104
S1(P) Ma1hema11cs 2A
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. nnn-co operation
absentees,
en1barrasstnen1,
height
not
known,
ST(P) MATHEMATICS Teacher's Notes and Answers
EXERCISE 26j (p.409)
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
l. Bostock,
B.sc_
S. Chandler,
B.Sc.
A. Shepherd,
s_sc
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?
E. Smith,
M.Sc.
Stanley Thornes (Publishers) Ltd
ruache1 ·s Notes and Ans1+ers
3. a)
fext (£! L. Bostock, S_ Chandler, A_ Shepherd and E. Srnith 1985, 1991 Original illustrations
6
~·
--- --- --- -
103
('-- - · J
·a s --0
g_ 0
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.
]
4 ...._"'" - 3
....
'
~··············
E 0
z
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.
Number of rooms
b) Too much sca!ler to give an opinion
4_ a)
Any person who co1nrnits any unauthorised act in relation to this publication may
6
---.-~---,-¥------
--·--
----
be liable to criminal prosecution and civil clai1ns tor dan1ages. -------·-
First published in 1985 by: S!anley Thornes (Publishers) l.td Second edition 1991
·.X:-~--
Reprinted in 2002 by: Nelson Thornes Lid Oella Place 27 Balh Road
l
f-·---
I
f- --
---------- -----1-+-f-
--- --- --*- -
I
--
--t---
O'-~,'-«-'--',~~~IL0_Jl2~.~14~1L6~!L8.-J20~2~2~2L·l_J26 Pens and pencils
CllELTEN11AM
b) No
Gl53 7TH
-i.
United Kingdom 03 04 05 / 20 19 18 17 16 15
•
A catalogue record for this book is available frorn the British Library
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
ISBN 0 7487 0543 O
1. S!roug. 1no
Page rnake-up by Cotswold Typesetting Ltd Although these exercises can he done 1nd1v1d11a!!y, the ideas do need rhorough d1st:ussion aherwaids_
Printed and bound in Great Britain by Ashford Colour Press EXERCISE 26i
(p.407)
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'!
102
ST (P) MathenHitics 2A
EXERCISE 26e (p. 401)
4~w
2. Wcig.ht,w(inkg)
8~w
~H:qu:~;------~1-·-,---~·--r--~--,-,---1
12~w<
INTRODUCTION
16
5. a) Suggested groups 50 ~ w < 55, 55 ~ w < 60, etc.
EXERCISE 261 (p. 402)
EXERCISE 26g
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°
90
1. a)
(p. 405)
85
T
_,,_ x x
"
x
70
65
!1
:ii
__,,
-
60
·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
x
55
50
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\.
- -><
80
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!
x
their own ideas
45 rhete are some !opics that can he done !alc1 or ornitted completely. [)c suggestions on !his are given in the teacher's notes
40
35 0
40 45
'
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
55 60 65 70 75 80 85
50
f renrh
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
b) Yes
2. a)
75 ~ ·--·-~=~-! ~~
t-
-·- _-,----- _____
---·-~
"'
;
---
-· --
-
6 5 1--+--+-·····•
-
lit.
- - --
---
---· ' - -
L__
---·
{-----
-··
>(
- I'----'------
.
---t-1----1----,/- "----
~
·----·-
--
70
o;
---
--~-
--···- .__ __ ----
-
f\1ost children also need cons1ant ren1indcrs ol the ordinary processes of arilh
60 -·····-
- - - l----- - -
55 ----
--'------
____ ; .....
For exa1nple. each 1i111e 1nultiplica1ion of fractions is involved they shol ren1inded of how !o do it
----
---·-··
---~---
~
150
h) Faitly likely
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
I 55
160
165 170 lle:igh! (cm}
115
1110
!85
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
Teacl1er·s Notes and Answers
11 6 I ~1 l-l ' 1-1·' 1
4. a) Number ol rooms
1
2244176)
frcquem:y
c)S
d)l40
'f
l-'Io 1 I 2 '_1 j 4 •L1L' 31 }! 2
s.• > ~""'""'-"'-"1""'"'J~j'L1\ rrequeucy
EXERCISE 26b 1. a) 3~- 'I 2. a) 59 (p. 396)
b) No (As soon as data is g1oupcd, sorne info11nalion is lost)
~1ark ----~~~~--~-~i=:~ ~"'-~~!.~~-7~180-89_
Frequency
I
8
]
II
~o
ofwo1ds
l·1equency
I I I
!8
3. a) 25
b)
1
d) 20
c) 14
b)
8
!-1
!1
_
J_1-51-6-~~t1_~_1 s_t6 101!~.126
I
I
J
I I 8
5
]
29 1
)
EXERCISE 26c 1. Whole nurnbcr (p. 397) 2. Continuous
4. ( 'ontinuous
3. Whole nun1be1
6. ( 'ontinuous
5. Continuous
d) l-le1gh1
EXERCISE 26d 1. a) 8 (p. 399)
101
Ill
cm
Frequency
------
---------
b) 4
8
!JO~h
c) 140~h < 145
--··-135:::,; h '-. 140
----------
14
------·
-
!40>i, h '-. ! 4)
18
14S~h<
Jl
!Sll
!50~h
roial
2. a) 47kg b) 5
57
c) Weigh! m hg 40~w~60
20
60~w<80
61
80~w<
J]
100
l
+-~
rota!
d) 6
e) 81
3. a) I
b) 7
c) 20
d) No
l
100
100
ST(P) Mathernat1cs 2A 19. a) 7! hours
b) 37l- hours
c) £106_50
d) Ii hours
EXERCISE 25c
1. f:S I 50
4. f 112 29
7. £74_09
10. £126 83
13.£9671
(p. 389)
2. £68 32 3. f81J_J()
5. £1()4 63 6. £116 21
8. £150 37
11. £7(1 12. £74 81
14. £133 84 15. Ul306
EXERCISE 25d Be careful with Nurnbe1s 13 {p. 390)
20_ f)o
suggest 1ha1 they investigate the 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. 10
4. 0 06
1. J 2. 110
5. L2:
3. I~
6. 0.25
9. 8
21. 16
24. 3
22. I 23. 12
25. 18 26. 1.5
31. 4hours
34. 10 hou1s 35. 2~ hours 36. 6~ hou1s
!- hour
33. 2 SO hours
CHAPTER 1
Working with Nu1nbers
EXERCISE la
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
no1
7. (I 06 8. 0.02
32.
EXERCISE 25e (p. 391)
9. £79 75
NOTES AND ANSWERS
e) f/1289
27. 0 144 28. 0.56
37. 3 p 38. 12 p
(p. 1)
1. 9
4. 12.5
10. 7
2. 4
5. 1000
11. 0_145
3. !00
6. 81
12. 2 13. 14. 15. 16.
29. 2
65000 \820 17. 27 ')
30. 0 84
40. 1t p 41. 18p
39. 3 024 p
18. 537000
22. 69 78
EXERCISE 1b /'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 (p. 2)
6. il04 7. £140
11.£7070 12. £11080
4.
)I l
7_ I!,,
5.
b~
8. pp
3. £79
8. £48JO
13. £9.l 24
6. S8
9. £92_78 10. £82 90
14. £85_44 15. £157 15
EXERCISE le (p. 3)
16. £1]5
19. £103
17. £98
20. £182-20
CHAPTER 26 Statistics -=-=-_,~-~-'"'"".=.--...,"""'"---"-~-
1. a) 3 and 4 2. o) 9 b)
EXERCISE ld (p. 4)
9. 9 1
4. HI-" 5. '/~ 6. I .':i~
11. 6 1 I
14.
12. 3)
15. c 3
13. 2 1
16. 29
()ll
10. p'
17. 4 1 18. o'
The. meanmg ol ··reciprocal"· peeds to be lnade dca1 \\llh cxainplc:;, such a ··~is !he 1ec1procal of -1'" ··4 1:;, the rcup1ocal ul 1·· ··wha1 1s the 1cciproca 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 Irue only if /1 .f O
F1eq11cncy
d) 29 e) Rabbit, harnsler f) II is nol possible to answer this
'Frequency o!"<>''---
1. 4 2
of JT' etc
b) 6
c) fypc of pd
3. a)
Discuss exan1pks wh1d1 do no! sn11p!dy. e g 31 '--:- -2'. as well as those 1ha1 do
2. Ji> 3. S'
18. £95 '}0
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.
10. 10000 11. 1000000 12. 27
19. 46 1 20. 503_2 21. 709
2. £42
1. £35
4. f!OO 5. fl 10
EXERCISE 26a (p. 394)
7200 893
7. ! 28 8. !O 9. 6·1
-1 "l-w-f~ I 9
c) 16 n1ales, 16 kn1ales
6
11" i,!4
16.
2. "l~
12. )'{;"
17.
3.
0
10
1.
7
d)
4. 5.
1!6
8_ 9. 10.
13. 14_
h
15. }.,
ris
mo
19.
i lo
20.
i:"4
18.
'
2
ST(P) Mathematics 2 A
reacher ·s Nates and Ansivers
21. O.O
26. 0.000 046 7 27. 0 ]06]
22. 0 26 23. 0.062 24. 0_008 21
6.
28. 0.028 05 29. 0_()05 173
25. 0.000 538
30. .1.004
31. 5 - l
36. 10·· 3 37. b "'
7.
3710
4_80
96
I J_80
49_60
76
IS 60
4.41
7 3.40
f 1_44 1_56
34. 2'
39.
"
48
40.
8.
t
1. 4 2. 'f5 3. 64
7. 81 8. l 9. 4
4. 5. l 6. 125
'
12.
'
13.
16. 0007805
18. 19. 20. 21.
17. 59 200
22. 0.00018601
15. 497.1
23. 2' 24. 4' 25. J' 26. a' 27. a'
28. 29. 30. 31.
9.
783.4 1050
,,
S'
33. 34. a" 35. ]' 36. I'
J'
6'
4• 32. 5 -- 6-
EXERCISE lf
37. 4'
38. 39. 40. 41. 42.
a'" 1- 1
b'
5- 5 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 7. -10400
2. 0 001 26 3. s -~00000 4. 740 000 000 000 000 5. 0.000 I J
EXERCISE 1g
(p. 7)
1. 2_5 x 10-1 2. 6 l x 10 1
3. J__5J x 104 4. 1 6 x 10~ 5. 9 9 x IO'
8. 00008SOJ 9. 4 250000000000 10. {) 000 000 064 J
6. 3907xJO-'7. 4 x 106 8. 5.J x 10 8
s
9. 4 x 10-' 10. 8 x 10 1 0
s 70
126 80
10.
11. 12. 13. 14. 15.
1 (i{)l x !()-'547xlO' 4 ~-06 x 10 6 4J)6 x 10 704xl0!
18.
f
14.
f
J 2 I 4
18 79 84 40
16 41
7 56 19.
[
[
214
I 68
J 12
7 40
1 I 'i
I 0 ]_)
LSJ
I 5?
f
6 .16
))
46
I 08 4.?
15.
16 01
£ ! 75 l 10 \4 !4
42
(p. 7)
71
!_86 ! 68 2_ 76
f ! 74
I 61 I 80
5 99
so
I 26
0 1074
f
')I 7S
44
8 04 13. 2410 14. 0_7032
17.
J7_60 32.95 4 50
J_
£ 4_40 I 68 I 96
10. n; ' 11. rooo 12. 2
6 __')0
f JJ)4
3.48
2~-h
£
61 2 08
38. 4'
l
16.
f
8.40 36AO
32. r' 33. 6 ·-) 35. a
EXERCISE 1e (p. 5)
H.
f
99
I 92
l 81 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 2. fl22.50
3. [91 48 4. 1!7618
5. t 1,tx 61 6. f 196 :!4
7. £120.41
8. a) ?hours 40rn1n bl '8hours 201n1n. flOl 97 9. 4'ihours_ fl4! 75 10. a) lJ h) 3X~, £87.57~
11. a) £11780 12. £20.194 13. £15715 14. £201_76
h) £164.10
c) £17160
15, £171 4J 16.£18837 17. f 144 80 18. £176_88
98
7eacherS Noces and Answers
57 (P} Marhernatics 2A 16. 26xl0- 2
b)JOkrn/h c}lSkm/h d)20k1n/h 7. a) Reily, Chris, A11drey f) Audrey 10 kin. fk11y 9 kni. Chris 15 kin e) al 2.JOpm, af1er 25 01iles
17. 48xi0- 3 18. 5 3 x 10·- l 19. 18x10-~
g) 2t km
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
20. 5 2 x 10·-l
79x!()-I 6_9 x 10·:;
36. 37. 38. 39. 40.
6 O'i x 10 1 )_005 x 10· _, 6_0005 x lO 7 08 x HJ" 5608x10 5
c) 26 01iles fron1 A
3. 4. 5. 6.
a) !4hours
80 kn1/h 70mph 5 kru/h 7. a) 15 krn
EXERCISE 24i (p. 377)
1. a) 175kln
c) 8 km/h
b) 2! hours b) Ii-hours b) 57 hours
EXERCISE 24h 1. a) 20 kru 2. a) 1"i km (p. 375)
1 34. 9.906x 10-35. 7_05 x JO'" i
c) \01nin
b) It hours
h) !}hours
l E
'fl
5 200
"
lOO
47. 506x 10·~ 48. 5_ 7 x lO • 49. 503x 10 8 50. 9 9 x 10 1
e) 45 km/h
T
EXERCISE 1h
(p. 9)
.~ 6 x 10
41. 53xl0 12 42. 5_02xl0- 8 43. 7.00809x 10 44. 708xi0 3 45. 4_05 x 10 1
'
56. 5_09xl0J 57. 268x10 5
'
1
58. 3 07 x 10' 59. S.05x 10- 3 60. 8_8x!l)-- 6
own
1. 1550 l.'100_ 2000 2. 8740. 8700. 9000
..
3. -1750_ 2800_ HJOO 16 840_ 16 800. -17 000 5. 68 ,11 o_ tiR ,100, 68 ooo
J
6. 5730. 5700. 6000
13. '14, ·15 14. 4) 499 44 ){)()
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 b)l~hou1s c)l7J~kmjh d)no 7. a) i) 125 kin ii)760kln b) Nina. 2~ h; Fa1hcr, I~ hours c) f'athcr. by 51nph 8. a) 35 n1iles d) at 1330_ 15 1niks froln Farley 9. <18 1nph
EXERCISE 25a Check son1e aclual supennarkel bills and go into lhe meaning of all cnl11es on (p. 380) 1he1n
4. £15 72. f4 28 5. £ 15 04, £4_96
7. ,-HJ 10. 4100. 4000 8. 7\111. 7500 8000 9. 'l J 800. 5J 800. 5,1 000 10. 6010. 6000, 6000 11. -1980< ')(100. 5000 12. 8100_ 8700, 9000
16. i 1 ){)() ooo 17. !YSO
15. ! S-19 1,1)0
EX~RCISE
(p. 10)
1i
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 2. 7_17_74,7
6. 390.39.4 7. 894,89_9
3. i6 99_ ]} 0, JI 23 76_ 23 8, 24 5. 9 86. 9 9,
8. 71 65, 7J.6, 14
••
CffAPTER 25 Bills and Wages
1. £11 32, £8_68 2. fj)_J6, £4 64 3. £ 12, £8
51. 8-4 x 10' 52. J s 1 x 1o' 53. 9 x 10 ' 54. 7 05 x l 0
55.
29. 7044x 10·• 30. 7_3x 10- 11
'"
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
0 Time m
•
7 5 x 10 4 x 10 684x 10-
d) 120kn1/h
1
400
"
d) I 0 k1n/h
c) the train stopped
' .
_500
Jill
'
46. 8892xl0'
2.
:
31. 79]x!0 1 32. 5 27 x !O 4 33. 8_06x!0
26. 9_07x 10- 1 27. 8.05 x 10-i 28. 8 808 x 10- 1
21. 22. 23. 24. 25.
11. 5.1 12. 0 009
'"
9. 6 90_ 6 9. 7 10. )5 )8, 55 6, 56 16. 0 9 /) 11. ) )"JI
14. J4 8
18. 281 6 19. 6 I
15. () 0078
20. lO_OO
13. 1 90
4
Sr( P) Mathematics 2A
EXERCISE 1j (p. 12)
This exercise is particulaily i1nponant wilh fullHe work in mind 1. 3
2. 8
3. 6
7. 0 8. 0
•- 8
5_ 7 6. 8
9. 0
10. 8
intended for use with a cak11la1or
1. 60000
5. 80000
2. 4000
6. 500 7. 50000 8. 4000
3. 4 OOOl~Xl 4. 600000
13. 14. 15. 16.
4700 57000 60000 890000
9. 700 000 10. 900 11. 30
0_008 46
0.876 5_84 78_) 46_8
17 12 km/h 18. 8 k 111/h
16. I JO k1n/h
20. "i m;s or 18 kllllh
EXERCISE 24e lnlended fm (Jl- 356} everyone
21 _ Sci rnph 22. )4 mph 23. 601nph 24. I OS 1nph
19_ !8 km/h
27. 80 km/h 28. 42~ k111/h
the above average only bu! can be U'ied for discussion \vith
17. 7000 18. 10000 19. 7JOOO 20. 440
24. 600
EXERCISE 24f Use
Numhcrs 7 to !() for discussion wilh all hut lhe above average_ In ques11on 10 a ruler can be used lo see how !he g1adien1s change
30. 000785 31. 7.51 32. 370
1. <1) i) 1215 ii) jJ,18 iii) 1445
33. 0.990
2. a) 40k111 3. a) Xkni
b) 1~ hours
42. 7000 43. 0 0709 44. 0 07
45. 1__,
so. 29
46_ 1.7
47. I J
51. 24 52. 0.23
48_ 13
53.
49. 14
54. 0.0004 l
b) 21 hours c) 17~k1n/h d) 21~ kin e) no b) JOJO c) 11-houts d) 6.4 krn/h e) 6 4 km
1 _ 100 2_ ]6 3. 0 35 4. 10 5_ 180000
6. 08 7. 0-48 8. J 6
9. I J 10. J 500000
1i) Zho11rs 121nin
40. "iOOO
5.
41. 37_9
11. 12. 13. 14. 15.
600 45 2 0_7 17
16. 0 001
17. 0 0056 18. 80 19. 90000 20.
!_)
a) i)
c) 80111ph
90k1n ii) )Olnn
h)
1)
c) 28km/h
yes
4l hours
d) 200 1niles frum A
b) )hours
f) no
n
e) noon
d) ?8krn
e) i) 42kn1
i1) 48 kin
6. a) i) 1309 ii) f'i09 b) 40rni!cs c) 20mph f)ll\4 7. a) 45 krn h) l ~hour"> c) JOrnph d) I hour c) 8m/s d) 801n e/ 8. a) 801n b) !Osec 9. a) 1) B ii) B h) i) 80 k1n/h ii) 64 krn/h c) j e) 58 1 kn1/h (co111111ng !he stop) 10. a) Rrniks b) 1 c) lhour d) !!hours g) the last one h) the firs! and second
0.0~6
Revise n1111fiplicatinn and divi:;ion hy deci1nals hefore working through this exercise. Allow sorue discretion in the nun1ber of sJ. accepted for the answer.
H hours
c) i) 11h111ns1i)
d) 64 kni/h
34. 54_0
35. 47 36. 0 006845 37. 600000 38. 500 39. 7 82
7. J knols
5. 75 km/h 6. ! 25~ kn1/h
3_ 7 1nph 4. 7 1nph
1. 9km/h 2. I01nph
21. 50000 22. 54000 23. 480
4. a) ii 125m1les i1) 17\miles 111) 60miles
EXERCISE 11 (p. 14)
31. 50 k mfh
29. 80 kin/h
30. QO kin/h
12. !Orn!
(p.356) 25. 26. 27. 28. 29.
13_ 80 kmih 14. 90 km/h 15. 64 km/h
25. "i!ikrn,'h 26. 4_, kn1/h
EXERCISE 1k Particulally i1npor1ant with fu111re work in mind_ N1unbers 41 to 50 a1e not
(p. 12)
91
Teacher's Nores
d) Hln1in
e) 13niiles
el 4'.i 1nph f) 31 mph 40s.ec f) ?m/s g) J\m/s hnut d) 1/ hour
e) 2~ ho111s
f) J_l n1ph
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
c) 'i6 mph d) .}61nph 4. a) 561niles b) 45minult's 5.a)i)08l0 ii)l~JO b)5h c)l!hours d)4km/h e)7hou1s 6. a) 80km/h. 1430 b) IOOkrn/h. I 154 c) al 1410_ 153 miles fron1 A d) 51 n11les
96
leacher·s Nores and Ans~vers
SJ (P) Mathematics 2A
21. lU
14.
22. () ]6
26. t:? 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 on page 15 is only an c;>;ampk and that 1hcic are many dif!e1en1 designs (p. 16) a) 2 miles
Tim~
b) 141n1les
'-
7 2. 1 3. ! 4. 8 5. 9
rn hours
08 55 02 S4 !9
6. 7 71 7. 7 49 8. 9 I\
9.
61 10. I )6
21. 172 15. a) 800 k111 16. a) 48 krn 17. a) I ?00 rniks 18. a) 90 kin
b) b) b) b)
19. a) 9 n1iles
b) !Soules
20. 4) 52.5 m
b)8915m
21. a) 32 miles
b) 38 1niks b) lj- kin
22. 23. 24. 25. 26.
a) 4 krn
26. J6 8 27. 19)0 28. J8 0
t:) S4 kin
1650 1niks 135 kn1
c) !Okin
41. o_ 1·21 42. () 0825
46. 1)4
51" 49 0
56. 9 83
47. \\ 8
52. 11100
57. () 691
43. 0 -~9 J 44. 0 103
48. 9 ! 7 49. 186
45. 0 !39
50. 957
53. 8 J.6 54. 2 28 55. 0 671
58. 0 742 59. 0 1?8 60. 10 300
65. 0 l6J 66. 0.0201 67. 0000123 68. 611
69. 0 000 000 096 I
72. 16 7 73. 0 000 14 74. I J 4
b) 4185miks
61. 6.3·10
a) 30
b) 11
62 0 006 08
6.~
36. 37. 38. 39. 40.
0 0481 I 79 0 0051 -197 0 548
~
b) 850n1
1. a) 2 hours 2. a) 5 hours
b) 3 hou1s
3. a) ~hour
b) 11 hours
4. a) 2} hours
b) 'i} houis
EXERCISE 1n
1.
5. a) I~ hou1 s
h) '}hou1s
(p. 17)
2. l/h)
4. \ 6·l x !0 5. ) 07 x 10
6. a) i101lfS 7. al 25 sec
b) 4~ hours
3
6. 60000
b)
I!
8. a) 24 min 9. ;i) ?J6ho11rs = 9days 10. ") 11 ho1J!S 11. a) 2} hours 12. a)~ hour
3. 60mph
20. 6.65
35. 4
b) /85rni!es
2. 60 kmlh
l S4 I 44
30. 14400
a) J7 mites a) 500 m a) 17551niles
1. XO kin/h
2 94
16. 11JO 17. 8170 18. 6580 19. 15 5
29. I lSO
64. 484 000
EXERCISE 24d (p. 352)
2 70 0 0196 0 0549 526
I 10
24. ! I 70 25. ! :: 600
63. 34. 8 EXERCISE 24c (p. 351)
3 80
31. 32. 33. 34.
22. !4 7 23. ! 1 2
I IOOkm 84 km
J
11. 12. 13. 14. 15.
4. 120 n1ph 5. 201n!s 6. 45m/s
J! hours
b) 200sec b) 54 min b) 5l days b) hours b) 5 hours 20 rmn
EXERCISE 1p (p. 18)
21
b)
70. '1YJO 71. 0 !74
J! huuis
7. 50 krn/h 8. 65 k111/h 9. } ') tt)ph
10. 8 mph
11. l6 lll,'S 12. I 7 1n/s
EXERCISE lq (p. 18)
'
j(,
4.
6. 46000
'
2. la
4. S108xl0 5. 10000
3.
6. 0 0508
1.
,
, s. "6 s x 1o~
1. 216
2. 3.
,
4
7. 0 0614
8. 3 71 9. 2 88
7. 2! 'iOO 8. !JSO 9. 0 699
,
7. 9
8. 9 89 9. 4 JO
6
ST(P) A1alhernarics 2A
CHAPTER 2
I eacher·s Notes and Answers
Prnbability
11.
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
ln several questions 1e!'erence is made lo sets of integers or whole numbers these do not include zero. lune
!>l
ho11rs
b) 111 km EXERCISE 2a (p. 19}
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!
12.
6. 4. (Ip. IOp. 20p. \Opi
J
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}
EXERCISE 2b (p. 20}
:!_:
0
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
'
10
'
4.
7.
~-!
s.
8.
t
9.
1'1
6.
3.
1io
h) 12~ kn1
a) 7~ km
used for d1scuss1on (ahei the coruhtions)
1. 2.
,J
13.
EXERCISE 2c
Nurnbers 9 10 15 rcq11tre an above average unde1s1anding of language_ Use
(p. 22)
1he1n for discussion w1!h everyone bu! allow only the ahove average to try then1 on their own
-~ 160
s:
lc
120
u
c
80
1. 5
6. 4)
2.
7. 8.
a)
9.
a)
3. !6 4. 1
5.
10
ls
a) ~
!
b) ~-
c)
d)
h) ~
c)
d)
b)\
c)
!
c)
b)
ib '
" d) ~
6 40
b} 44 rnilcs
() I
une
10
1-ioms
95
94
Teacher ·s Nares and AnsH'ers
S f(P) Mat11ernat1cs 2A
5.
10.
8.
,;
]{llJ
e "
" g
'l
j
u·+
I OU
J
l
,,'
12. 46 ' 13. a)
.!!
e 50
100
"
EXERCISE 2d
~"
(p.24)
g
0
lime in hmHS
1l Jim<'
Ill
"
14. l6 b) ~
11. al
homs
c)
15. 4\ '
l
16. a) j~
"
36
b)
t:}
b)
1
!
c)
'
i
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 6.
7. 8. 9. 10. 11.
9.
CCI lau1
0. vutually 1n1pr>ss1bk !. I! !llU~l be 0 aim PSI 1rnpnss1b!e
L 1ld} week \ 1nlikdy
you will wa!d1 IV ll11s wn:\,. vnu will he
;i
111ill1unanc
!l
you will get 1na1hs humcwofl.; will snow Ill Brna1n on nut! Slln
da:
EXERCISE 2e
(p. 25)
Nu1nbers lO lo !4 can be used Im '11sn1ss1011 with evnyon.:
1
2. I 11lle in
~cc
lime"' hours
.,
""
3. ~A
EXERCISE 2f (p. 27)
7. ~~
5.
10
8.
6.
i
11. a I '
tiJ
rU
cl
12.
a} i"l
b)
1
c)
!_}
b)
13. o) 14. a)
.
4.
Can ht>
"'
!!
h)
i1 Hi "
~JI
9.
•O
10.
.!_Q
"
di tli
i /-J
c)
-ro'
<)
n "
d)
r1
d)
d) ()
OllHIH:d
1.
..,, .,
•
()
I l
()
--~·----
(J
(C)
(l)
(( )
(_))
i("J
\_))
10.
(!
t Cl Cl)
((_)
( l)
(()
UI
{()
()
i (_) ())
IU
())
(()_ {_))
( ()
(_))
1• OI
1•.
• ,. ,. •
l 1m« •n
hour~
le
())
{_))
1•
(J)
())
• •
(().
10
•
{(__).
•
1• •1
1•
•
llil
1•
•
.,
8
Jeache1 ·s Nor es and Answers
ST(P) Mathematics 2A [)ice
2.
CHAPTER 24 Travel Graphs 5
4
3
2
------------
H
(II. 1)
(H. 2)
(T. 1)
er. 21
\Op
T
(H, J) (T. 3)
·-~·-
6 Al! ahihly groups find this 111teresllng
--~·-~------
(11. 4)
(11. 5)
(ll. 6)
(T. 4)
(T, 5)
(T. 6)
EXERCISE 24a (p. 345)
Isl bag
3.
y
R
R
B
- - - - - - - - - - - - - -----------R
(R. R)
(R. R)
(R. Y)
(R. B)
y
(Y. R)
(Y. R)
(Y. Y)
(Y.
y
(Y, R)
(Y. R)
(Y.
(B. R)
(9. R)
1. a) 90km 2. o) 146rniles
b) ) hours h) ) 2 hours
r) 4) km
3. 4.
a) 10 krn
c) !Okm
5. 6. 7. 8.
<) j()
h) 3 hours h) 6sec b) 8 sec h) 11 ho111s h) l hnu1s bl ?hours
!6111
a)
Ill
•1 107km <) l'iOmiles
') 50 nnks
9. a1 20 rn 10. 'I \Jm
C)
24 Ill
c) ! 2Sm c) 1 J 4 kn1
c) 7'i miles c) 2 n11les c) 4 Ill d lm
~ec
hi I I sec
B)
2nd hag
EXERCISE 24b !"he scales
B
b) 'i
c) 28 ni1ks
Yi
(Y. ll)
(B. Y)
(B. B)
(p. 349)
111
some of these answers have been halved
3.
1.
]00
Ml E
'
40
<
- !00
0
IS!
4.
"
20
c_';:
'
3
( l. 1)
(1. 2)
( 1. ll
------------------
2nd spin
"
spin
5
0
l nnl' rn hu""
2
(2.
II
(2. 2)
{2. J)
3
(3. 1)
(l. 2)
(l. 3)
JOU
l HH~ !!l hnnt\
Penc-~I
5.
Red
Green
Yellow
-------------------- -------· ---------..------·Round
0 n n
Square
Round. Red
Square. Red
Roun
Square Clreen
Round, Yellow
Square. Yellow
' 0
:no 150
0 0
"
"'
4.
2.
f"riangular
rriangular. Red
Triangular (lreen
Triangular. Yellow
6
>00 50
EXERCISE 2g (p. 29)
()1ni1 this exercise if Exercise 2f was no1 covered 1. a) ~
0 l ulw 111 hn11<>
Tim<' in houis
97
leck:her ·s Notes and Answers
ST(P} Mathe1narics 21\
23. 183'/ rniles 24. 2583 kin
27. 114 28. £I 10
25. 72 nun 26. 131 6hours
30. 9 35. 36. 37. 38.
31. 61, 21
EXERCISE 23c (p. 342)
1. 2. 3. 4.
'
68; reduces it to 67 158cin; ii;:icreases it to 159cm
n
b) )~
i!t:
h) ~
I 8
7. I 8. 8
1. 5 Z. 41 3. 17
3. a) 45
5. a) 28 6. 77, 77, 73 7. a) I 57 Cfll 8. a) 54
-
7. 98 8. 36
6. 12
9. I 885
b) 157 Clll
b)
\1
c) Zl c) 69 c) 45
d)
c) J2 c) 27
dJ 80
c) IY7cn1 c) 12
9. 83. 84, 81 5 10. a) 0
b) 0
r
er. HJ
(f, I)
6.
?od
c) 1.5
16
d) 16 d) 7
·I
al
a)
A
d) 54
4
•
(L I)
(I. • l
(I
JJ
(I. 4)
(I. • I
(I. 6)
(211
U.•I
I' Ji
(14)
(1.
•I
('. 6)
(1
I)
(l.
•J
(J. 1)
(1. 4)
(1. ii)
(1. 6)
14
I)
(4.
el
(4, 3)
(4 ·1)
(4.
•>
(4 6)
(\
I)
(5_.)
{ ~- i
n.
4)
(5.
•>
(\ 6)
(6, I)
(6. • l
(6. 1)
{6. 4)
(6.
•>
(6. 6)
h) jli'
c)
,,'
I
cl) l'l'
"
Fusi bag
1.
10 p
d) 6 cl) 10
•
---
dice
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?
4. a) ·1 _1
(11.
9. 155 cm
4. 16 5. 3_2
b) 21 b) 66, 67 b) 43 b) ll b) 27
(ll, II)
10. ll. J 11. 36. 6
6
a) 71
n
I! Ip coin
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 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 dividing the 1nixture into 20 equal portions
1. a) 23
r
I!
l
2.
i
5 p coin
I 364 kg
5. 5.9 6. 26-4
56
d)
5.
43. 2652
12 9
c) r~
6-1610, 12 722. 8294
42. 285 Clll
39. 160_6crn 40. 55_6 kg 41. 26
EXERCISE 23b (p.340)
a)
•• 'ol
29. 92
32. 23J. 193 33. 106, 238 34. 10_5 hours, ]~ hours
z. 3.
10 p
10 p
50 p
50 p
JO p (I Op, I Op)
(!Op. I Op)
{!Op, !Op)
(!Op.50p)
(!Op. 50p
50 p (50p, !Op)
{'>Op, I Op)
(50p, !Op)
(SOp, SOp)
(50p.SOp
2nd hag
JO
ST(P) Mathernatics 2A
Teacher ·s Nores and Answers
8.
First shelf Story
Story
Te:» I
rext
Tex I
e!c
------~···
n
St or)
(S, S)
(S, S)
(S,
S!ory
(S. SJ
(S, S)
(S. T)
(S, T)
(S.
n
S1ory
(S, SJ
(S, S)
IS. T)
(S, 1)
(S,
n
rexl
(T. S)
(T. S)
(T, T)
(f. T)
IT.
l)
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 c) ! hour 49 minutes 5. constant speed a) 825 km b) ?475 kn1 d) 4 hours J.1 minutes
211d shelf
o) i~
b) n,'
9. o)
b)
fa
c)
i
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,
··---·(S. T) 15. I')
·-~·----·--
~)
d)
6. a) )4''.~. 77~,~ 7. a) £43 75 8. a) J4 mpg 9. a) 19m/s
1
b) _12~ . .S2
bl f84
c) f! !7 2)
d) £! 14 \0
b) 22 km/{
c) 64 1npg
b) 166kin/h
c) 6)kn1,lli
e) £2)1_4_)
d) 8 kn1// (lo nearest unit) d) 4iJm/s (to nearest unit)
10. 9 5cm. 5 Bern, 6 5crn. 9 2cm
EXERCISE 2h Can be done earl!e1 111 the chapter. e.g. afl<'r Exercise le. At this ~tage It 1s (p. 31) nnt wise 10 plau:- too niuch en1phasis on !he difference be1ween !heorelica\ EXERCISE 22b (p, 329)
and experimenla\ probability
4. 5. 6. 8.
CHAPTER 3
,'''
16. 50
17. About 500 heads It is unlikely,
;
hnl possihle, that you will get 1000 heads or JOO() lails
~
10. JO
18. Any nu1nber of heads from 0 lo
12. Roughly rectang11lar 13. Ten throws is too few 15, No. All the same. number.
19. Very unlikely
1. a) a) 3. a) 4. a) c) 5. a)
z.
!190g h) ?mm 1) B~s i1) l"i~s b) 1) lJ4 kn1/h i1) !91 kn1/h i) '05g 1i) 9\0g b) t) 6'idays ti) !"iOdays c) 240g 84111/s when t = 4)'i b) i) Rlm/s 11) 6! 5111/s
d) 10g
2.2)s and 6 6s
19 knots. i !6 40 17 0.1
b) 14 5 knots and 2,1 2 knots
c) i) £ 17.57
ii) f
JO_
1i) l ~40 g bl i) 3 82 crn iil 5 Scm 6. a) t) jl\6g 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
Constntctions Revision nf the facts learned in Book lA is nece:<>sary
EXERCISE 3a (p. 36)
Revises the geonietry covered in Book IA.
1. 60" 2. 75" 3. JOO" 4. I JO" 5. d= 60",
{)o 1101 progress 100 quickly; thlC IS a frequently !l\ISlllldCfSIO()d IO{llC. rry IO keep dose lo the pupils· experience
6. 70°
e~
120"
7. 8.
p ~ I JO", J =
70",
9,
I~
60".
10. d = 30",
q I= 111
=
= 5ft' I Ill° 100°,
e = 75'',
"= 20~ 1~
105"'
EXERCISE 23a I Jse 1he restihs of Nurnbers I! lo ?.O lo d1sn1>-s the interpre!ation of the n1ean in each case
(p. 334) EXERCISE 3b (p. 38)
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
1. 8 2. 7
4. 29 5. 16
3. II
6. 28
13. 63 14. 96 15. 16.5
16. 6.\ 17. 74 18. I .l'J
ls
7.
10.
8. 40
11. \0 12. 0 61
..
6 2
19. 0 8'l'i
20. \ 8
21. 2 rn1n 22. 86 kg, 81 kg
90
l&dcher·s No1es and Ans~vers
ST(P) Mart1e1natics 2A
26. IJ On1 27. 11 Ocm
24. 2-6lcn1 25. 35_0cn1
22. 8 64cm 23. 17-4n1
3. I JO min 4. 7.Scrn
EXERCISE 21c 1. JOnn 2. !8-4c1n (p. 312)
EXERCISE Jc (p. 40)
11. 90~ 12. 45" 14. they are parallel
EXERCISE 3d
N11mbe1s 1 lo 9 can be uscJ
2~ CUI
5. 26 m
7.
6. 31 Ocni
8. I] 8 CHl
(p. 41)
EXERCISE 21d 1. J!cn1 (p. 313) 5. 4_90C!ll 6. 2.65nn
7. l.73rn EXERCISE 21 e (p. 315)
EXERCISE 21f (p. 317)
EXERCISE 21g (p. 319)
2. 48cm
3. 14 Clll
8. 4 ':18 cm 9. 7.48 m 10. 7.94 cm
11. 6 24 CHI 12. 16nn
4. 10111
13.671011 14_ 117nn
!01
d1scus$ion
6.
2. they are equal 3. AB and Cl) 4. coincidcn!
the 1n1dpm111 of AB the nudpmni of CD 8. 90" 9. each is 9()C 7.
5. co1nc1den1
" "
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
1. 6.71 cm 2. 8_67 CTTI 3. )_'j CIT\
4. )_66011 5. II 5un
7. 146nn 8. 8 15 Ill 9. 88_5 cm
10. 265cm 11. 9 )J cm 12. } 'J CHI
1. ll.5cm
2. !Onn
••
5. 11.J CUI
4. I he pnpend1cular biset.:101 ol I l'VI
1. l 71 cm
3. J0.4cu1
5. The perpendicular biseclor of PR does not pass through Q 6. fhe pnpendiuda1 b1secior ol ihe cho1d AB which passes through ll
2. 4.69cm
4.
••
4_25 cm
9
Clli
I0.2
13- 6 8111
EXERCISE 3e (p. 43)
14. 89 6crn 15. J51rn
3. 150crn. JOcrn
5. 12 7crn
Numbers 8 to 14 invohe co11s!fuc11ng urcumnrcles and 1nc11ck:. !'hey a kngthy and. Im inn1ck~ 111 parucular. 1he construc111 drawing 1s accu1ale Ahle duldren can cope. bu! u
suaightforwa1d bul works only if ihe d1sne1ion w11h !he Book JA and of the
pas~cs
through N
centre C
C!ll
6. 743111 7. 83 I rn 8. I 6Jm
EXERCISE 21h 1. 2 60n1 2. 781nn (p. 320) 3. 14 I cm 4. 105 IH 5. 7 55111
others fhe foima! consl!1JClion of a nrcumcirde is incirdc in Book 4A
EXERCISE 31
Use firrn cartodge papei
(p.45)
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
9. 14._I nn
If used lor C!111strnas decorauons. ellhtr colou1 wn
Jogethcr
10. 6_22 kni
EXERCISE 21i ()roil if lligonomelry has no! been taughl (p. 322)
1. 71
14nn~
4) 6". 4)6°,888c
2. 265111,414" 3. 18 9 kin, 058"
••
164crn, 66_6-', 11 -1 4'"
5. ,O 6rn, 12
601
6. a) 27_2k1n b) 7. !79cm. 20cin
54~.
306",
126~
CHAPTER 4
8. 7.81
J ntroducing Percentages CalculaLors are not necessa1y but 1he weakt1 pupils 1nay benefit front usir
9. 7 07 10. 12.6
lhe111_
EXERCISE 4a (p. 49)
Emphasise 1he conunon result~- c_g farmhar aillL 1f necessary, karncd
8.
1.
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
_)()"ti"--'-~
15.
1"0 ' l • ~i
0 5 These should be niad
"
22. :iO 23. lb
'
"'
16.
3.
9. Hi 10. n "
4.
\~
11.
"
18.
1{i\i
12. 13.
19. 20.
f)
.
25. 26. 27.
14.
21. 40'
28.
2.
5.
6. 7.
'
'"
"
j{i{j
17.
"
24. }~
rA
"'
12
S r(P) Mathen1at1cs }A
leacher s Noles aod Answers
29. 0 47
34. 0 18
39. 0 92
44. () 08
30. O I 1
35. 0}
40. 0 6'1
45.
EXERCISE 20h Ihe
n 01
(p. 305)
31. 0 05-5
36. 062J
41. I 1
46. I 8
32. I 45
37. J 5
42. ! JI
47. 0053
33. 0 58_1
38. 0 <187
43. 0 857
48. 0
5,~
1nore
ahk cl1ildren may be 1111en.·s1ed
1. 50 ~;, 2. 70 /~
6.
6S';-~
8.
3.
4. JJ! ·;;,
!'";"!
"
11.
75~-~
16.
60~~
7. IS';{,
12.
45·;~
17.
35~-~
16''-~
13.
-
9. J7.S'%,
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 )
I
5. 52.5 ~~
10. 18t '.'{,
50~~
18. 124 ';~
19. 87~ ·:-~
15. 266t%
20.
31.
15''.~
36. 16 ~..
27. 4~-~
32.
74~,,
37. 16".;,
23. 8 .J ·;;
28. '15 ·;~,
33. 125'\,
26.
1. 6 10
7. 8 19 22. 374. 250_ 250. 8'19
38. IJ9~,,
24. 172 /;,
29. 264 °',,
34. J41 ''.,,
39. 615/;,
25. 62.5 /~
30. 84 5 ·;~
35. I I'\
40. IX 25 ""
EXERCISE 4c
Questions _) to
relationships between fractions, percent<1ges and decimals
EXERCISE 20i
b) ~~ b) 0_68
40~~
b) 85'";,
a) ?0~- 0
b) 61 ~-~
a) i~
2.
a)
3. a)
4.
10 provide a very convenient way of confirn1ing !he
0-44
1.
Fraclion
14. 4 36
21. I 0 1
19 . ., 81
268. 118
)71_ 2(M
6•1 'i_ 12?. 6?9
1 _ o lOS 2. 0 h48 3. () 110
199. 27 )_ 275
15. 0 208
8. 0 )-77 9. 0 167
16. 0 0980 17. 0 9!2
-No
6. 0 701
13. 0417
20. 0 866
7. 0 775
14. {) 811
21. 000854
18_ 0 )66
0
EXERCISE 20j (p. 306)
d) I JR", Percentage
Decimal 0 75 OK
60~,,
06
7.
70"-~
0_7
8.
55 ~~
0 'IS
9. 10.
44'\
0 44
32 '/~
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. 9.]2 CITI 2. 11 Onn 3. 22 4 Ill
5. 0 _1 4)111 6. J 89cm
4. 5h6rn
8. 290 kin
J. )7 4
9. O 09.~2 kn1
10.768nn 11. I 5 S n1
!JHll
12_ 7R!cm
EXERCISE 21a So1ne histoiical backg1ound would in1erest most child1en (p. 307) 4. \Jcrn 1. !Ocm 5. I! 4nn 2. 11.7c1n 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
4. 92·;;,
j~
5. 88 '.\
J6~{
6. I:?~~
10. J8 ~; 11. ] ~~
20. 1700
d}0.165
80".,,
9. 10~-~
18. 8\ l
12. 7 62 13. 4 90
19_ 0 _1_28
5.
2. I J
11. Ll\
12. 0 4!6
6.
3.
15. I 0 I 16. fA.! 17. 11 0
5.00IH:I
75 ~~
1. 52 ~~
tu l sf
10.00)21 11. O'i48
d) 11 J!, "
".,
CO!!CC!
4. 0 748
d) c) 12~
447
8. } 19 9. 25_ 5 10. 8 06
2750. 64.2. 27 0. J 9L I 92. 6 28. 19 'J
(p. 306)
(p. 51)
= JiO--""
2. 4 45 3. 20 7 4. 6'i 0 5. 'J f-i6 6. 1. 11
160~~
22. 22 ' .<,
21.
90~-~
140~{,
14. 62~/~
manual rneihods for fin(hng
111
square 1001s lle1e ts a !n1d tkscrip11011 ot one such 1ne:!hod
20-'-441 = 4474
EXERCISE 4b (p. 50)
89
7. 4J '.:~
EXERCISE 21b (p. 308)
8. 68 /~
1. !Ocm 2. I 3 CUI 3. 20un
11. J_6lnn
12. 252 13. 14()() 14.a)l~.:_
h)IO/~
c)66~~
d)22~.:_
16. 5_40c1n 17. 121 cn1
7. I I 7cm
4. 9.85 cm 5. !08cm 6. 10_6nn 12. ll.4cn1
8. !26cn1
13. 6_40m
18. ] 11 crn
19. 9.57cn1
9. 12_1
CIH
10. I0-4rm
14. !l-4m 20. 44 7 HI 21. 0_361cin
15. 12.2cn;
BB
!edcher·s Notes and An.,;vvers
SJ (P) Mathernarics 2A
17. 51 98 18. I 34 6 19. 58080
21. 07726 22. 0001110 23. 5242
20.
24. 1419
I)
6790
25. 0 0601 26. 0 005 184 27. 201 6 28. 20160
29. 0 020 16 30. 94 67 31. 1912 32. 0 005 285
EXERCISE 4e
Although rtearly all the ques!Jons give nuinheis wllli units, none of the
(p. 53)
answers involve unHs
1. :is~ 0
EXERCISE 20c (p. 301)
1. 55696 2. 212521 3. 27 667 600
4. 17 305600 5. 1049_76 6. 103041
EXERCISE 20d 1. 5 76cn1 2 (p. 302) 2. 92.2 Hli 3. IOSOnn 2
EXERCISE 20e Po nol use cak11la1ors_ (p. 302}
7. 628 849 8. 38937600 9. 2 044 900
2. 60 ~-~ 9. 10 Go
10. 4078 56 11. 152881 12. 21996100
4. Ll2 rn 1 5. 296cin 2
7. 0_003 84 rn 1
6. 2700nun 1
9. 00961crn"
D1st:uss1on ol ·-wha1 has happened 10 lhe un11.;· rs
wo11hw!11k In ;,orne ques1ions 11 1;. necessary to make the u1u1s c:o1npa1ible
34. c) 30. 70. 164. 185
33. c) 4 8, 3.2, 9.6, 7_3
3. Ll~ ~-~ 4. JJ~ ~~
50"-~
12.
17. :Z5 '.'.~
20. 40 ~G 21. 60'.'-;,
18. l7f 0 .,, 19. 20''.-0
13_
11. )0 ""
10. ?0°,:
22. 2:5
5. 7) '.::, 6_ 60~-;; ?tHl~u
7. 15 8. 25
°,, ·:~
15. IO":,
14_ 62~ ''.~
16. 66j ~~
23. 1 !
25.
u"
12·;~
24_ } l_I\ ~;,
26. 41
35. I 3~ ~., 36. )! "' _,,,
';.--~
"-~
8. I05000km 2 Z7. ,10'.'-~
30. b()~ ~-~
33. ) l)'
28. 65 °; 29. 1 )~ ''.~
31_ 1~~" 32. J6'_'.;,
3-4. ·I'.'-;,
40. !5 ''.., 41. 400~;.
1.
4. 9 5. 10
7. 7 8. 8
37.046''.,,
2. 3.
6. 6
9. I
39. 65
38. ')00 ~~ ~/;,
42.
10. 90
13. 70
16. 20
14. JOU
17. lO
EXERCISE 4f
1. 48
4. 286 krn
12. 0 8
15. 0.2
18. JOO
(p. 55}
2. 96g
5. 16p 6. ] 08 kg
19. ()_] 20. () 4
21. 0_02 22. 500
23. 2000 24. 0_004
11.25?m 12. 14-'1 in 1 13. 3_13
45. 666~ ;;, 46. 8 ~'~
!O",~
11. 0. 9
3. 55 5cn1
43~
44. 2) •;;
~i
14. 198 kg
15. I 44 1n
7. 252 B. 989 g
9.
'~
7]
Ill
10 . .206un 2
17. 0 34km 18. I 61!tres
19. I. 75 20. 198111
2:9_ !4 p 30. f 5 \ 'l] 31. ·18p
33.2Jrn 34. i 10 35. 2 kg 36. 14 llHTl
16. £1 ){)
EXERCISE 20f Do not use calculators (p. 303}
1. 4 2. J 3. 6 4. 6
5.
EXERCISE 20g no (p.304}
6. l --
11. 0 4-
7. 9.---8. 4. - -9. 2_ 10. 0.2- -
12. 9. 13. l
21. 90 _i; 22. 1.94 min
23. 18crn 24. 9m 1
14. 0.7--15. 2. EXERCISE 4g (p. 56)
nol USC
calcuh1101s
1. 40 ~~ 2. 70 ~--~
25. 320ni2 26_ 45 knl 27. 5 kin 28. 149un~
6. JOO 7. 50
11. 600 12. 10
3. )()
8. 200
4. 80
9. 60
5. 20
10. JOO
13. 20 14. 200 15 . .?000
16. 60
20. 3
17. 20
21.
18. 20
22. JO
19. 6
23. 60
24. 6 25. 10
26. J 27. 200
4.
6. 75 "-~
11.a)46~~-~
EXERCISE 4h (p. 57)
9. 65
1\J'_'.-~
13. a) I 2
14. a) _\6
h) ?04
1. a) ~
2. a)
60~1~
3. 8 ~~
~--;,
10. !960 b) 53~ ~< b) ?8 b) 18
12. a) )2
32. 6g 7' 75 '.'.~ 8. 66{- '>~
5. 30'\
3. 20 ~-~
1. 30 2. :100
13
b) ~~ b) 78 ~~
c-)
15. 5760
16. 78
1'7.£6240 18. l ! l
1b
c)!lt~-~
4. ! 2J ~~ 5. )4
Ill
6. 97 ~--~
14
ST (P) Marhema11cs 2A
EXERCISE 4i (p. 58)
l"eache1 ·s Noles and Answers
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
h) 0 }6
2. a) 62~~-~
b) I l 3 '/~
81
EXERCISE 19g C<1n be used for discussion (p. 294)
3. 51 c) 250~~
3. 12}~-~
4. 289 rn'
7. 48.2", 8"L6" 8. A= 65-4", 65-4", 49.2'' 9. l !R''
1. 48_6" 2. 5_}j COl l~
4. 53_ 1~
10. 9.59"
5. I 69 m
11.574• 12. 2 87"
6. 7 45
Clll
5. £840
EXERCISE 4j (p. 58)
1. a) 12~ 0 2. a) 28.6~~'
bl b)
3.
b) 0 125
0
17~ ,,~
c) 50~~
27_9/~
c) 122/~
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. 90p
2.a)08
b)08;90"
5. 54
3. O.J
a) '
Answers given fo1 1neas11re1nen1s are calculated and lhis accuracy is not anainable fro1n d1a\vings, so allow for this when deciding on acceptable accuracy
EXERCISE Sa (p. 59)
11. 5001n
(p. 63)
EXERCISE 19i
1.09925 2. 585°
3. 0 8829 4. JO_{)"
5. 6 25 cm
(p. 297}
EXERCISE 19j (p. 298)
1. 0906
2. 68.6''
3. I 00
5. 12.J crn
6. lll O'
7. 7 14 cn1
4. 21 4"
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
CHAPTER 20 Squares and Squares Roots EXERCISE 20a Do noi use calculators (p. 299} 1. 9 2. 25 J_ 81
4.
1. ?1m
3_ 50m
2. ?: ?: Ill
4.
5_ 70m 6. J2 Ill
7. S'lm
9. 9m
8. "iH rn
10. '9lm
13_ 0 000016
8. 0 0004
14.
16. 900 17. 10000
20. 64 21. 1600
24. 0 0009 25. 8100
18. 16
22. I 000000 23. 4900
26. 0 0064
15. 0 0009
-~X rn
11. IK01n 12. _91 rn
1. 86111
2. 77 Ill
3. 71
5. _119m
7. I I~ rn
8.
m
9::'.~
rn
9. :'i::'.8m
6. 8_1 4 rn 12. X660m 13. HI
14. I J4 n1 15. sx_:i rn
27. 40000
4. Xl m
(p. 65)
10. '14 rn 11. I I 70m
11. 0 09 12. 4 000000
6. 2500 7. 90000 9. 250000 10. JOO
900 5. {) 16
19. 0 09
EXERCISE Sc
7. 6.75 cm
6. 5.i /"
Mosl questions have- the scale given bul Nun1hcrs 6 10 10 do 1101 fhere is a short no1e n1 the C;>.:e1cisc
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
EXERCISE Sb
4. () 8 5. 45'', isosceles,
16. "'80111
EXERCISE 20b \Vi1h very able children_ Nurnbcr 28 can be expanded and much more made (p. 300) of ii
1. 2. 3. 4.
60 84 1444
5. 0 0256
62 7J
6. 0001024 7. ?J1J
0 1681
8. 117 7
9. 16_11
13. I 040
10. 96 {),j 11. 146 4 12. 8 644
14. 185 0 15_ ?:89 16. 1.232
86
ST(P) Matheniatics 2A
Teac·her·s Noles and AnSl-Vers
EXERCISE 19c 1. () 515 (p. 285}
9. 0.954 10. 0 904
5. 0 498 6. 0391 7. 0.139
2. 0 669
3. 0 998 4. 0_708
EXERCISE Sd Explain lhe meaning of con1pass pornls (can be confused wirh the point uf ;; (p. 68)
11. 0_070 12. 0.985
8. -0.971
13. 642" 14. 24 6°
18. 194° 19. 34 9°
23. 89.3°
15. 44.4" 16. 45.6° 17. 75.J"
20. 55.5° 21. 76.1" 22. 20.3°
25. 51. J" 26. 818° 27. 32 5°
pair of con1passes) 1.
24. 424°
2.
6. 7 nn
EXERCISE 19d 1. 8.48 cm (p. 286}
7. 3.08 Cill 8. 3.22 cm 9. 2. 78 cm 10. 0.799crn
2. 2 68 Clll
3. 5.07 cin 4. 3.75crn 5. 10.2cm
14. 38 9° 15. 329°. 16. 600°
11. 53 I" 12. 41.4" 13. 38 7"
17. 41.4"
19. 66.4" 20. 56.9"
18. 63.J"
••
JY' .f~
3.
JO() 7.
...
320~
13. 81
9~.
2.44
6. cos M 31-0~,
CO\,
48_6°, 33_1", 4.90 Clll, 6-43 Clll,
14. 36 9°
17. 610°
15. 49 5" 16. 41.8°
18. 41.4'
19. 32 6°
59.fJ", 68 O" 0_647 Cnl, 30.9
Clll,
20. 3 06cn1 21. 32 7nn 22. ()_282 Clll
J 3_9
/
a.
N
rn·
A
10
M
10. Siil N 11. tan x 12. cos F
""
~)
/\
N
useful: Some old hands can always have tickels on application!
7. 1an A 8. E 9. cos p
N
1
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
4. sin p 5. tan X
N
r
~-
1. tan A 2. cos A 3. Sin Q
](>()"
•• r
COl
/
N
.)
!R0°
9.
23. I 09cm 24. 2_37cn1
25 . .320c1n
s
ty (;
EXERCISE 19f (p. 292)
4. 7.61 cm 5. 35_3 cm 6. 59". l66cn1
1. 44-4". 45.6°
2. 4_50crn 3. 71.9'', 18_ I~
7. 12.2cn1 8. 15_9m
••
I J 4 rn
10. 41.8''
5.
N
H
11. 45 6'' 12. BC · - l 69cm
13. BC
1.95 Cfll,
14. 66.4'' 15. ;; '"" 52.I~,
f
c -·
~
72
17 9Q
16. 17. 18. 19. 20.
1h
5 56 crn S2 .tl" 5 5 2'" ;; 54·' (~ - 36" AB= 17.0cn1, RC
10.
N
') ""' 270:')
~
~
I0 6cn1
----
1fi
ST(P) IV1alhernatics 2A
11.
l"ear.·/1er ·s Notes and AnSJNers N
16.
N
~0
A
11. ll 5nn·1
13. 690 nn 3
12. 450cm 1
14. 614 Cll\J
15. 864 cm 1 16. 720cn1 3
17. 'l_ 184 ml
18. 11.6 ml
1 19. I J44 nn
20. 624n1 1
EXERCISE 18c Ask for aciual nb1ects !hat are cylinde1s An interes11ng discussion point. why arc cylinders. ra! her than ct1bo1ds, used for canned soup. baked beans etc_? (p. 279) 6. 15_ J 1nl 16. 2810cm 3 1. 126cm' 11. _l22cm 1
A
2. 11 3 cn1·1 3. }14 CJTil 4. 59 4 cm-1
II
12.
9. 2'100nn 3 10. 2880 CJTI)
7. 8. 9. 10.
S. 1 !4cm 3
N
17.
8 ~)
37.7 nn-1 50. 9 crnJ 4520cni 1
12. 13. 14. 15.
!J90nn 1
1
17. 941 rnrn 3
J_Hlcrnl 652 cm'
18. 82S cm 3 19. i.60rnJ 20. 44 Ocn1·1
407
Ull
70800cn1 1
N
EXERCIS.E 18d The pupils c;in be asked to dcsuibe wtlill lhese C"ould be sections of
(p. 280)
r
1. IOIOcrn
_1
2. 402cm 3
140•
3. 34 S crn·1
5. 628 crn 1
4. 204crn 1
6. ll60cn1 1
CHAPTER 19 Sine and Cosine of an Angle 13.
=""-~"'~..=====
()p1ional at this stage and omit if Chapler 16 was not covered. This work is
18.
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
14.
19.
t:J"
,v~ 20.
EXERCISE 19a Sorne of these can he done 01ally lo de1nonsfrate the use of a calculator. (p. 281) 16. 4Jr 6. 0.951 1. 0 4 38 11. 56 5" 17. 40.3" 7. 0 289 12. 24 4" 2. 0 995 18. 20 9" 8. 0 07) 13. ]9_ 1" 3. 0 419 19. 25.3" 9. 0 886 14. 44 7'' 4. 0 601 20. 15 I" 10. 0 946 15. 69 6'' S. 0 981
rn· EXERCISE 19b 1. 8_8J Clll 2. 6 11 crn (p. 282) 3. I 95cn1
4.
1.0'/ cm
5. 6 02cm
6. 1 68 Clll
11. 44_4''
7. 2-61cnl 8. 2 51 cm 9. 9.54 cni 10. 4 85 Cfll
12. 236°
15. 21. 2.06cin
22. 6_64cn1 2J. /\ ~ 36 9". 24. 28.2" 25. J 72 CTII
f
53. I"
13. _36_9"
14. 51 1" 15.
23.6~
16. 33-4" 17. 220" 18. 30" 19. 42.1° 20. 45.6°
84
ST(P} A,ta1hema1ics 2A
4.
Teacl1er's Nares ar1
Stall
4. SI m
2. 161 In
EXERCISE 5e (p. 70)
1. 87
EXERCISE 51 (p. 71)
1. 860crn
in
2.
••
~ 17°
I )0 m
tower
3.
N
5.
No
numhcr/
'/
-]-
)0!)
Yes
...•
Write dnwn e value ol
l
-f~
(Sior)
EXERCISE Sg (p. 72)
2.
1. 94 m
3.
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 5. 1600 1nn1J 6. 58 'i c1n 3 7. 403 2 mm 3
8. A9.68 n1 3
2. 432ni 3
9.
3. 180000cm 1
0_000008cn1 3
10. 39 680cm 1 11. 112_5c1n-3 12. 189cn1'
4. 105 4cm'
sn rn
13. 129 6cmJ 14. I _1}_28
ITIJ
15. J44_6cin 3 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. 720cm 3 2. ) 16{) CITI 3
3. I 120cni 3 4. 7 )0 CITI 3
4.
5. 1242cm 3 6. 12Rcn1 1
7. 660nn-1 8. 19?c111
1
N
N
~~·~-o-·~~~~~,o-,-,o-,-,,~~~-+~..::.i ;~
n
101
--·
rfiA TAB so /\TA is isosceles Ar= Bf
ST(P) l'v1a1llemat1cs 2A
EXERCISE 5h
leache1 s Nou:s and Ans1vers
1. 154 In
2.
(p. 72) 2.
"
4.
32°
45 m
I Om
3.
5.
N
"
N
No
x>4 A
210"
7, 9, 11, I J
SOm
x
b) The mnc lrn< .eplacc
l
B is nearer to T 1han A is
3. CHAPTER 6
Equntions and For-n1ulae
~----~-~~-~---
Much of lhis chapter repeals wo1k that is in Book IA, but with shorter exercises.
EXERCISE 60 (p. 73)
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 2. 4 3. 12 11. 4 12. 5 13. J
4. 2 5. J 6. 4
7. I 8. J
14. 4 15. 16. I
17. J 18. 8
~----~
l---::::i:::=_ '""''' J Write down !he value ol n 1 +2
9. 2 10. J
19. -2 20. I 3, 6. 11, 18, 27, 38
0
by
(>
BJ
82
ST(P) Matfletnatics 2A
5.
Teachers Nores and Answers
21. 2 22. 4
_star1
23.
(\V;~do.wn ~mber
34. 2 35. 1 36. 2
31.
Is it divisihle
ls il divisible by 8
Yes
by ]
EXERCISE 6b (p. 75)
No
divisible by 8
sihle by 3
t.._. .
_--_~
_L
_
_,f-~
"
fl is not~ divisihle ~~---}
S1ar1
/,~
(ill~
Yes ls the ~e• ~ second angle //
' {The lnanglc No 1s ~~~mbte1al
~
60"
~'/
EXERCISE Ge (p. 77)
__,/
G . .±o f) The triangle is net equila__~e~
c·.
-o··
The lri<1ngleis_--=quil~-l~al
h)60
a) To give no 1nore than the first four tenns.
c)
4. 6t-
9. J(J_, 14 10. 47. + I 2-\
1. 6-9x 8. 35 - 2~h-
10
5. 12 - 8 \ 6. 2{h t IO
19. 4 ,- I 25 20. JO, I 47
21. !Or+_) I) 22. d 23. 17, - }3
24.
27. 7 \ -+ 32 28. x+ 21
29. 2 I."\ 19 30. 6.> +1
4 \ I 14 f(h I 14
25. 26.
36~
-! 26
35.
39.
43.
36. 37.
40. -4
44. 45.
!l
41. 42.
38.
)!
'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
1.
3. 1.
40. 2
17. 28x + 27 18. 18,.- -4'1
2.
EXERCISE 17d (p. 271)
39.
14. 8 \ -l 4 15. 2 I\+ 5 16. JJ, + 19
31. 32. Ii 33. I 34. 2
Is 1he first angle
Sl
38. • 1
11. 8' 1 18 12. 26> )l 13. ,4_l ll
'
/
'
Repeats the work done on brackets in Rook 1A. 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 2. 6-t + 3 12 3.
It is not
I is nol
37.
30. I!
Yes
'
' No
29. 4j
27. 4 28. I
25. 26.
lhe
32. 33.
6.
24.
19
11. 12.
0
13.
2
'
6 Jx
5x 8
IR
'·'
4.
5.
h
3
4, 5
7. h
io
•-
h
2
9. 6.1
10.
"
6
6. 2x 14. 15.
16.
x 4,
5 h 10
17.
'·'
19. 9x 2_.,-1
18. 9,
20.
.1
20
ST( P) Matfle1natics 2A
EXERCISE 6d 78)
(p.
Teacher ·s /Vores and Ans;vers
nccc:-.sary at e,ich stage of 1his exercise N111nbcrs Plenty of class discussion 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.
''11'
-14_
11. 12. 13.
"-· 22. 1 lf 21.
23. Ji~
31. 32.
-l
19.
18.
20. I !J
1!.!.
27.
24. 25.
6!"
"'
.,
,,~
.li
"
- lk
29.
28. 20
30. 1l
41. I' 42. 51
46.
26. 31
'
I\
37.
..
38.
35. I~
..
•'
17_ '-
15. 1• 16. I 11u
36. ~~
_!_
'
2")1
1
•
33. II 34.
3.
"
l)
' ' !ff
39.
''I;
44_ 1!.l
40.
Ii
45.
43_
"
I }0
47. )!~ 48_ 2 49_ "'4'
"
50. ~~ 4_
EXERCISE 6a (p. 82)
Use for discussion 1. £150
2. 40 3. 30c1n
EXERCISE 6f h>. 83)
Even 1hc mosl abk children are likely
d1fficul1_
4. 12 5. 1•1 COl 6. 5 crn
7. 9 8. 3
"'
find lhese
9. 12
11umbc1
10. £1000
Ntunbers I lo 10 revise 1nuhiplic11ion of directed n1J111bers N111nhers II 16 use these results for sinlp\ify1ng brackets and solvmg cquauons: again a good (1 \ -- 4) can deal of class discussion necessary and ponll (>Ill 1hat written as . I (2.\ - 4)
'°
'"
"
2. 15
4_ - ] 5. 12
3. --24
6. 28
1. -8
11. --2:t+ 17 12. 17x- 10 13. --15x -- 30 14. 15~ 14x 15. I 5x ·- 20
16. -9x-t-6 17. 2 18. 25' 46
19. 5t - 17
zo_
21-.,., --- 29
1. 2 8.
9. -9 10.
-45
21.
26. !1
22. 3 23. 2 24. ll
27. 10
25.
!_}
"
"
28. 7
29.
-4
30.
L
"
~
w~~lowi~h~ _)
81
80
Teacher's Noces and An.s»'ets
ST(P) Mathematics 2A Put in value for
EXERCISE 6g These exr11nples on constructing formulae are not very dillicull, bnt a go< (p. 85)
:t
1nany examples should he used for dass discussion before children are allowe 10 hy any on their own
a) 1
4.
b) 0
Put in value for
1. 21+ lw 2. JI
from 12
b) J
-
·-,r 1 ~~,m
( --- - -
vaueor:t
a)
29
sqnare~--rc·, --
~----
7. p
.--·· Get oul..0···
=
21
5. 2/+s+d 6. IV= x-f-y
3. ll+d 4_ 51 ~
21. d
2h
y
= b--a
T- N-!- Al 9. T- N I. 8.
~alue for ~-~·-t 4
'
10. A = 1' 11. N - !On
b) 4
12. C= nx 13. I. •.. I- d
6.
a) 12
\_)
14. p - 61 15. A = ll' 16. N .. S· T+S 17. IV 18. s -· N-l R .. p--q, 19.
h) 75
EXERCISE 17c ·rhere are alternative arrangements. (p. 268) 1.
22. q
'
20. IV ·Does she want
Yes
EXERCISE 6h (p. 87)
'" '
/
No
@~;-i~·er ~;c·
Kn
Does wan! sqn:1sh
'
No
Does
she wanl
ny
24. A
JOO 100/h
25. T-
It
60
1. 10
4. 2
7. 24
2. 100 3. JO
5. 20
8. 15
9. 25 10. )!
'
6. 200 14. 1) 15. 50 16. 19
17. 16
19. !OS
12. . 12 13. 5
18.
20.
21. 15 22. 200 23. J~
24. 25. il 26. 21
27.
'/
·--:--.....::::::.:r-
di
c) 8
d) . I l
h) 20
c) 96
d)
4
h) 1
c)
18
d)
"
I 2t
' di '1"4 d) 0 J8
"'
1. a) 48
b)
2. ') 4
h) .?O
..
3. a) 52
[ (iive her le·;::~~Je]
c) 6
EXERCISE 6i
(p. 90)
a)
H
h)
• 6. a) I 'i
h)
5. a)
7.
c"""'
~On_
18
4l
'I -15 9
I
600p
01
£:6
8. I ·-
.ll
29. 11
"
28. '.!~
30.
No
\'Ola
"'
"'
"'
Sta11
~he
5
rnind ·11: rhis e:o;crcise covers an nnpo1lan1 topic with the fuhue hrackels the fi1s1 1nstanL 11nportance ol putltng nega!lve nun1bers canno! he stressed loo much
11. -I
Slop
=
1
23. L
orr-,,,qp
2.
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
;i;
a) 6
5.
2
",. 15
1
12
7eacher·s Nores a1Hi Ans1-vers
ST(P) Ma1hematics 2A
V = /bd. I 200cm 3 /' = la -t 2b. 70crn
9. 10. 11. 12.
P""'6:1:,6cn1
P= L
Nr. 5m 24c111 14. JV= Ng+p, 45 15. A=2lw+2lh t-lhw, 6200cn1 1
13. P
EXERCISE 6j (p. 93)
=
]a.
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.
r
N- G
.. 11--( 6. 7. d ... S-1-r
y 5,
8.
'
9.
r
lb
10.
"
. P--b 11. 12. T = N R
16.
)'
17.
'
1.
2. x 3. J
4.
~
~
x
5. a
"
~
~
.
I. t y
s
"
13. c . b· !' 14. u ~
15. EXERCISE 6k (p. 94)
. x+z . /' --ab ~
Ln 1·-at
20. v ;;;; s-at
~
1. 6_3, 6-4 2. 94, 9 5 3. 5.2, 5.3
R L-b-L·
~
19. u =
r/
N
"
c
18. m
d
"
p ·- 2y
.
EXERCISE 6m (I'· 97)
'
24. L
6. 11.9, 12.0
9. 4.0, 4 I
(2 83)
14. 2, ]; 25, 2.6 15. 3. 4; J_S, J_6 16. 3, 4; 3.8, J 9
1. 2.
''
117,328; J.56, 3 57;
l
]
(l 89)
l 77, J.78
5. 7.
6.
I ST
(2 54) (l.56)
3 64, 1_65;
8. /'-.oc:tl/1/l·q 9. ..) 10. N~ R1D
"
l
"
5. I~
3. 6,
4.
(l 65)
6. 14
10
(17_89)
(l 27)
"
PR ~
(4 08)
10. 17.8, l '1_9
12. 3, 4; J.2, 3.3 13. 3, 4; .J.6, J_-,
1. -! 2. J~ 3. 6> 4. 6x
'
(11.92)
11. 2, J; 2.8, 2 9
17. 282,283; 2.54, 2 55;
"
4. 14.1, 14.2 (14 14) 5. 89,90 (894)
(6.l2) (9 49) (5.29)
7. 6.3, 6 4 (6 32) 8. 14.1, 14 2 ( 14.14}
EXERCISE 61 (J>. 96}
21. r=q .. p 22. a= s ---by 23. =1-
8
EXERCISE 17b 1. (p.267)
") 22
x, 1
7. 'i-i~ 8. I 5
10
9. N =11 t-b t-c 10. N = t1 t <1b 11. b) _1_45
----·--)
~tin e fo1
2.
Ge! out
va~~~~~~. b) 57 Gel out 1 ~Q+ value fo1 8-~0
Pu1 in value fo1
a) 9
bl 41
I !l
18
ST(P) fvlathen1ar1cs 2A
8.
rl1cse are suggestions only
Teacher·s Noles and An~vers
EXERCISE 6n (p. 98)
1. 2.
Is~
5.
4
9. P = 6a
4
6. x -f 6 7. . ' 8. 10
'
l
10. p
"'
3. 2 llx 4.
x
~
I .. )q
11. b) 32. J .1
12
c)
]_2
CHAPTER 1 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_
EXERCISE 7a (p. 101)
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)
2. 3. 4. 5. 6. 7. 8.
b) 6 b) 4} b) 2 b) ···8 b) J
c)
a)
a) 3} a) - 7
a) IO a) I a) 3 b) -6 a) -2 b) 4 9. a= -- 5. b = 3, c= 10. a= -2,b~s. c ~ 11. y = 3x
12. )'
=
7
8 c) -6 I c) -_
EXERCISE 7b
d) 8}
d) 4 l
c) 7
d)
c) ,.. 2
d) d)
c)}
-,'
c) .. 4
d)
52
j 4.1
1
18
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,
(p. 103)
d) ! 2 d) -20
-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
1-6
1eacf!er s Notes and Answers
4_
5_
S;op
7-12
6.
7.
77
76
SJ (P) Mathemaf/cs 2-J\
reacfler·s No1es and Answers
EXERCISE 7c (p. 105)
B
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
26 6' l his is a good place lo introdw:e division by zero - one of !he children
1
we!!
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)
4
9. 75.6", 104_4°, 75.6°, 104.4"'
10. CAB~ 2H
0 ,
11. 15Acm
L ;1) 2 2. al -
1108"
'
5.
b) 1
·•
b)
EXERCISE 17a (p. 265)
1.
h)
d)
a)
7+5= 12 or 5+7-= 12
b)
12-~-3=4
EXERCISE 7d (p. 108)
or 12""-4=3
c) f)
"
=
4
h) 3 b) -4
+
),
4. '
d) 3x3+4= 11 or 4+3x3=- 13
2.
3. a) 4. a)
Explain 1hc nwamn_g ol steep and sleeper in !his context Rcfe1 10 olhet t 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.
c) 2x3---2=4 or 2x3-4=2
c) -- 4
)
6. ~05 7. e)
CHAPTER 17 Flovv charts
«)
4
I
= 5\
3.
'-=----·
()
Z.
."i\
0
J.
I
o=,-
5.
~-t
!
-= l{h
10,
,,
0
()
ST(P) l\Aathernaf!cs 2A
6_ }'-'-"
reacher ·s Nores and AnS\IVers
-~_\;
EXERCISE 16i Answers given correct-to (p. 258) ,_ 23_0"
7_ y
=
y
-6x
= -
6r
3. 383"
9. 62.1" 10. 177"
::XERCISE 7e p, 110)
1. g1adienl
17. obtuse
14. acute
18. obtuse 19. ob1use 20. obtuse
16. ac111e
"'
1.
---
'
)",
I. 4.
2·
'
y
1ntern~pl
4.
I.
_I' 1nlercep1 y 111tercep1
3. l.
2, 7. gradicn1 2. 8. g1adicnt J. ! 9. grad1en1 10. grad1en1 -- '1·
'
r 1n1en:ept ·-1 4 4 r rnte1ccp1 J
_v 1111<:1n::ri1 F 1nte1cep1
_,, 1u1ercep1
5.
') a) a) a) a)
7, 3,
7. 4,
b) 4 b) . b)
'
'
'·
g1 adient gradient -- 2, gradient -. J l grad1en1 15. gradient !·
11. 12. 13. 14.
17. 18. 19. 20. 21.
}__~
''
Hr 26 6"' _11_8"
29_7° 59 o~ 33.7°
22. 66 8" 23. 24_0"' 24. 53 I"
9. 59 OQ 10. 8 8°
14. _l6 9'' 15. ]J 7'' 16. 24 ·1" 22. 23. 24. 25. 26.
51 '.\'' 18 7" 41 7°
30.Y' 51 3~
y mlcrcepl 1·
27. 425"
1nlercep1
v 1111ercept -t 2 ullcrcept ,. u11ercepl 1·
6 ~I
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 (p. 112)
7. 12 8"
8. 26 6"
_'jl)
10. 16 J"
11. 68" 12. 67 4"
3. 55 O"
2. lJ_ 7''
4. Jil.7°
12. HF' 13. 5 7_ 5"
bl 7 b)
19. 21 2° 20. 12_5" 21. 3S Y'
5. 36 9" 6.
F1cqlieru 1en111Hkrs of us meaning are necessary
y rn1eicep1 r 1n1e1cept
6. gradient
16. 39 8" 17. 49 ,r' 18. 59 O"
0
J. J.
•·'
11. 8 4" 12. J6_ 3"
EXERCISE 16k 1. 42 O" (p. 259)
11.
Introduces y-in1e1cepl
2. gradient 3. gradient 4. g1ad1ent 5. g1adienl
a cu le
15. acu1e
21. approx1matdy
13. 18-4° 14. 16_5" 15. 48.4" 16. 50.7" 17. .5! O" 18. 45.0"
EXERCISE 16j Answers given conect to I deci1nal place. (p. 258) 7. 5 L3° 4. 21 8" 1. 31 0° 8. 20_6" 5. 35.0'' 2. 387" 9. 66.()'' 6. 8 5" 3_ 26 6°
13.
10. obtuse 11. obi use 12. acute
1. 64_ Ja 8. 67 _4"
13. 18 4" 14. 8 I" 15. 95"
9. acute
deci1nal place
2. 34_4''
4. 42.8" 5_ 31.7" 6. J 1.2°
75
Discuss what you expect in 1he way of a sketch We fed 1ha1 pupils should develop 1he ab1l11y 10 draw co1nple1ely freehand sketches. v.-iihoul even using a 1ulct. but app1ena1e 1ha1 !ahcll1ng 1he ske1ch is necessa1y
28. 41.2" 29. S6_J" 30. 52 I"
EXERCISE 161 Discussion 15 uecessary HJ remind p11pds of ihe 1ne,_in1ng ol ·be;urng· {p. 262) of ekva11011·· etc
1. 310" 2. 266" 3. 59 tr. 59 O'', 62-0" 4. S6_J"
5. 10_2 krn 6. 26 6", -t)_O", 18 4°
7. 108111
'"angle
74
Teacher's Nares ancf Answers
ST(P) Mathen1atics 2A
13. 4_ 50 Clll 14. 7_0)cni 15. 6_43 nn 16. 6.24 Clll
1.
17. 16.9c1n 18. 1 44c1n 19. 9.33 cm 20. JO 2 COl
21. 5_22 cm 22. .l001n. 23. l7_8cm 24. 9_23 cm
4
~
••5.
'
"'
~
~
"'m
'
~
'
~
-4,
m
7'
6.
-
,,! '' 3. "' 3, 2.
4 2
-- 5 6
-3 "' ''" ' -· 7 "-3,' 4 "'m -;. ' -- 6 ' ' J 7. m -· ' ~
7. m
~
8.
~
9. 10.
~
..
~
15.
11.
~
y
grn
-+----'>.,.,->- ' EXERCISE 16f (p. 253)
1. 5 17 C!ll 2. 4_60on 3. ]_68 CIH
4. S 60 nn
7. 9.99cm 9. .34 5 cm
10. J SOnn 11. 17 9crn 12. J 26cn1
1. 14 3 cm
3. 8 l6cn1
2. 179cm
4. 10.1 cm
6. 69 9m
8. 30 8c1n 9. S.66rn
0
5. 8.96cin
6. 6 64 cni
16. 8. 14 I Clll
EXERCISE 16g
(p. 255)
7. 3.23 cm
12. gf3dieul 4
5. 5_10rn
0
10. 1_40nt 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
17.
t
13.
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" 2. 19_8" 3. 12. 3°
4. 76 J"
7. 9 I"
5. )4 5'' 6. 17.2"
8. 31.8"
10. 34.l) 11. 44 8' 12. 20_6'"
13. 29 J" 14. 59_7° 15. 74_4"
16. 64 4" 17. 69 4' 18. 18_4~
,..
25. 20 9"'
21. 37 6" 22. ,10_0"
26. 29 9c 27. J4 9" 28. lQ ll°
31. 32. 33. 34.
23. 44 1"
29. 487°
35. 45
24. 4_,
30. 74. ·1"
36. 50 4'
0
19. 2) 20. 1<1 4"
6~
0
grndi~nl
- 5
9. 39 O''
51 6" 41_7'' 48_ I" 59 ._,. _r'
18. gra
14.
()
1
78
leacJier s Notes and Ans;vers
S F{P) Mathematics 2A y
20.
19. gradient
25.
I
Angle
() 62)
))"
0
0 gradient \ -j
27"
O :i!O
37"
0 7 )-l
JI"
0 601 I 19
50~
EXERCISE 16c (p. 248)
25.
y
21.
'
gradierH :
- I
,
7. 0
1. 0 217
)')!
2. 0 S68 3. 0 202 4. L74
8. 0 18) 9. 0 180 10. 0 0664
5. 186 6. I 05
11. I I\
13. () 9 ! 1
19. 0 J78
14. ? 9~ 15. I 11
20. 0 0122
16. I 6S 17. -! I 7 18. ! ()8
12. () 642
21. 2 75 22. 0_279
23. 0 836 24. () 969
I)
()
22.
26.
EXERCISE 16d (p. 249)
2.
1.
.
"'"~
~opp
OP!'
0 grJdiem -1
4.
hyp
23.
27. 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. -- -"" ---:- =tan l2° Some 1eache1s, however, may plefe1 4 adJ 28.
24.
0
_,
lo stan with the trig 1atio, i c_ lan
1. 5 64cm 2. 5.81 cm
-~2"
5. I 4Jcin 6. S 38cm 7. l·Llun
3. 0975crn 4. 4.55 cm
8. 5.40cn1
9. 7.77cm
11. 7 _00nn
10.
~-12cm
12. 5 40c1n
=
~£~ adj
=
_:
4
72
leacher ·s Notes and Anstvers
S F(P) MatfJemat1cs 2A
2'
29.
EXERCISE 16a In Question 14 we expect angles measured by a protractor lo be given lo !he nearest ~", e_g_ 26!" (p. 244)
(Angles given to neatest half degree)
2w
c) 0.5 c) 0.5
4.
3. b) 2#"
c) 0.5
6. yes
7. h) 37~ 8. h) Jr 9. b)W
c) 0.75 c) 0.7.'i c) 0 6
1. h) 26tc 2. h)
b) 26t"
c) 0.5
5. b) 26t"
c) 0.5 6
13.
B,C,
B,C,
AB 1
AB~
c) 0.6 c) 1.2 c) 1.2
10. h) 11"
11. b) 10° 12. b) 50"
f.rMhcn!
B3 C 3 AB,
EXERCISE 7g (p. 115)
14.
BC
Angle A
Numbers 11 to 16 require changing lhc form of the e-quation
1. "I hey are pinalkl Then 2. J hey are paia!lel Their 7.
3. Yes
26!~
0.5
2
26f"
0_5
3
26j~
0_5
••5. No
values are equal \;Jines ;ne equal
Ye~
6. No
8 . Yes 9. No 10. Yes
Yes
4
16~"
() 5
11. Yes
14. Yes
5
7.&!''
05
6
3T'
0 75
12. Yes 13. No
15. No 16. Yes
7
17"
0 7)
8
31"
06
9
JI"
() 6
JO
50"
I 7
II
50''
I 2
EXERCISE 7h (p. 116)
IT can he useful
9. 0 J!M 10. I Oil
17. :?8 18. 0 700
11. I 80
19. 0 0875
12. 2 75
20. I 2J
21. ?
6. 0 1)8 7. 0 _14'1
13. 0 0699 14. 0 754 15. 0_966
8. 0 :i l_l
16. 57_3
61
22. I II 23. 3A9 24. 0 306
!(l
ask pupils
the r-a;o;is and pa1allel lo it negauve values f()r both
EXERCISE 16b Ciive a rrmintkr ahonl si~ni!\cJnt ligures One of !he dass wdl probably ;i~k aboul 1.10 9\)' C 1nnrnen1 on it ;ind use 11 ;1,; another npporluni1y 10 disc11ss (p. 247) division by lero: see the notes for r_:,e1n~e 7c.
..
m
AB
---·----·
1. 0 Jf>4 2. 0 5.l::' 3. _1 Ol:i I lJ 5. I 66
111
I'
-)
--4
!he equation nf a line 6 umts lo 1he rig.ht o lndud1
fl'f
Sin1ilady f11r lines parallel to the x-axis
-o-j
'
'
0
2 I
:io
Teacher·s Noles and A11s1·vers
ST(P) Mathen1a11cs 2A y
2.
y
6
=
x ..,, -- J
-6
x""
0
6
" 6
4
4
y =
33. 34. 35. 36. 37.
140 310 493 748
-
u_ 30. !00
'°"
38. 39. 40. 41. 42.
2768
48. 49. 50. 51. 52.
43. 70 44. 170 45. 189 46. 652 5 47. 2448
-1 4
_§_Q_
55
4
.
29.
5
-6
JO
104
185 J 19 2415 3312 62 91
26 15'i
12. 13. 14. 15. 16. 17.
3. 84 4. 18\l Clll 5. J3
8 6
9.
£1 !O a) £J6
b) f76.SO
61 b} £4624
19. ll 4\8
8. £9.20
20. 27mpg 21. a) )6 p
f8;~
10. fl05
y "' lx
!98 kg 414
94 ] kg 18. a) f)4·10
6. £747_50 7. £8-40
,.- "' 5
H 32.
31. 1%2-0
849 J
EXERCISE 15b 1. 6'l_2Skg 2. £226.80 (p. 240)
3.
71
b) 6161iues
c) LS 04 less
11. £7SO 4
- 6
y
6
EXERCISE 15c (p. 242)
~ ~5
(s.
JO). (5. -5). ( 2.5. -5) A r1gh1-angled 11ianglc
4.
y
6
x=4
a} 16% a) 45 'j~ a) 0.85
6
h)
to
16
6. 12 5 ~~ 7. .!_.'.!j '"°98cm 8. a) 9. £43 _)()
b) 960 sheep
42 rn 1
EXERCISE 15d
1.a)45~'~
(p. 243)
2. a) 85
'j~
4. 42~ % 5. 2 ! 7 rn
y=J
b) () 16 h)
20 ~-~
3.a)064
4
6
1. 2. 3. 4. 5.
b) 0 4) b) ~J
b) ~
6. 7. 8. 9.
'i8 ~;, 0 82 a)
94_5
a) Ul 05
b) 8.81niles b) £14"760
' Ct-IAPTER 16 Tr-igonometry: Tangent: of an Angle
-4
-6
(4. l). (4. -2). ( -6. l)
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
A right angled triangle
•·1rigonorue1ry"
70
leaclw :, Nores and Answecs
ST(P) Mathernat1cs 2A
7. 8-lcm 8. 4} cm
5. 7-5 cn1 6. 7_5 CIU
9. 10. 11. 12.
4cm
Cl)= 9nn, DE= I0.5nn Sctn
l)E = Pinn, AE
=
1. 2. 3. 4.
yes.
P
yes, no
Q
yes,
13 Snn, CE= 4_5cm
5. 24c1n 6. 6cm 5. no 6. yes, 7. yes,
P
4 CITI 2-4 crn
5 12 cn1 56~
14° 32"
E,
6.f yes.
HQ~
7_2 crn
5. yes. 6. no
AC~
JO~cm
9. yes, 10. 11. 12. 13. 14. 15. 16.
)'
7. 5 I cm 8. Jcrn
b) 2. 0 = - 4. h b) 3. o) l
4
1" a) 1
F,,
'' '
l)
1 ~r~
I 05 cn1
.
0
'
yes !0 HI
19.2 rn 60cm
••5.
3. I ?O ~~
6. 115 '.'~
5. a) ob111se
-"'-~~··="'""-«'-~====·-~"'-""-""==
160~-~
175 ~~
'"'
7. 148 % 8. 400% 9. 275 ~-~
c) obtuse
b) an!le
6. (- L --6}
'"
10. 112_5 '%
11. 157 ~~
EXERCISE 7j
12. 115 /~
h>- 118)
16.
BO
13.
"'
14.
17.
so/~
20. I 5 ~~ 21. 6" ~i
23. 96~~ 24. ]4 /~
26. 66i ~-~ 27. 41 /~
22. 58 ".~
25. 37~/-~
28.
i(Hj
18. 71 /~ 19. 10 ~-~
4), (4_5, 5). ( ---4.5. An isosceles hiangle
{((
+
J~ cni
yes, l8cm AC= 3 !SCin, CF 14-1nn
2. 125 ~-~
150~-~
4- J,:
- I
Revise earlier- work on percentages_ Explain the nieaning of the words "percentage increase" and "percentage decrease". 1"
- 5
i
c)
••
CJfAP-TER 15 Percentage Increase and Decrease
EXERCISE 15a (I'- 238)
~
!hey are parallel EXERCISE 7i (p.117)
4.
' -6
B
p
EXERCISE 14g 1" yes, CR = ]_6ctn 2. no (p. 232) 3. yes. RQ - 35cn1 EXERCISE 14h 1. yes, (p. 235) 2. yes. 3. yes, 4. yes, 5. no 6. no 7. yes, 8. yes,
-
4. 30cm
EXERCISE 140 1. 8cm (p. 227) 2. 6nn 3. IOcin EXERCISE 14f (p. 229)
y
5.
3. no 4. yes, 6.3cm
EXERCISE 14d 1. yes, 2.5 cm 2. yes, 7.2c1n (p. 223)
:J I
H>ii
15.
HH'.i
11'0
oo~~
b) 1. a) Ill 2. (1 = ~5. & 3. ') I b)
••
-
') ?
"
J.
'
•I
"
mtern·pi
;1) gradien!
4.
b) gradit"nl
1ntncep1 "' ' l. r 1nten·er1 2 - i· ' ' rn!e1cep!
I'
<) gradient d) .i;radient 5. a) Yes b) NP
-4
d) ob!use
- 5)
:J 2
S l (P) J\.1arf1ernatics 2A
ti '.l y
6.
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~
·----4
saint ra!lo
EXERCISE 14a <;ive 01 ex1uicl (p. 217) e:o.c1usc
itD!H
ihc class
txampl,;s
before
lhcy begin the
7. yes 8. no 9. !l\'! 10. no 11. A ;ind I>
1. yes 2. 110
3. yes 4. no 5. yes
--- ]
iu11lici
6. yes . -4
EXERCISE 7k (p. 118)
1.a)ll
2. a= 3.
-
h)
10
-J. 4). (8. 4). (
I I)
EXERCISE 14b Number l can be 1epeated wh<.'.n 1he pupih have h
c)-JI
4. b ""' 11,
J,
= 5
= 'l I cm. CB d) all are equal 10 .[ b)AC = 86cm CB= 71un c) Ct1ch 1s O 67 or~ d) all equal 0 67
1. a) yes
c) each 2. a) yes
.
5. :i) yes c) each
yo
6. 7. 8. 9.
h
6 4 Clll
b) AC
1s
2
3. a)ycs b)AC c) each is 0 5 ~)r j4_ a) )"CS b) AC c) each is 0 75 01 ~
I
It
(p. 218)
lS
l9cn1
LB,,--6.lcm
A-C
)_7cnl.
·s·
)_!cm
,\(.
~9cin_
C"B"
]2cn1
7 6nn.
c·n
4.9nn
c·tr =
IJ 8cm
d} all equal 0 S 10 I cm_ CH =.c 6 6nn. ;\ d) at\ equal 0 7_)
b) AC=- 6 ! cm. CB= 9 lcrn d) all equal ! ) !
c
AC '""9 2c1n_
! 5 ur
80°, 52°, yes Tl'', Tl", yes
70", 70", yes 93"', s2~, no
4. H1 -
11
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
" = -''
1. yes
2. yes.
AB
BC
AC
PQ
QR
PR
AB
BC
AC
PR
RQ
P<)
3. no gradienl 5 1- 1nte1cep1
_,
4. yes _
5. yes
6. yes.
7. yes :\C
CB
AB
QP
PR
<)R
8. no
AB
BC
AC
PQ
QR
PR
AB
BC
AC
RP
PQ
RQ
All
BC
AC
IU)
()P
RP
68
ST(P} Mathernatics 2A
li:!acher·s Notes and Answers y
12.
33
5. a} r """' 2x ----4
6
b)2v=xl-10 c) y =
-..'..4::r -3
6.
y y=4
-·-4
-6
·-· 2
,
,. _, I 0
()
6
4
-- 3
I
---4
c (I. 4). (I.
4). (-). 4)
---6
13.
CHAPTER 8
Reflections and Translations 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
EXERCISE Sa (p. 120)
Ri:::vises I he wo1 k on line sy1nrnct r y n1 flook I 1. a) and c)
2. ll
,.
14.
., .
---,/~
-.,-------,
0 - JO
- 8
-4
/
/
3.
CHAPTER 14 Sirnilar Fiuures !(>ptc
{"haple1
I~
is
l"t)\TfCJ
wilhl'll!
1ha1
snn1e
1e;1chcrs
ha_~
llllKh
m;iy
rdi'-rt."fl\T
n.11
heen dDne. lh('n similar
do
-B-&X'
ll
c
rh1S
6.
)\
/
tt'n)gnise
4.
!O
a1n
11iangk~
<:'11!<11).'ClllC!!tS
bCC\!J)('
W('
"111"
I!
Hanslo1niat1nn
can bf" approached 1hro11gh
s.
I
~ I
I
34
ST(P) Mathematics 2A
EXERCISE 8b (p. 121)
h~crci1er·s
Revises the wo1k on line syn11netry in Book I
'-
'
-~
'
"
I 2.
\
IJ
A
Ccn11e: (2, 3),
()
S..:ak factor -- J
- 4
b
7.
I
67
9.
6.
I
Nores and Ans•vers
b
- ]
6
8.
/
None
4.
\
I
I
/
I
',~\vI,,-
--
/
/ /
I
/
\
I 5.
I
~
- 4
,,
'
I
-~-\
10.
0
"'
.__,__.L-__j___l
9.
)
/
/
/
0::-I\"
/
10.
/
a)
(~euhe
(0,0). Scale factor -I
b} f{ota1ion about 0 through 180" t'
[)"
-4
66
ST(P) Marhen1atics 2A
6.
12.
11.
"
,. ~
--~
~
'1~ ~ --
----
I
' " .,
I -
"
3!)
Teacher·s Nares and Answer~
-6
Cenue (I. 'i).
"
Scak !annr
Noni'.
--,-
0
-·4
-------
,,
1
16.
13.
c
"
/
/
"
I I
7_ B
"
I
--+--
\
,,· -6
-4
I I I
\ c \
-
.
-
-----0
- ----"\
Cen!ie- ( l. 0)_ Scale lannr _ )
\J/'
17_
I I I
14.
'
-'
--+-I
I
I
j I
-~--
8.
I
- b
c
18.
o·
Li\
4
A'~o-c::
o·
--6
- 4
--
6
"'- '--.
\ -
D
-4
Scak
'
0
)
C~ntre
"
A
\'
15. I -- 1. 1;)_
lac101
I
I ---L-I
I
I I I ___ L __ I I I
I
36
l'edcher -s Notes anJ Ans1vers
ST(P) fv1atflernatics 2A
EXERCISE Be (p. 123)
The words ··ob1ec1"' ··unage .. ··minor line" are 1n1roduced A good deal llf 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
EXERCISE 13e ()n11t 1h1s w!!h .ii! bu! the (p. 212) 1. ( )_ 6)
3.
'
1no~1
2. iO
4.
1.
/
,ibk
I)
I
·.l
/';;/ /
. .. /
....I - -..-·
.. ·
'///
(
5.
2.
3.
6.
I
-=-r=I
D
\...j...J
7. c
B
~ ~ ""' D "
c
B'
""
8.
H
,,
."
"" 5.
9.
---A'
0
4.
·A·---
A
('
A~B
I {
c
Ce11lle (0_ !).
Sco~k
fano1
64
Teache1 ·s Nares and Ansive
ST(P) M athemarics 2A
15_
10.
rs
E
f"
8
I I
6
c
B
:_~
I
0
/\I
6
4
I I
A
11
I) 8'
I
c
I
c
cl
I
I
B
A
[)'
A"
A'
16.
I
A
I A'
I
l
EXERCISE 13d 1. (6 2. I ·· I. 01. (J•. 2101 1).
''
4.
5.
I
l l
3. Cl!. 4l. (!, 2),
ll
I
y
,,
/
,-
.
qc A'
B
B
./
/~~:~ "' 6
rzr
17.
8
0
//n·
' ,/c
'10
6.
I A.
13.
I I I
f.
A'
A
c
c
B
B
18.
10
8
6
4
14.
~t=7
B
,\
0
A
/
A'
0
(
A
12 .
c
I
c
(
. -----
I o'
B
8
10
c
c c
••
--BB-><-
:rn
leache1-'.<; Notes and Ans~vers
ST(P) f\..1atheu1atics ZA
19. <)9: A and A'. QI!: Band l!". Q12: A. A'; B. B'; C, C'.
5. (
10
20. Equal distances; perpendicular Jines. 6
21. Equal distances; perpendicular lines
I l •---~-------~" 22.
\
y-,--
c
B
)I)
6. !O
4
c
B"
A'
(
H
A
I
-
-
J
l
-
I
?
---l~-
,. l_...
A
IJ
"
A' -·~-
-.---+
0 6
9.
8
IJ)
y >O
'
23.
-
('
" 4
p
Q
l
"
-]
l--~~-~-'
()
6
'"
63
li 2
Teacher·s Nores and AnS\vers
ST(P) Mathen1at)cs 2A
24.
2.
-4
- i
_, 0
W'
ll'
3.
)'
'"
y'
C' 8
25.
6
-8
y ··---
-
·---
-1
----("
6
4
26. 4
A'
c
0
_,
6
0
'
8
A
B
--0
4.
4
c
Ill
I
I
6
,-
A'
I
4
Ir_
/
/
B
, 0
6
8
Ill
&
+ -3-
fl 5
7
-
61
Teachers Notes and Answers
ST(P) "A1a1hemat1cs 2A
40
EXERCISE Bd
(p. 128)
The iu1ioduct1011 lo
of inv;uianl p oints is optional of the inirror line
I- I the equauon UH
3.
Abk ch1id1en can be asked
B
J.
I
1.
I
B
A
COD
I
c
D
B'
I
Cenue o f c·11largcn1en I
b. ( ),
2)
A
0
-2
I
6
6 - 2
Ill
A
4. Hl ·
y
2.
y
4.
/
/
/
/
/
c/·
Centre o I- eulargemenl
·«1
0 -2---
IS ( \, ])
B
.,
0
·-;
!l'
j()
6.
5. y
·o: !.d
7
y
EXERCISE 13c (p. 208)
{)
- 5 --4
4
B
'----7-;
6
:~-----···· --'
--4
Fii
I
s·
y~l
I
o
1.
l'
----y·
/
/_/,,.
I I
B -·
------o~--.----:---~--~.~--;1~11--;,\, (
-
. 3' poHllS X, X' are inva1rn1
.
60
ST(P) AJ!athernatics
Teacher~'>
2A
8.
7.
7.
41
Notes and Ansi-vers
y
10
5
/ ~
z x·
"" ""
~~
8
/
• 1
-4
/
x
6
/
/
Cenlrt" of enla1gement is (10_ 2)
/ ()
/
II
4
I)
r
·4~()
/
/
0
6
4
-\ A
--1
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
10
R The1c are none
EXERCISE 13b
..
1.
(p. 206)
9.
R (
Cen!re of enlar!!emen! is(:!_ 4)
I' ()
I' - ]
()
4
6
R'
Cenlre of enhH!-'-eflle!ll is (.?. ::0)
Teac/1e1·s No1es and Ansn/ers
ST(P) Marflerna11cs 2A
~2
12.
y
10.
3. l
ll
'-..
'\]
'-..
"'-.. 4
-
c'
'
"'
•
/
0
N
X~Y
''
cl-
/ ' - --
( "cntrc of enlargn11cu1 1s (8, 4)
4
"""
M
l)
Q'
"
-l
"
"
0
-4
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
/ ,(
4
'
/
A
/
'
-3
') -4
11.
''
A
-l
59
y
5. Q
/
c
0
/ Ct':nllc of cnla1ge1ncn1 is (1. I)
r -4
3.
EXERCISE Be (p.131)
0
\
1. Yes
6.
2.
\ \
\
•
\
.. x
•
A
'-..
..--
6
\
Ccntn: of t:nlargemenl is {9. 5)
\
B 0
"'-....
'
..
\
4 A
"
.
y
9 6
~---r---1-0~,..,,----.,-,-
~----------~--·--t6
8
~'
\
6
4
\
-\
8
c'
\ 4. Gradient Equa1io11 1·
r 1nfefcept -
~l
+- 7
DC
7 _l~·+7x--21
=0
0
6
10
58
ST(P) Mathematics 2A
EXERCISE 12j (p. 201)
5. 8i 6. IOOnt 7. I I 8. £13.IZ~
1. ; 2. 5. 8 3. £40. £52' £8 4. a) 2 : l h) 8 • 27
EXERCISE 12k 1. 10 (p. 202) 2. 7. 6 EXERCISE 121 (p. 202)
1. 257 . 144 2. 32 - 24
EXERCISE Hf (p. 132)
1.aandc 2. Translation e and b Reflection a and c
Neither d
3. 2· 5 4. 9. 7
: 500000 6. 5}
7. fl). f6, £8 8. 510
3. IOkg 4. 33m
5. 6: J ' 6. 3.2 krn
7. 91 . 20 8. £154
5.
3. Translalion 2: 1dlcc1ion ! , neilher 3 and 4
EXERCISE 8g
CttAPTER 13 Enlargements
1.
4.
Omit if Chaplers 8 and 9 we1e no! covered
1.
(p. 204)
N
~
(p. 133)
Wt!'
'>' v
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
43
Teacher ·s Nores and Ans1vers
[7 ,.
Y
8·
2.
'
6
A
H
A'
fl'
DD
Cen11e of enla1gernent is (6.0)
o·
0
c
0
()
6
6
2.
3.
y
N
5.
s· R /
/ R / 6 /
~.~
-h,~ ()
6
Centre of en!argenlt'nl i~ ( 1. il)
·-.......__
Q.
~-
()
4
6
6J
6
8
44
Teacher 5 Noles and Ans-.vers
ST(P} Mathematics· 2A
EXERCISE Bh (p. 134)
Revise the work on vecto1s in Book IA before Joing this exercise_ 1. (7. J)
4. 11. 5)
7. (
2. (6. 9)
5. (I. 1)
8. (
~2.
4. -2)
9. (9.
6)
10. (2. 0)
27.
,
26.
11.
G)
14.
G)
17. (
~:)
12.
( :)
15 (;)
18. (
:)
G)
16.
19. (
~)
_11
•
1. 21~-p 2. 18cm 3. 98 cm
20. (:)
(~)
l
,,'
ZB. 1\ 29.
,
18. I! 19. I~ 20. 7~
21.
30. 16~
32. Jl
31. l}
33. J~
j
22. 10 23.
I;
•
EXERCISE 12f Use many 1no1e examples for chscuss1on These questions can b' used for d1su1ss1on with eve1 yone bu1 only the fllOS! abk ~hould work on their own (p. 195)
4. lOjcm
1. lOcrn
5.!0~CHl
8. llm
6. '27cm
EXERCISE 12g Much class d1su1ss1on usrng d1lle1cu1 examples_ 15 advisable (p.
23. { --
21. (5. 6) 22. (2. 2)
'
24. 5Jl 25. 7l
6. (6. - 7)
3. (2. 7)
13.
2)
15. 6~ 16. Ii 17. o'
lI. 2 13. 14.
57
26. (-4. -5)
25. (9. I)
24. (1. 5)
196)
1. 48 p.
..
6. 16 7. [_~ ){) f 17 )0 8. "I 2S2 rn' b) lO'i rn 1
J] p ~Ocm
2. I 2 un
3. f20. £2S Dick
"
fom 2)
9. L!
5. JOp --15 p
EXERCISE Bi
1
AA ~ (-;) RB ~ (-:) ('(' ~ ( :)
2.
Lr· = (~)- ~·t~r
Yes. Yes
(p. 135)
(~)- NN· = (·~)-
=
3. (:) 5
a) (
4
:)
6.
x
_,
(_:)
l
Im'
l-l1n'
1n1crc~11ng
u~c:
500000
••5_
':>00000
2. 3.
!00000
6.
~
nl ra110
100000
noo ooo
10. ~000000(fll !Onu 11. I 8 crn
EXERCISE 12i 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 (p. 199) propml!on p1obk1ns 1~ to 111ull1ply by ,; scak LJ,:101 e g 111 the wo1k.el1 example 111 ihis exeichc. 1hr- ~cak lanoi is {cnn1pa1rng jMgc ru1rnbe1s).
H«
B
thu::k•1ess of 1he !a1ger bnok =
R
I ) x y~g (we wan! the !a1ger book_ S{) !he
hnger nun1b.:1 goes ou !op 01 the scak factor)
0
' r
:) b1C) d(
1. 12 m
4. J6un
2. l6
5. 105
3. IR nn 1. 7'
•J
., <>l (
EXERCISE 12h Not essen1ia! at tlus s1agr- but an (p. 198) 1. soooo
8. 70m 9. 200m
A
y
12. --1! rn !
7. ) km
c) ( : )
c
'
z
l
~)
b) (
C~)
No. Nn
10. rn f !O, f8
11. 6cm. 8 Clll. IOcm
~)
d) (::)
11. S4nunuks
6. I hou1 s 7. 9 hou1s 8. fl I 90 9. fX400
10. )til 1111nutcs
1 Z. f I__! (must buy Lolllpk1c kngths) 13. 1-LHtlly a11y 1 (no 1oom to wn1I-} 14 . .q k;ISpoous
5\ 1-.rn
56
Teacher ·s Nor es and AnsM,-ers
ST(P) Mathematics 2A
1. 4 .
'j
2. 5 4 3. 2. 3
4. I •4
7.
5. I• 3 6. 9. 200
8. I • 6
14. L 4• s 15. s • 8 16. I • 8. 7
11. 2
3. 5 12. l . 4 . 6 13. - 5. 10
16. J
17. 3 . 4· 7
••
18.
. 8 . 4
9. 16
10. I
17 IOOO
7.
19. 12 . . 2 20. 14. 9· 2
F
6
EXERCISE 12b Revise n1ulliplication of fractions.
{p. 190)
2. 8. 3. J . 2 11. 8
7. 35 . 24
4. 3 5. 4. 9
1. IS •
8. 9
4
9. 16. 7 10. 10.
2.
19. 4
()
A
6. 7. 10 14. 2
'j
17.
IS
12. 2 . l
15. 15 • 19
13. 40 • 9
16. 5. 4
18. 4· J
Yes.(~).
2 20. J • 4 . 6
5. 6
2'1·i2=f·
8
24 _.__,, ~ : ~
6. I 0
parallelogram ·--!he opposite sides are parallel
8. a)
(
[ [
"I
A
3. 5 8 4. 7 - 10
1. 5 7 2. IJ 8
6
J
EXERCISE 12c lnlended for the ahove average and can he ornined. (p.191)
4
"
b)
7. 8 . 64 = j~ t 8. ~ _1 = 4 . 18
ll
c
D
EXERCISE 12d 1. 2.
)
3. 4.
2
5
4. 9. 16
{p. 192)
l
5
R
}_
2
3
5. 2 .
A
6. B) 2. 7. 8 11 9 8. l
9. 4)
b) 9. 5
c) 18
ll
9.
)
"
h) 2 -
"
c) 5 · 3 .\
---'--1
EXERCISE 12e Reinind pupih !lrnl sorne1i1nes a· h is u~nl in die !orrr. olb bul
(p. 193)
\\
d) I
Iha! !hey
should USt' consi~ten! no!ation within an equalion Of sentence_ i e_ \ 4
c:::
H
1: J . 1
and ~ = ~ ate h01h cOHcC! h111 t: 4 =- ~ is not
1. 10 2. ·1
4 . .? 5. 8
3. )
6. 12
11. !J 6. I?
7. 6
9. 9
8. 6
10. I
·"'
~,, n,
"l
.,
"' ( ~) b)
( -;)
>)
(:)
()
AA'(~'C. B~'("'C
S r(P) fvfathe1natics 2A
CllAPTER 9
Teacher ·s Nores and Answers
Rotations
EXERCISE 11g Nu1nbe1s I to 1 aic ~u11abk fut (p. 185) re1naindc:r of this. exercise
Omit if Chapter 8 was nol covc1cd. Again n1uch discussion is necessary at every s1age of ttus wo1 k
cve1yone
but
use Jisc1c11on w11h 1he
1. 707 Cflll
EXERCISE 9a (p. 139)
Revises the woik on 1olational syuunetry in Book IA. b)~
1.a)}
c)~
3. 491
2. a). b) and c)
lllllll
5. No EXERCISE 9b (I>. 140)
6. 21.'icm 1 7. 8, I IOcm" 8. 11 700un 1 9. l
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
2. a) 6,
3.
6.
b) 2
EXERCISE llh 1. 17 6null 2. 9 SS rn
(p. 187)
I
4.
1
7
EXERCISE 11i
1. 61 8 Ill
(p. 188)
2.
4_~2
3. 57 _lcm 4. SO l mi
5. 89.? llHI\ 6. 40 9 C!H
1.
8l_)crn~
J_ !4m
5. J2 2 un 1
I
7.
l 95 c1n
6. .?8 6nun
I --*~ I
5. 491 cn1 1
3. JI 7un 4. 26 4 m 1
EXERCISE llj (p. 188)
crni
1. 12_6 ~n1 1 2. .108 lllf)l
7.
4. !)4crn
1
6. 18 l 111 1
,~--
I I
I I
I
5.
8.
CHAPTER 12 Ratio EXERCISE 12a Scale d1aw1ng can be used a~ ano1he1 exainpk_ a scale of lcn1 to 500rn can (p. 189) be cxp1ess.cd
9. 91Y, 120". 180'. 90". 120". 180°
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
Teache1 ·s Notes and Ans~vers
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 3. 18.Jcm 4. 205cm 5. 27_9nn
7. 94.Jcni
EXERCISE 9c (p. 142)
7. both
5. both 6. both
8. bolh 9. 1 olalional
9. 20.6crn EXERCISE 9d
EXERCISE 11d Nrnnbers I and 2 can be done hy everyone
Except ror the able, use the
Simple models may help some p11pi\s to see exac!!y what is going CJn 1. 90" clockwise 2. 90n clockwise
3. 180° either way 4. 90° clockwise
5. origin, !Rtr 6. (I, 0) 90" anticlockwise 7. (I, 0) 180"
9. (2. I) 90" clockwise
re1nainder ol this exercise for discussion
1. 78_5 n1m 2. 62 8 rnm. 88 () fTI!ll
8. 94.J cm
~ ; ~
3. 4.40111 4. 194nn 5. 176c1n 6. 176c1n, 200
....•...
7. l2_6c111
EXERCISE 11e 1. 700cm (p. 180)
4. lrne
10. 45 I CITI (p. 143)
(p. 178)
II is wol!hwhik d1awmg 1he d1ag1arns and p111tt11g 1he line(s) of synunelry on them
1. rotational 2. rolation11! 3. line
8. 62_8 mrn
2. 19-' 1nn1 3. 87.5 Ill 4. 41 8nn 5. 7.~ 5 mm
6.
___
9. 62.8 in 10. 6.28 secs, 9 55 revolulions 11. 3140cn1 12. 17.6m 13. 70 7 14. 94.Jm
8. (I, 0), 180°
10. (1. ll. 1800
11.
J l? CITI
7. 5 76mm 8. 6)] m 9. 92_6crn 10. JJ 9rn
12.
J
c 12. 59 81n
15. 4 93cm 16. 955nn each
19. 4 77 c1n 20. 9 55 Cln
13. H Rnn 14. 20 Om
17. J 82 nn, 45 8 cn1 18. 17 7 OU
21. 9.55cn1, 29.1 Cnl
11. 16 5 Ill
,,
;.'------"'-~'
EXERCISE 11f fhe de1nonstr
1. 50 J cn1 1
2. 201
till]
3. 78.6m
1
4. 78 6 llllll 1 5. 38.5 Clll 1
7. 45-4 rn 1 8. 9.62 km 1
6. 11 JOO c:nl 1
9. 20 Jci01n 1
13.
c
10. 25 I on 1
11. 'iLJ mi
12. 58 9c111 1
13. 118
14. 451 nun 1
16. 457 crn 1
18. 943 etn 1
20. 193on 1
15. 374nn 1
17. 714m 1
19. }540cin 1
m1n
47
l ln.;_-lrnnged
1
"
"
48
ST(P) Marl1e1nat1cs
Teacl1e1 s Nores anlf
2A
14.
c
D 4
.. .
';I:
A'
'
5. 60 cm~ 6. 7)cmi 7. !8cm 1 8. 68 cm'
1. 78crn 1
D.
0
2. 22 ::i cm! 3. 20cm 1 4. .'i4cm 1
9. -18 5 crn 1
10. 48cmz
11. 14~ sq unns 12. 24 sq Ul\!!S
6
4
-2
r'
l!lH!S
lllHIS
·1s . 28 sq 16. ! o sq
U!UIS IHlllS
1 3. !Ocm or 1000 111Hl! 1 4. 48 nn
[)'
15.
6. 6 5cn1
5. 14cn1 EXERCISE 10h (p. 172)
y
••
("
4
1. 6cin 2 2. 36cmJ 3. !OOcn1 1
4. _iOcnic
°'
c CHAPTER 11
A'
•
A
0
-2
v
B"
lllfll
5. 60l!l1 6. 6nn
1
5)lould
be
used
fiedy
fo1
al!
..-,1ku!a11ons
Revise
2. !Om 3. 10mn1
4. 7cm 5. l km 6. 9 1 cm
1. approx J 14
8. approx
1. l 2cm
A"
)
.,"
c
, 6
4
''
wnh can be used ;1s illl ;1pp1ux1ma11
'"
"
'" "
"
"'
"
" idlSWO
cm1espond1ng 1mplu:a11ons fo1 the accuracy or 1he
17.
1. l 4 5 fl\
4 A
••
"
c
c
0 ·4
()
-l
A'
significant
figures
4
y A
!0000
Circles: Cir-cumference and Area Calcula101s
x
EXERCISE 11a (p. 173)
16.
13. 20sq
14. 14 sq
EXERCISE 10g 1. ! 80crn 1 2. 20cmi (p.171)
··4
. 4
53
EXERCISE 10f Can b' used for disc1i:;s.1on Wllh the average but dnly the above average should a11en1pr 1 hese ll!l their own (p. 169)
y
6
. 4
Ans~vers
4
[)'
2. 28.9cnl 3. l8.lcn1 4. 331 mn1 5. 5,, 7 m
16. 17. 18. 19.
970 min
88cm 241n I JOO mm
6. I S701nm 7. 126nn 6 . JO Zin 9. II l HI 10. 0 0880 km 20. 220 C!ll 21. 1600mn1 22. 2000cm 23. 29rn
11. 44 0 cm 12. I 76 mm 13. 8 80 Hl 14. ])() Hllll 15. 1S 2cm
"'
52
S T"(P) Mat/Jen1atics 2A
Teacher's Nores and Ans1vers
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 CTIJ 1 2. 600cin 1
3. 17.2cin 1 4. 0.02R8tn 1
5. 1280ciu 1 6. I 7J6 10 1
,.
18.
7. 24.48 ctn 1 8. 7 CIU 2
c
B'
9. 38.88cin 1
10. 28.8 cm 1
11. 26.4 cm 1
12. 352cm 1
13. 63c1n 1 14. 48cm 1
15. ll.25cm 1 16. 110cn1 2
17. 36cm 1
18. 180CTTI 2
19. 8 sq units
20. 15 sq units
21. 9 sq_ units
19. 4
22. IS sq_ units -6
- 4
A
ll"
EXERCISE 10d /\gain use tb!"' questions lo discuss whi(J1 1neasurenwnt is the heigh! (p. 164) exan1ple for discussion is !hal of a tree blown over by 1he wind:
0
A"
A good a) a semicude
b) OC
4
!low high is the 1op of the tree 7 How long
JOm
llm
is the Hee? How high wo1Jld a helicop1er have to fly to clear ir1 Etc
20.
3. 80cm 1
4. -1 2 Clll
1
5. 100cm 1 6. J99 Clll 1
7. 24cm 1
8. 14.4nn 12. 45 Clll 2
19. 2,l_4cin 1
22. 96cm 1
15. 540cni 1
16. 1) C111 1 17. 7 <; i:-rn 1 18. 70 Clll 1
20. 82_5 nn 1 21. J0cm 1
23. 21 nn 1 24. 8 31 cm 1
25. !Osq IJJHIS 26. L? sq units
27. IOsq um ts 28. !_',sq uni1s
29. IOsq units
30. 7~ sq units
13. 44nn 1 14. 64cm
1
10. 32-4
111
1
60°
1
11. 22-2 cn1 2
9. 40crn 1
B'
\! ~
Nun1be1s 25 lo 30 are intended !or ordinary sq11a1ed exe1c1se paper. II graph paper >S used. a scale of I c1n to I unil is S;ltisfactory
1. 48nn 1 2. I 56m 1
c
O-JA-·
EXERCISE 9e (p. 149)
EXERCISE 9f
B
e) 90'"' clcx-kwise
1. c) (0, 4) 2. c) ( 2, 2), 3. c) ( I, \),
e) 90" clockwise
e) 90" anticlockwise
l. 90" anticlockwise
2. 90" cl
(p. 150)
EXERCISE 9g
Si1npk 1nodels may agarn prov!.' 11se!ul
(P- 15-1)
EXERCISE 10e (p. 168)
1. 8cm
4.
2. 6c1n 3. 6cm
5. ] Clll 6. _lficin
~Clll
7. J cm 8. l~ cm
9. 0 4 nn
10. 6cn1 11. 8ctn 12. 4cm
(
1. rranslation given hy ' 2. Re flee! ion in
1
0
-
·,'')
~7- ()C',
OB
<)B
teachers Nores anti Ans1vers
ST(P) Pv1alhernalics 2A
3. Rcfiect1011 in x
=.
~
19.
(--:i)
4. I 1ansla11on given by
5. Reflec1ion 1n r
= --_'( II
I.
6. Rotation tluough 90" an11dockwise about
(
7. Ro1ation 1h1011gh 90" anlidockwise aboul
(0.
I)
f)
8. Rotation through 180° aboul {O. 2)
9. Ro1a11on th1ough 180"
about(~-
10. Refte:ction in y = x+ I
D
-I
-- )
11. Rdlec1lun in BC, roiation abou1 B 1Juough 90" clockwise
VI
12. Rctlcuinn in y-ai\iS. rotation about {O. lj) through 180". uanslation parallel to x-ai\is
- l
IV
VII
13. I) Rcftcc1ion in <)B
2) Translation parallel lo AB ]) Ro1auon about R tlul>t1gh 120" dl)Ckwisc 4) Ro1a11on about() 1hrough 120" clockw1sc Retleuwo>> l--!V
14. I) Rellccuon in BE
20. a) Relkc11011 111 lhr line y =
2) Transla11on parallel 10 AB
Rot<1!1<1m V VII
hi Yes
x
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 (
CHAPTER 10 Area
~~)
Revise si1nplc mul1ip!icatio11 of decin1als and fractions
EXERCISE 10a Revises the work on are:as of 1ectaugles in Rook IA (p. 157) 3. 384 Ctl)l 1. 41 2 m' 4. 40crn 1 2. 0 2108cm'
16. Transla11on given by 1hc vcc1or (:) 1 17.
1 5. 1 84 cm 1 24 840nn 6.
11. 21 6cm'
\.
\.
I
\.
/
\. \.
v
12.
/
1 17. 8·1cin 18. I 28cmi
/
/
ccnhc of the 1urnlng ci1de
18. Ro1a11ons aboul difh:ren1 venices, reflec1ions, t1anslations
J2]cn1 1
7. () 0008
IH
1
8. 4 56 il\ 1 13. 552 cn1 1 14. 672cin 1
9. I~ nil 1 10. 4\cm
15. 2870 llHH l 16. 862 2J2 ITI 1
19. 78 cm 1
20. 90cm 1
EXERCISE 10b Revises !he wtHk on 1ec1angles in Book lA
h>-
159)
1. (l :1 Clll
5. 5crn
2. 5un
6.
3. !Om 4. 4 Hl!ll
7. I 25crn
5 rn
8. Jm S. 7 Ill 10. 6cn1
51
