Archive 5: These questions are taken from Board of Studies VCE 1994-97
Further Mathematics - CAT2

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Question 5 A least squares regression line calculated in an analysis of the relationship between fuel consumption (in kilometres per litre) and the weight (in kilograms) of a car has the following equation fuel consumption = 15.2 - 0.005 x weight Using this equation we predict that cars weighing 1000kg have a fuel consumption of A.  10.2km./L B.  14.7km/L C.  15.2km/L D.  20.2km/L E.  1000.0km/L (1997 Further Mathematics CAT2)

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Question 6
When the product moment correlation coefficient r was calculated for the data displayed in the following scatterplot it was found to be -0.3951.
If the point (7,25) was replaced with the point (7,5) and the product moment correlation coefficient r recalculated, then the value of r would be
A.  unchanged
B.  positive but closer to 1.
C.  negative but closer to zero.
D.  positive but closer to zero.
E.  negative but closer to -1.
(1996 Further Mathematics CAT2)

Question 7
The time series plot shown represents the average daily use of electricity in a home in successive quarters.  The pattern revealed is best described as

A.  seasonal
B.  trend only
C.  random
D.  cyclic but not seasonal
E.  seasonal with trend
(1994 Further Mathematics CAT2)

 

Question 8
The following table gives the number of births in a country hospital for the period 1980 to 1987

year	1980	1981	1982	1983	1984	1985	1986	1987
number of births	99	74	88	103	92	110	109	118

Using the three term moving average method, the smoothed value of the number of babies born in 1984, to the nearest whole number, is
A.  92
B.  94
C.  99
D.  102
E.  104
(1996 Further Mathematics CAT2)

 

 

Question 9
The time series plot shown here is best described as showing

A.  random variation only.
B.  an increasing trend only.
C.  an increasing trend with seasonality.
D.  seasonality only.
E.  a decreasing trend only.
(1997 Further Mathematics CAT2)

Question 10
Ice cream sales for 1994/5 and the seasonal indices for an ice-cream maker are shown in the table below.

	summer	autumn	winter	spring
ice cream sold (1994/5 litres)	29 465	20 875	18 187	19 345
seasonal index	1.30	1.08	0.79	0.83

When deseasonalised, the amount of ice cream sold in winter is, to the nearst litre
A.  14 368
B.  18 187
C.  19 345
D.  21 968
E.  23 022
(1995 Further Mathematics CAT2)

Question 11
Which of the following sequences is generated by the difference equation t_n = 2t_n-1 - 6 with t0= 6?
A.  6,0,0,0,0
B.  6,6,6,6,6
C.  6,12,6,12,6
D.  6,0,-6,-12,-18
E.  6,12,18,30,54
(1996 Further Mathematics CAT2)

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