maths_2_O_june_1999

Extracted Content: maths_2_O_june_1999

Page 1

Extracted Text

E 2houwrs 30 minutes TRUCTIONS TO CANDIDATES ; ; war booker” COM Auber and candidate number in the spaces provided on tho anewer po ‘Wer all questions in Saction’A and any three :

‘© your answers on the separate answor paper provided.
Sor or anne Siaty shown, B should be dave on the same shat ae the fest ofthe arewer,
$siOn of essential working will resuh in loss ol marks. aan)
idegrae of accuracy IS not epecified in the question anni if the answer is nl exact, the answer st
"onvo twee sriicantigures. Answers in degrade should be given fo one decal place
lumber OF marks is given in brackets | Jat the end
Smatical tables may be used to evalimte explicit

---

Page 2

Extracted Text

: Section A {64 marks . Are 8 the questions hs seen -@) Prakite 2 253,

® Ti pd 120 mer bs we of © sa, Hou ce!
-_ CRERBme: Coleuinte iis pay for a weck in whic he works fr 48 hows

© © O raneenie cg taal
@ Find:the number of boys. . ,

Given ‘that § of the boys are studying Agricul ture, expres the number of bc
o Aes pana oe

© Ce et do 2 a a. 8 pe

. z $9), O) Pactotise completely ax 4.2 30-3, ‘
a. Pectotise 22” ~ 7x +3, .
wD Write down the LCM. of
: arta Sa 3 and 252 Te 43,
@) “Given that p= Var

® fad the value of p when g = 20,
® expres q in terias of p.

©) Simplify 2-8

FL xa§

B

---

Page 3

Extracted Text

2 table below shows the number of pupils from edch form who went on a tup to Great Zimbabwe.

). Using ém-wide iro represent ctch fom anda vera al of no represent 0 pip
draw a labelled bar chart for the given data, By
) For these pupils, find . . .
‘@ the m6dal-form,
i) the mean number per form.

. “BI
) wo pupils are chosen at random ftom those who went nthe ind the probaly ht
_ they were both in Form 3. _ i

1) Given. that the total sumaber of pupilé'at the school was 1080, find, as a single fraction in its
lowest terms, the probability that « pupil chosen at fandoni from the whole school, went on the

trip and was in either Form 2 or Form 4. : . ec
1) Find the value of r for which the matrix| 3 is singular. ; &
. 3 2\fx\_ [16
» Given that (? JG)-()- | |
calculate the values of x and y. ; . : 3)

2) WY. Yand Z are fonr prints with conedtirates (- 2, 3 4.6}, (8 Prand (7, 2) respectively.
%® Find XY as a column vector.
@ Fad | F1, .

(tii) Calculate the gradient of WX."
i) Find ie exis ofthe ine paral o WH wih ess trong Z

(oF

9 -

---

Page 4

Extracted Text

= Amswer the whoie of this question on a sheet of plain paper Use rider rand compasses only for ail constructions and show dlearly all the construction

(a) 0 “Constmutt. a “quadrilateral ABCD im which AB= 90cm, DAB = 90
- AD= 75 om and BC= 63 cm.

“i Measure and write down the size of BCD.
. ‘®) Ou the sume dizgram construct _ . , Loy
@ the locas of pats that ar 5,0 frm Lo, . a

™H

---

Page 5

Extracted Text

5 :

tn 9 suey, 20 pope wee std ih of ire me ek iter pre ‘they liked. The
“smal Are Geplayed in the table belo

) Write-down the vaines of
@® a,

@®@ ¢,

Ga fF,”

Gy) 2,

in A.

’ How many people liked exactly twé types of meat?

voy

| Caleulate the mimber of peopié who did not Be my of hemes an te
Sumber surveyed Give your answer as a fraction in its lowest terms. .

2

---

Page 6

Extracted Text

. °_ “The dingrace shows a.réctangie aad 3 right-ragled age triangle, The lengths of the sides o a Get Thee eye! (72) om The lags of two ofthe see aa ence . / (a) Write down an expression, in terms of, for the area of * @ - wenngle M4, . , ; @ triangle N. (6) Given teat the area of Mie wwice the Lol thniagte $Y, Seem on ght nee Mie EMC Sten off ssiningte am eg

2x? ~~ 3400,

32

---

Page 7

Extracted Text

BOPalaane SEEAIBR GED REARAR AED anan

a

i

2

5

4,2) and C1,
re

2h,
{-2,

Describe fully the
(i)

vertiogs AC 3.
has vertices A

ABC has
5,

\ .
~Dand C\(~3,- 1).
snaps AABC onto 4A

Fi oa

B

Bi

Cc.

=
2
2

3}.

18,C,.

*

Write down the matrix that represents

2]

transformation which is tepeesented by the

triangle ABC yby a

——

8

| ABLE

45,2) and C{8, 3),

that maps AABC onto AA B,C

G2

6. -2F

) Find the coordinates of A,

a

-Z

[3]

B

a

has vertices A

BC,
ulfy the

Triangle A
- Describe fi

are over

---

Page 8

Extracted Text

D .| Inthe diagram, AB is parallel to DE sind AE is poratie! to oo ACE and BCPD ave straight ines and. AC = Per inti Pel g Explain way triaugles ABC sed LDC ave timnitor : ers) Given that AC = AE asics thet

the area of triswigle ABC is 2 icyusre units, fine

a

ey

; Dae TREN quate, M5 mK ma Hs
@ Calculate 7g. ren

@ Given also that MEL = 95° asc KL = 11 ma, catcutare the length of MZ.

---

Page 9

Extracted Text

) -

Bog Tree my, Ou US CAUPIOYEO 1G GO We JOD mn Y days?

Take 1 to be 3,142

4 crlindrical hole of radius 3.cm was deilled completely through a metal cube of side 15 om

Grecton perpendicular to dae of the faces of the cube, as shown abo.

@®' Calculate the volume of the metal retiioved. an ;

@ Express the volume of the metal removed as a percentage of the volume of the org

(iil) “Calculate the volume of the remaining metal,

(ir) All the metal removed was melted arid made into 43 identice! sa
tadius of each sphere, giving your answer correct to te eae. i.

[Volume of sphere = § ur]

36

---

Page 10

Extracted Text

Ww Ameer ike whole ofthis question on single sect of graph pape

The velocity .Y mls, of a ball after time, r seconds, is give by -
veda Sr #

TE
ofc
. @ Calcilate the 2 waits ofp.

’ &) Pking en them if reg -
os paking 2.cm to represent 2 ros, draw a vertical ats for” 4ivei2 .
Draw the graph af v= 445- Pior0<t<6, ——

mc) Use the graph to estimane ol,
; @ the time at which v= 0, :
wy -the manimséti speed reached by the bali,
Ga) the distance covered by the ballin the first 2 seconds.
‘@ @ By drawing a tangent, find the gradient of the graph whon = 4. -
@® SMP DOERY what this gradient represents,

36

---