The curve C has equation
The point P lies on C and has coordinates (w, – 32). Find
the equation of the tangent to C at the point P in the form y = mx 
c, where m and c are constants.
(5)
g(x) = ex
1 + x − 6
Show that the equation g(x) = 0 can be written as
(2)
The root of g(x) 
0 is 
. The iterative formula
is used to find an approximate value for 
.
Calculate the values of x1, x2 and x3 to 4 decimal places.
(3)
By choosing a suitable interval, show that = 2.307 correct to 3 decimal places.
(3)
Figure 1 shows part of the curve with equation y = f (x), x 
. The curve passes through the points Q(0,2) and P(
3,0) as shown.
Find the value of ff (
3).
(2)
On separate diagrams, sketch the curve with equation
(2)
(2)
Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.
(3)
Express 6 cos
+
8
sin
in the form R
cos(
), where R 
0 and 0 
α 
Give the value of 
to 3 decimal places.
(4)
Calculate
the maximum value of p(
),
(2)
the value of 
at which the maximum occurs.
(2)
(i) Differentiate with respect to x
Without using a calculator, find the exact value of
You must show each stage of your working.
(5)
Show that cos 2
+ sin 
= 1 may be written in the form
(2)
Hence solve, for 0 
< 360°, the equation
(4)
Hence, or otherwise, find h
(x) in its simplest form.
(3)
Figure 2 shows a graph of the curve with equation y = h(x).
Calculate the range of h(x).
(5)
The value of Bob’s car can be calculated from the formula
where V is the value of the car in pounds (£) and t is the age in years.
Find the value of the car when t 
0
(1)
Calculate the exact value of t when V = 9500
(4)
Find the rate at which the value of the car is decreasing at the instant when t 8. Give your answer in pounds per year to the nearest pound.
(4)
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