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CALCULUS – PAST PAPERS (QUESTIONS & SOLUTIONS)
November 2008
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February 2010
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February 2011
QUESTION 9
9.1
Use the definition to differentiate
9.2
Calculate Dx
9.3
Determine
f ( x)  1  3x 2 . (Use first princip les.)
4
1

4  x 3  x 4  .

(4)
(3)

2
dy
if y  1  x .
dx
(3)
[10]
QUESTION 10
Given: g ( x)  ( x  6)( x  3)( x  2)
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 DIA GRAM SHEET 2.
(4)
10.5
For wh ich values of x is
g(x). g / (x)  0?
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(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.
y
N (0 ; b)
T
P(x ; y)
x
O
R
M (a ; 0)
11.1
Determine an equation of MN in terms of a and b.
11.2
Prove that the daughter's land will have a maximu m area if she chooses P at the midpoint of MN.
(2)
(6)
[8]
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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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*****
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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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