. 4 . 'j
2. 5 4 3. 2. 3
11. 2 3. 5 12. l . 4 . 6 13. - 5. 10
4. 5. 6.
14. 15. 16.
I •4
I• 3 9. 200
L 4• s s • •• 8 I • 8. 7
EXERCISE 12b Revise n1ulliplication of fractions.
{p. 190) 1. IS • 2. 8. 3. J . 2
11. 8 'j
12. 2 . l 13. 40 • 9
4. 3 5. 4. 9
7. 10 6.
14. 2 IS 15. 15 • 19 16. 5. 4
7. 16. J
8. I • 6
17. 3 . 4· 7 18. . 8 . 4
7. 35 . 24 8. 9 4
17. 2 .
18. 4· J
EXERCISE 12c lnlended for the ahove average and can he ornined. (p.191)
EXERCISE 12d {p. 192)
1. 5 7
2. IJ 8
5. 6 8 2'1·i2=f· 6. I 0 24 _. _ _,, ~ : ~
1. ) 2 5 2. 4. 9. 16 3. 5 R 4. l }_ 2 3
5. 2 .
6. B) 2. b) 9. 5
7. 8 11 9 8. l )
9. 4) " h) 2 -
3. 5 8 4. 7 - 10
7. 8 . 64 = j~ t 8. ~ _1 = 4 . 18
c) 18 ll d) I
c) 5 · 3
9. 16 17
10. I IOOO
19. 12 . . 2
20. 14. 9· 2
9. 16. 7 10. 10.
19. 4 J 2
20. J • 4 . 6
EXERCISE 12e Reinind pupih !lrnl sorne1i1nes a· h is u~nl in die !orrr. olb bul Iha! !hey
(p. 193) should USt' consi~ten! no!ation within an equalion Of sentence_ i e_ \ 4 c::: 1: J and ~ = ~ ate h01h cOHcC! h111 t: 4 =- ~ is not
1. 10 4 . .? 7. 6 9. 9 2. ·1 5. 8 8. 6 10. I "l
3. ) 6. 12
11. !J 6. I?
Teacher ·s Nor es and AnsM,-ers
7. F
6
()
A 4 6
Yes.(~). parallelogram ·--!he opposite sides are parallel AA'(~'C. B~'("'C
8. a) (
"I [ [ A
" b) ll c
D
A \\
9.
" .\ ---'--1
. 1
H ·"'
~,,
n,
., ()
"' ( ~) b) ( -;)
>) (:)
S r(P) fvfathe1natics 2A
CllAPTER 9 Rotations
EXERCISE 9a (p. 139)
EXERCISE 9b (I>. 140)
Omit if Chapter 8 was nol covc1cd. Again n1uch discussion is necessary at every s1age of ttus wo1 k
Revises the woik on 1olational syuunetry in Book IA.
1.a)} b)~ c)~
2. a). b) and c)
This extends 1he work on rota1ional symn1et1y a lillle_ fl is worth mentioning thal !he order of rolalional sy1urnc1ry cannot be I as lhis would be ro1a1ion through a co1npktc revolution
1. 4. 2, 3
3.
4.
5.
I I
--*~I I
9. 91Y, 120". 180'. 90". 120". 180°
2. a) 6, b) 2
6.
7.
8.
Teacher ·s Nores and Answers
EXERCISE 11g Nu1nbe1s I to 1 aic ~u11abk fut cve1yone but use Jisc1c11on w11h 1he
(p. 185) re1naindc:r of this. exercise
1.
3.
5. 6. 7. 8. 9.
EXERCISE llh 1. (p. 187) 2.
6.
EXERCISE 11i 1. (p. 188) 2.
1.
EXERCISE llj 1. (p. 188) 2.
7.
491 lllllll
No 21.'icm 1
8, I IOcm" 11 700un 1
l
17 6null 9 SS rn
.?8 6nun
61 8 Ill 4_~2 crni
8l_)crn~
12_6 ~n1 1
.108 lllf)l
,~--
I I
I I I
CHAPTER 12 Ratio
707 Cflll
3. JI 7un
4. 26 4 m 1
7 l 95 c1n 1
3. 57 _lcm
4. SO l mi
J_ !4m 4. !)4crn 1
5. 491 cn11
5. 89.? llHI\
6. 40 9 C!H
5. J2 2 un1
6. 18 l 1111
EXERCISE 12a Scale d1aw1ng can be used a~ ano1he1 exainpk_ a scale of lcn1 to 500rn can
(p. 189) be cxp1ess.cd <is tht: 1a110 ! SOOOO_ Bdo1e Nurnbc1 11, gwe an exaniple of
con1paring three qua11t1Hes. e g. using 1he bt)at and 1he two rnodds 1n !he text.
lhc 1atios of the lengths of the s1nalkr rnodd 10 !he liugcr n1odd to 1he ac11ial boa1 a1c Im 2 rn 10111 nr l 2 10
54 ST(P) Mathematics 2A
EXERCISE 11c "Quad1an1" is introduced in Number 2: quadrant moulding is an everyday
(p. 176) use of this wo1d For all compound shapes at least 4 sf should be used until the final answer is reached which should then be corrected 10 J s.f
1. 10_1c1n 6. JJ_6crn 2. 10.7nn 7. 94.Jcni
3. 18.Jcm 8. 62_8 mrn
4. 205cm 9. 20.6crn
5. 27_9nn 10. 45 I CITI
EXERCISE 11d Nrnnbers I and 2 can be done hy everyone Except ror the able, use the (p. 178) re1nainder ol this exercise for discussion
EXERCISE 11e (p. 180)
EXERCISE 11f (p. 183)
1. 78_5 n1m 8. 94.J cm 9. 62.8 in 2. 62 8 rnm. 88 () fTI!ll
~ 10. 6.28 secs, 9 55 revolulions
3. 4.40111
~ ....•... ___ ; 11. 3140cn1
4. 194nn 12. 17.6m
5. 176c1n 13. 70 7
6. 176c1n, 200 14. 94.Jm
7. l2_6c111
1. 700cm 6. J l? CITI
2. 19-' 1nn1 7. 5 76mm
3. 87.5 Ill 8. 6)] m
4. 41 8nn 9. 92_6crn
5. 7.~ 5 mm 10. JJ 9rn
11. 16 5 Ill 15. 4 93cm 19. 4 77 c1n
12. 59 81n 16. 955nn each 20. 9 55 Cln
13. H Rnn 17. J 82 nn, 45 8 cn1 21. 9.55cn1, 29.1 Cnl
14. 20 Om 18. 17 7 OU
fhe de1nonstr<ition befo1e this exe1cise is rnore convincing if !he end sector is cul in h .. lf and one h<1lf pl<lced at the 01her end of lhe "rectangle" <is shown in !he diagra1u on page 183
1. 50 J cn11 4. 78 6 llllll1 7. 45-4 rn 1
2. 201 till] 5. 38.5 Clll1 8. 9.62 km 1
3. 78.6m 1 6. 11 JOO c:nl 1 9. 20 Jci01n 1
10. 25 I on 1 11. 'iLJ mi 12. 58 9c111 1 13. 118 m1n1
14. 451 nun 1 16. 457 crn 1 18. 943 etn 1 20. 193on1
15. 374nn 1 17. 714m 1 19. }540cin1
Teache1 ·s Notes and Ans~vers 47
EXERCISE 9c II is wol!hwhik d1awmg 1he d1ag1arns and p111tt11g 1he line(s) of synunelry on (p. 142) them
1. rotational 4. lrne 7. both 2. rolation11! 5. both 8. bolh
3. line 6. both 9. 1 olalional
EXERCISE 9d Simple models may help some p11pi\s to see exac!!y what is going CJn (p. 143)
1. 90" clockwise 2. 90n clockwise
5. origin, !Rtr 6. (I, 0) 90" anticlockwise 7. (I, 0) 180"
11.
12. J
c
;. '------"'-~' ,,
13.
c
"
"
3. 180° either way 4. 90° clockwise
8. (I, 0), 180° 9. (2. I) 90" clockwise
10. (1. ll. 1800
l ln.;_-lrnnged
48 ST(P) Marl1e1nat1cs 2A Teacl1e1 s Nores anlf Ans~vers 53
14. EXERCISE 10f Can b' used for disc1i:;s.1on Wllh the average but dnly the above average y
6 (p. 169) should a11en1pr 1 hese ll!l their own
D c 1. 78crn 1 5. 60 cm~
D. 2. 22 ::i cm! 6. 7)cmi
4 20cm 1 !8cm 1 3. 7.
4. .'i4cm 1 8. 68 cm'
9. -18 5 crn 1 10. 48cmz
A' ';I:
14~ sq 28 sq .. 11. unns 13. 20sq l!lH!S ·1s . U!UIS
. 4 . ' 0 4 6 12. 24 sq Ul\!!S 14. 14 sq lllHIS 16. ! o sq IHlllS
-2 EXERCISE 10g 1. ! 80crn 1 3. !Ocm 1 or 1000 111Hl!
(p.171) 2. 20cmi 4. 48 nn1
r' [)'
··4 5. 14cn1 6. 6 5cn1
EXERCISE 10h 1. 6cin 2 4. _iOcnic
15. y (p. 172) 2. 36cmJ 5. 60l!l1
(" •• 4 3. !OOcn11 °' !0000 lllfll
1 6. 6nn
c
A' CHAPTER 11 Circles: Cir-cumference and Area
A • Calcula101s x
5)lould be used fiedy fo1 al! .. -,1ku!a11ons Revise significant
. 4 -2 0 4 figures
EXERCISE 11a 1. l 2cm 4. 7cm
(p. 173) 2. !Om 5. l km
16. y 3. 10mn1 6. 9 1 cm A B" A" v 1. approx J 14 8. approx ) ''
EXERCISE 11b \Ve have HK!l\l()fl{'.d thal " can be used ;1s illl ;1pp1ux1ma11<H1 '" " b111 wnh ., c (p. 175) the use or cakulatois 1h1s no louge1 secins usdul rhose using calculalors
wllh ' " bull on should be CfKOUfageJ <o llS<C " and "' 1gno1e the 1nstruct1on ,
lo take " Co J 141 If answeis are requned COi ICl.:l <o J s f then "' leas1 4 ;[ 4 6 are required th1oughouL 1ndud1rig the value used fo1 " II 4 is used. nu1nhcrs
16 <o l,3 a1e S\IHah\e. po111t out that " gives " CO! !CCI to I ;f only. wilh -.,-cm1espond1ng 1mplu:a11ons fo1 the
17. accuracy or 1he idlSWO
4 1. l 4 5 fl\ 6. I S701nm 11. 44 0 cm
A " 2. 28.9cnl 7. 126nn 12. I 76 mm
•• c 3. l8.lcn1 6 . JO Zin 13. 8 80 Hl
4. 331 mn1 9. II l HI 14. ])() Hllll
5. 5,, 7 m 10. 0 0880 km 15. 1S 2cm 0 c
() 4 16. 970 min 20. 220 C!ll ·4 -l
17. 88cm 21. 1600mn1
18. 241n 22. 2000cm A' [)' 19. I JOO mm 23. 29rn
52 S T"(P) Mat/Jen1atics 2A
EXERCISE 10c Counling squares can also he used to illust1ate the fact !hat lhe area of a
(p.160) parallelogram is the base nn11liplied hy the heigh!. En1phasise 1hal •·tieighl" means perpendicular height llse the q11es1ions in the exercise to discuss which din1ension is the height_
1. 84 CTIJ1 3. 17.2cin1 5. 1280ciu 1 7. 24.48 ctn 1
2. 600cin 1 4. 0.02R8tn 1 6. I 7J6 101 8. 7 CIU
2
9. 38.88cin1 10. 28.8 cm1 11. 26.4 cm 1 12. 352cm 1
13. 63c1n 1 15. ll.25cm1 17. 36cm 1 18. 180CTTI2
14. 48cm 1 16. 110cn12
19. 8 sq units 20. 15 sq units 21. 9 sq_ units 22. IS sq_ units
EXERCISE 10d /\gain use tb!"' questions lo discuss whi(J1 1neasurenwnt is the heigh! A good (p. 164) exan1ple for discussion is !hal of a tree blown over by 1he wind:
!low high is the 1op of the tree 7 How long
is the Hee? How high wo1Jld a helicop1er
have to fly to clear ir1 Etc
Nun1be1s 25 lo 30 are intended !or ordinary sq11a1ed
paper >S used. a scale of I c1n to I unil is S;ltisfactory
1. 48nn 1 3. 80cm1 5. 100cm 1
2. I 56m 1 4. -1 2 Clll1 6. J99 Clll
1
9. 40crn 1 10. 32-4 1111 11. 22-2 cn1 2
13. 44nn 1 16. 1) C1111 19. 2,l_4cin 1
14. 64cm 1 17. 7 <; i:-rn 1 20. 82_5 nn1
15. 540cni 1 18. 70 Clll1 21. J0cm1
JOm
exe1c1se paper. II
7. 24cm 1
8. 14.4nn 1
12. 45 Clll2
22. 96cm 1
23. 21 nn 1
24. 8 31 cm 1
llm
graph
25. !Osq IJJHIS 27. IOsq um ts 29. IOsq units 30. 7~ sq units
EXERCISE 10e (p. 168)
26. L? sq
1. 8cm 2. 6c1n
3. 6cm
units 28.
4. 5. 6.
!_',sq uni1s
~Clll 7. J cm 10. 6cn1 ] Clll 8. l~ cm 11. 8ctn
_lficin 9. 0 4 nn 12. 4cm
EXERCISE 9e (p. 149)
EXERCISE 9f (p. 150)
EXERCISE 9g (P- 15-1)
Teacher's Nores and Ans1vers
18. ,.
B' c
19. 4
-6 - 4 A
ll" A" 0
a) a semicude b) OC ~7- ()C', OB
4
20. c B'
\! ~ 60°
O-JA-· B
1. c) (0, 4)
2. c) ( 2, 2), 3. c) ( I, \),
e) 90'"' clcx-kwise e) 90" clockwise e) 90" anticlockwise
l. 90" anticlockwise
Si1npk 1nodels may agarn prov!.' 11se!ul
(- ·,'') 1. rranslation given hy '
2. Re flee! ion in 1 0
2. 90" cl<x:kwisc
<)B
ST(P) Pv1alhernalics 2A
3. Rcfiect1011 in x =. ~
4. I 1ansla11on given by (--:i) 5. Reflec1ion 1n r = --_'(
6. Rotation tluough 90" an11dockwise about ( I. I)
7. Ro1ation 1h1011gh 90" anlidockwise aboul (0. f)
8. Rotation through 180° aboul {O. 2)
9. Ro1a11on th1ough 180" about(~- D 10. Refte:ction in y = x+ I
11. Rdlec1lun in BC, roiation abou1 B 1Juough 90" clockwise
12. Rctlcuinn in y-ai\iS. rotation about {O. lj) through 180". uanslation
parallel to x-ai\is
13. I) Rcftcc1ion in <)B 2) Translation parallel lo AB ]) Ro1auon about R tlul>t1gh 120" dl)Ckwisc 4) Ro1a11on about() 1hrough 120" clockw1sc
14. I) Rellccuon in BE
2) Transla11on parallel 10 AB J) Roia1ion aboul B 1hro11gh 90" clockwise 4) Ro1ation aboul 1he r11idpoin1 of BE, lhrough 180" 5) Ro1a1ion ;ibout E lluough 90° an1iclockw1sc
15. T1ansla1ion givco by 1he vector ( ~~)
16. Transla11on given by 1hc vcc1or (:1)
17.
\. / \. I
\. / \. /
\. / v
ccnhc of the 1urnlng ci1de
18. Ro1a11ons aboul difh:ren1 venices, reflec1ions, t1anslations
teachers Nores anti Ans1vers
19.
II
-- ) -I
VI
IV - l
VII
Retleuwo>> l--!V Rot<1!1<1m V VII
20. a) Relkc11011 111 lhr line y = x hi Yes
CHAPTER 10 Area
Revise si1nplc mul1ip!icatio11 of decin1als and fractions
EXERCISE 10a (p. 157)
Revises the work on are:as of 1ectaugles in Rook
1. 41 2 m' 3. 384 Ctl)l
2. 0 2108cm' 4. 40crn 1
5. 1 84 cm 1 7. () 0008 IH 1
6. 24 840nn 1 8. 4 56 il\ 1
11. 21 6cm' 13. 552 cn11
12. J2]cn1 1 14. 672cin 1
17. 8·1cin 1 19. 78 cm 1
18. I 28cmi 20. 90cm 1
EXERCISE 10b Revises !he wtHk on 1ec1angles in Book lA
h>- 159) 1. (l :1 Clll
2. 5un 3. !Om 4. 4 Hl!ll
5. 5crn
6. 5 rn
7. I 25crn
IA
9. I~ nil
10. 4\cm 1
15. 2870 llHH l
16. 862 2J2 ITI1
8. Jm
S. 7 Ill 10. 6cn1
51
