stella maris am f4 p1 2007 midyr1

8/2/2019 Stella Maris AM F4 P1 2007 MidYr1

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+(rrk 3t'^ iin e. 45STELLA MARIS SECONDARYSCHOOL

MID.YEAR EXAIMaOOT

ADDITIONAL MATHEMATICSFORM 4PAPER 1(2 HOURS)

DO NOT OPENTHE QUESTIONPAPERUNTIL TNSTRUCTEDO DO SO.INSTRUCTION

l. This questionpaperconsistsof 25 questions.2. Answeral l questions.3. The diagramshown are not drawn o scaleunless ndicated..4. Answersmust be written in the testpad given.Show all your working as tmay help you to get marks.5. You are allowed to use a non-programmablecientific calculator6. Read he questionscorrectlybefore answering hem.

(Thisquestion aper onsists f 6 printed ages.)

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ADDITIONAL MATHEMATICSPAPERT[80marksl FORM 4( ;) .==J(

A tunction/isdefinedy f(x) = !-L^ ,xJ t3 .2x' \ -

tile arrow diagram alongsideshowspart of the mappingf :x-px+3.Find hevalueof(a)p,(b) q.

[2 marks]Function ,h: x

-!:t-, is defined or all valueF f x except2x+3

(a)Statehevalueof k'q9 ninOan expressionor h''(r).3irina theelements which2iare unchangedunder his mapping. [3 marks]

(a)Expresshe equatio 2x2+ 4x -3 :0 in the ormof a(x* b)' * c : 0. Hence,statehevaluesof a, b, andc.

(b) Find the quadraticequationwhich has he roots [2 marks][2 marks]

Ifp andq are he rootsof equation x' - 5x + 3 : 0 for whichp > q, find thei . - ' rvalues f(a)B^+g^(b)p" + q'

Thediagram howshegraphof y: f + mx + n which ntersects-axisat -l and3. Find hevalues f m andn. y

k2

4.

[3 marks]

[3 rnarks]

- l u"d3.24

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fiagram alongsideshowshegraph f the unctioril ':(a) the valuesof h and",(b) the nterceptsofy-axrs

[2 marks]

(x';1$?.+,P)Find

II

( )- '

).A,/ )

The diagramshows hecurveof y = r? t px +Find(a) thevaluesof p andq,(b) lhe m_!1i-umpoinr.

.rai I! , r

4 which crosses -axis at -2 and6.

i ii)

/t l Sketchhe.graph f 7=&-- 3)2+ 2 for thedolnain_dx5;s: StateJheange hatb correspondso the giiiendomain.[3 marks]

Function/andg are espectivelyefinedbyf : x _, lac2Find he4gg=of values f kif fg(x)=0 hasieal oots. +.r+5and{:x-->x+3.[3 marks]

[3 marks]

-3-


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:iiiiiir,ti"

12.) Solve he ollowing simultaneousquations'Y + 5--73x5w {- rr: 8 [3 marks]J^ ' t

-Oi(@Evaluatelo9,16 og,8 logo

\-/ (b) solve heequatio )' ' : 11,.8[2 marks][2 marks]

Solve he ollowingsimultaneousquations.3x -y: 3

y(x+y)-x(x+y):5

Find the value of logo.t2, gle youranswer o two places-of ecimal't2marksle. ' ' '

Solve he ollowingsimultaneousquations."Y.:y ' -x-22:!5x+y=8

Solve he following simultaneous quations.* t *yt: 124-y:3,Give your answercorrect o two decimalplaces.

-4-

[3 marks]

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19.)

(a)Given hat 3 logt x : 4 og y, express in termsof v.1

(b) Find the value ofx if -8roe"" *64

[2 rnarks]

[2 marks]

20( '-t- -'. \.i ' r. r,,'

Diagram at the side showsapiece of rectangularcardboardABCD. The areaof the cardboards 35cm'.A half-disc CED is then cut from the cardboard,

Express heequation2y+3x-4 : 0 as L * * : l . State hevaluesofa+- . ' i'

" ' ; t ' - t ,' / i*,, [2marks]

(b) A (1,3)andB (3,ft)are wopointson hestraightine 2y : mx + 5. Find thevalues f m andk. [2 marks]

/ r 61, .23.y' Givenhat (x) = 2x+ 3andg(x)= : .\---t' X(a) find the compositeunctions f(i) .fs(x)(b) calculatehevalues f(i) fs?) [4 marks]Printed from www.epitomeofsuccess.com


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If o andB are he ootsof 2x2the roots ur"9 undE .22

- 5x - 6 = 0,fonn a newquadraticequationwhere[3 marks]

.Xt)/M-Diagram shows hegraphof the(-/' andk>2..

thevalueof k,the equation fthe maximum -

stella maris am f4 p1 2007 midyr1

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