SPM F5 Ch3 PDF Darker Sample
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SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 1
SPM PAST YEAR QUESTIONS ADDITIONAL MATHEMATICS
FORM 5 CHAPTER 3 : INTEGRATION
marks) (3 axis.-y about the 360 through rotated is
diagram in theregion shaded when thegenerated solid theof volume theCalculate a)2
marks) (2 .2
2)(for value thefind ,8)(Given b)
marks) (4 5)-(3x
18 ii)
,x)x)(4-(4
i)
Find 1a)
1993 SPM
0
3
0
3
0
3
2
dxxf
dxxf
dx
dxx
marks) (7 door. new theof surfacefront he t
of area thefind ,maintained are AKD arc theof shape theand BC of
width the whereas4m, toincreased are DC and AB ofheight theIf (iii)
surface.front sdoor' theof area theCalculate (ii)
BC. of width theCalculate (i)
BC. of level thefrompoint highest theisK and 3mDCABGiven
.4
x-4ygraph theofpart with shape same thehas
that arc lsymmetrica a is AKD ly.horizontal lying is BC andcally verti
standing are DC and AB door. a of surfacefront theshows diagram The b)
2
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 2
marks) (3 1. when x6y if x of in termsy find ,14dx
dyGiven 4.
marks) (2 .7)(2x Find 3.
1994 SPM
3
x
dx
5.
marks) (5
region. shaded theof area theCalculate x.-7y and
74xy of graphs theshows diagram The 2
x
marks) (4
axis.- xabout the 360rough th
revolved isregion shaded when thegenerated solid of lume vo
theCalculate R. point, maximum at the curve thengent to ta
a is PR .3x-6xygraph theofpart shows diagram The a) 6. 2
1
1-
2
2
1
2
marks) (3 g(x)dx.for
value theFind in x.function a is g(x) where2g(x)dx
dy and
x
1-2xyGiven b)
marks) (3 .3x
3)3)(x-2(x Evaluate a) 7.
1995 SPM
marks) (4
curve.each ofequation thefind (2,4),point at intersect curves theIf ly.respective 2
9-2x
and2x -6by given are curves two the to tangents two theoffunction gradien The b)
dx
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 3
marks) (4 region. shaded
theof area theCalculate axis.- with xparallel is PQ linestraight theGiven that Q.point at
1 xlinestraight with theintersects that )1(4y curve theofpart shows diagram The a) 8. 2 x
marks) (6
axis.-yat 180 angle through revolved is OKMNsector when thegenerated e volum
theCalculate .90KON and Oat centre with thecircle a ofsector a is OKMNGiven
axis.-yat lsymmetrica is which 2 xcurve theofpart is KMN diagram, In the b) 22
y
marks) (2 .14kx-g(x) ifk b)
marks) (2 g(x)dx, 2f(x)dx a)
of value theFind 6.g(x)dx and 5f(x)dxGiven 9.
1996 SPM
3
1
4
0
1
3
4
0
3
1
dx
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 4
marks) (6 1. xline and -2 xline axis,- xcurve, by the
boundedregion theof area theCalculate 3).1)(x-x(xy curve theshows diagram The a) 10.
marks) (4 k. of value theFind .unit 18
is generated volume theaxis,- xabout the 360 rotated isregion When thek. xline
and 1 xline ,12xy curve by the boundedregion shaded theshows diagram The b)
3
marks) (5 region. shaded of area the(ii)
h, of value the(i)
Find (h,3).point at
intersect which 4)-2)(x-(xy curve a and 12xy linestraight a shows diagram The a) 12.
marks) (2 dx. 5-2f(x)for value thefind 6,f(x)dxGiven 11.
1997 SPM
3
1
3
1
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 5
marks) (5 k. of value the
Determine .unit 6 is generated volume theaxis,-yabout 360 revolved isregion shaded
When theaxis.-y andk y ,x-4yby boundedregion shaded theshows diagram The b)
3
2
marks) (5 axis.-yabout 360 through revolved isregion shaded when thegenerated
volume theFind .153
x linestraight and 2xygraph theshows diagram The b)
marks) (5 6. xline and axis- x,4xyby bounded
region theof area thefind Hence 6.x0 of range in the 4xygraph Sketch the a) 14.
(3marks)
.3,2
1point through and 1)(2x ofgradient a has that curve theofequation theFind b)
marks) (2 .1
2x Find a) 13.
1998 SPM
2
2
2
3
4
2
y
x
x
dxx
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 6
marks) (5 region. shaded theof area thecalculate Hence,
mark) (1 B.Point of coordinate the(iii)
marks) (3 , f(x) (ii)
mark) (1 A,point of coordinate the(i)
Find a)
.4x(x)f'Given
B.point at curve theo tangent t theis axis,- with xparallel is which BC, linestraight The
B.at axis-y cuts andA point at axis- xches which touf(x),ygraph theshows diagram The 16.
marks) (4 x.of in termsy Find .3dx
dy and
2
1y -1, When x.14Given 15.
1999 SPM
2
3
2
2
x
xdx
yd
marks) (6 a. of value thefind
,unit 2
1 is produced volume theIf axis.-yabout 180 through revolved is ay line
and 1xy curve by the boundedregion when theproduced ish block whic a is Q b)
region. shaded of area theCalculate a)
questions. following answer the diagram, the toreference With 18.
marks) (4 .11kxf(x)dx f(x)dx ifconstant k b)
mark) (1 2f(x)dx, a)
of value theFind 4.f(x)dxGiven 17.
2000 SPM
3
2
2
1
5
2
5
1
5
1
dx
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
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marks) (2 xdy. of value thefind Hence, (ii)
xdy.by drepresenteregion theShade (i)
graph. curve a ofpart ofsketch a shows diagram The b)
marks) (3 .6x
2 of value theFind a) 19.
2001 SPM
5
0
8
2
8
2
2
1
3
ydx
xdx
marks) (3 .g(x)-xfor value theFind ).(1dx
dGiven .20
2
0
2
dxxgx
x
marks) (6 axis.-y and axis-x
,5)-(xy curve theg(x),y linestraight by the bounded area theFind (2,9).point at
5)-(xy curve theintersects which g(x)y linestraight a shows diagram The (ii)
2g(x)dx. of value theFind (i)
function.linear a is g(x) where14g(x)dxGiven a) .21
2
2
0
2
2
0
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 8
marks) (4 k. of value thefind ,unit 8 is axis-y about the 360 revolved
isregion when thegenerated volume theIf constant. a isk where2-k isA point for x of
coordinate theand axis- with xparallel is AB linestraight theknown that isIt axis.-y and AB
linestraight the,1xy curve theofpart by boundedregion shaded a shows diagram The b)
3
2
marks) (3 12. t
when of valuemaximum thefind 6, when t4 Given that ).12(2
1
dt
dby given
is s, t time, the tocompared , re, temperatuin the increase of rate theday, specific aOn 22.
2002 SPM
t
marks) (3
k. of valuespossible theFind constant. a isk where,3
7816xGiven b)
marks) (2 x.of in termsy Express .4dx
dy23xGiven a) .23
2
1
0
2
dxkkx
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
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marks) (5
t.of value thecalculate Q,region
of area the times threeis Pregion of area at the th
Given Q. and P regions, twointo axis- xand 5 x
1, xlinestraight the,1
y curve by the bounded
region shaded thedividest xlinestraight The
.x
1y curve theofpart shows diagram The a) .24
2
2
x
marks) (5
generated. ish block whic theof volume theFind axis.-y
about 360 through revolved is 16y linestraight and
-2 xlinestraight curve, by the boundedregion shaded
The .xy curve a ofgraph theshows diagram The b) 2
marks) (3 n. of value theandk of value thefind ,)1(x)(1
5 25.
2003 SPM
4cxkdx n
marks) (3
k. of value thefind ,units 64 isregion shaded theof area theIf
k. xlinestraight a and 3xy curve a shows diagram The .26
2
2
marks) (3 x.of in termsy find -1, when x6y and 22dy
Given .27 xdx
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 10
marks) (6
axis.-yabout 360
throughrevolved isregion shaded when thegenerated
volume theCalculate A.point at 2x 3y linestraight
aintersect which 1y xcurve a shows diagram The .28 2
marks) (3 curve. theofequation theFind
.63x is A(1,-12) through passes that curve a offunction gradient The .30
marks) (4 k. of value thefind -1,k where,6)32(Given 29.
2004 SPM
2
k
1-
x
dxx
marks) (6 . of in terms generated, volume theFind
axis.-about x 360 through revolved isregion The (b)
region. theof area theFind (a)
3. xlinestraight and 2, xlinestraight axis,- xcurve,
by the bounded isregion A A(1,3).point through passes
which 1)-(2x
3y curve a ofpart shows diagram The .31
2
marks) (3
curve. theofequation theFind (1,3).point through 43x offunction gradien a has curveA 33.
marks) (4 k. of value theFind .10kx-2f(x) and 7)(Given 32.
2005 SPM
2
6
2
6
2
x
dxdxxf
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 11
marks) (3
axis.-y about the 360 through revolved is
3y linestraight and axis-y curve, by the bounded
region when the, of in terms generated, volume the(b)
marks) (4 region. shaded theof area The (a)
Find A(2,3).at 12
xy curve
the tonormal a is PQ linestraight diagram, In the .34
2
b
a
2
marks) (2 2f(x)dx.
of value thefind ,units 5 isregion shaded the
of area theGiven that b. xand aat x axis- x
thecutting f(x)y curve theshows diagram The 35.
2006 SPM
marks) (4 .10g(x)-kx ifk of value the(b)
g(x)dx, of value the(a)
find 8,g(x)dx Given that .36
5
1
1
5
5
1
dx
marks) (3 axis.- xabout the 360 revolved is Qregion
shaded when the, of in terms generated, volume the(c)
marks) (5 P,region shaded theof area the(b)
marks) (2 k, of value the(a)
Find
B. andA points at the 2)-(xy curve thengintersecti
4xy linestraight theshows diagram The .37
2
SPM Past Year Questions : AM Form 5 Chapter 3 - Integration
Compiled by Miss Ng @ www.epitomeofsuccess.com Page 12
marks) (3 curve. theofequation theFind
(1,8).at point turninga has ,x
2-2xfunction gradient with curveA 39.
marks) (4 h(x)-5 (b)
h(x)dx, (a)
find ,3h(x)dx Given that 38.
2007 SPM
2
7
2
2
7
7
2
dx
marks) (7
axis.- xabout the 360 through revolved is axis-y he t
and axis- x thecurve, by the bounded is which R
region when the, of in term generated, volume the(b)
P,region shaded theof area the(a)
Calculate
A.point at 3 xlinestraight theintersects curve The
.1)-2(xy curve theofpart shows diagramgiven The 40. 3