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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.)
, t\ \ ' t , " tri t ' i: , . . ! ,
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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 -
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