ST (P) Maths 2A Answers - Original

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 (

- 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''---

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.Ol

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 JimOp, 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-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>.:e1cisc 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 lriIll 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 - ' 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. 14 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. - 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'

ponding vertict~ )

(:)

()

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