ADDITIONAL

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ADDITIONAL
MATHEMATICS
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CONTENTS!
Introduction - slide 3 Temasek Secondary
School Preliminary Examination 1999 Paper 1 8,
11 Paper 2 5ai, 5bii, 6ci, 6ciii,7a Thanks for
viewing our presentation!
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INTRODUCTON
Are you daring? Do you enjoy a challenge? If you
are, then try out the mathematical games that we
have prepared for you!
PLS CLICK ON THE HEART TO KNOW THE ANSWER!
GAMES
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8a
The figure is a sketch of the graph
yx(x-2)(3-x). Find the equation of the tangents
at x2 and x3.
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yx(x-2)(3-x)
y-x35x2-6x
when x2, y0,
Equation of the tangent at (2,0) is y2x-4
when x3, y0
Equation of the tangent at (3,0) is y-3x9
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8b
Find the area of the region enclosed by the curve
and the two tangents at x2 and x3.
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To find the intersecting point of the two
tangents, 2x-4-3x9
The intersecting point of the two tangents is
(2.6,1.2).
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Area of the triangle
Area under the curve
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Area of the triangle
Area under the curve
The area of the region enclosed by the curve and
the two tangents at x2 and x3
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11
A particle P travels in a straight line so that
its distance, S m, from a fixed a point O is
given by
Where t is the time in seconds measured from the
start of the motion. Calculate the velocity of P
when it is next at its starting point.
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When t0, S18 When S18, t2-8t0
?t0 or t8
When t8,
the velocity of P when it is next at its starting
point is
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TEMASEK P2 5(a)
Cos(2x-30o)sin2x
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Cos(2x-30o)sin2x ?Cos(2x-30o)cos(90o-2x) ?
2x-30o 90o-2x or 360o90o-2x or 720o90o-2x
or 1080o90o-2x ? 4x120o or 480o or 840o or
1200o ? x 30o or 120o or 210o or 300o
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5b(iii)
Given that
find in terms of p, for
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6c (i)
Given that V12-12sin6t Find the range of values
of V.
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Graph of V12-12sin6t
V12-12sin 6t
Range of v is 0?v ?24
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6c(iii)
V12-12sin6t
The distance travelled by the particle from O to
the first instance at which it is at rest.
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V12-12sin6t
When V0, 12-12sin6t0
Sin6t1
The distance travelled
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7a
Find
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Where c is a constant
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