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Unformatted text preview: is known that the speeds of vehicles
travelling on the highway are normally distributed, with a standard deviation of l0 km h–1, and
that 30% of the vehicles using the highway exceed the speed limit.
(a) Show that the mean speed of the vehicles is approximately 44.8 km h–1.
(3) The police conduct a ‘Safer Driving’ campaign intended to encourage slower driving, and want
to know whether the campaign has been effective. It is found that a sample of 25 vehicles has a
mean speed of 41.3 km h–1. (b) Given that the null hypothesis is
H0: the mean speed has been unaffected by the campaign state H1, the alternative
hypothesis.
(1) 135 (c) State whether a onetailed or twotailed test is appropriate for these hypotheses, and
explain why.
(2) (d) Has the campaign had significant effect at the 5% level?
(4)
(Total 10 marks) 194. In this part of the question, radians are used throughout.
The function f is given by
f(x) = (sin x)2 cos x. The following diagram shows part of the graph of y = f(x).
y A C B x O The point A is a maximum point, the point B lies on the xaxis, and the point C is a point of
inflexion. 136 (a) Give the period of f.
(1) (b) From consideration of the graph of y = f(x), find to an accuracy of one significant
figure the range of f.
(1) (i) Find f′(x). (ii) Hence show that at the point A, cos x = (iii) (c) Find the exact maximum value. 1.
3 (9) (d) Find the exact value of the xcoordinate at the point B.
(1) (e) ∫ f ( x ) dx . (i) Find (ii) Find the area of the shaded region in the diagram.
(4) (f) Given that f″ (x) = 9(cos x)3 – 7 cos x, find the xcoordinate at the point C.
(4)
(Total 20 marks) 137 k − 4
195. Find the values of the real number k for which the determinant of the matrix −2 equal to zero. 3 is
k + 1 Working: Answers:
....……………………………………..........
(Total 3 marks) 196. Given functions f : x a x + 1 and g : x a x3, find the function (f ° g)–l.
Working: Answers:
....……………………………………..........
(Total 3 marks) 138 197. For the function f : x a x2 1n x , x > 0, find the function f′, the derivative of f with respect to x.
Working: Answers:
....……………………………………..........
(Total 3 marks) 198. The boxandwhisker plots shown represent the heights of female students and the heights of
male students at a certain school. Females Males 150 160 170 180 190 200 210 Height (cm) (a) What percentage of female students are shorter than any male students? (b) What percentage of male students are shorter than some female students? 139 (c) From the diagram, estimate the mean height of the male students. Working: Answers:
(a) …………………………………………..
(b) ..................................................................
(c) ……………………………………..........
(Total 3 marks) 199. Calculate the area bounded by the graph of y = x sin (x2) and the xaxis, between x = 0 and the
smallest positive xintercep...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.
 Fall '13
 Apple
 The Land

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