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CALCULUS – PAST PAPERS (QUESTIONS & SOLUTIONS)
November 2008
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November 2009
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February 2010
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November 2010
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February 2011
QUESTION 9
9.1 Use the definition to differentiate 231)( xxf . (Use first princip les.) (4)
9.2 Calculate
43
144
xxDx
.
(3)
9.3 Determine dx
dy if 21 xy .
(3)
[10]
QUESTION 10
Given: )2)(3)(6()( xxxxg
10.1 Calculate the y-intercept of g. (1)
10.2 Write down the x-intercepts of g. (2)
10.3 Determine the turning points of g. (6)
10.4 Sketch the graph of g on DIAGRAM SHEET 2. (4)
10.5 For which values of x is ?0(x)g.g(x) / (3)
[16]
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QUESTION 11
A farmer has a piece of land in the shape of a right-angled triangle OMN, as shown in the figure below.
He allocates a rectangular piece of land PTOR to his daughter, giving her the freedom to choose P
anywhere along the boundary MN. Let OM = a, ON = b and P(x ; y) be any point on MN.
11.1 Determine an equation of MN in terms of a and b. (2)
11.2 Prove that the daughter's land will have a maximum area if she chooses P at the midpoint of MN.
(6)
[8]
x
y
O
T P(x ; y)
R M (a ; 0)
N (0 ; b)
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November 2011
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February 2012
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November 2012
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February 2013
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November 2013
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February 2014
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November 2014
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EXEMPLAR 2014
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February 2015
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NOVEMBER 2015
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FEBRUARY 2016
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NOVEMBER 2016
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***** SOLUTIONS TO FOLLOW *****
FEBRUARY 2017
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***** SOLUTIONS TO FOLLOW *****
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IEB - 2012
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IEB 2013
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IEB SUPPLEMENTARY 2014
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