The line segment is the diameter of a circle.
has coordinates (—7, —9) and has coordinates (9, 3).
Find the coordinates of the centre of the circle and the length of the diameter.
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The line segment is the diameter of a circle.
has coordinates (—7, —9) and has coordinates (9, 3).
Find the coordinates of the centre of the circle and the length of the diameter.
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Find the equation of the curve passing through the point (-2, 3) and given by
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In a computer animation, the radius of a circle increases at a constant rate of 1 millimetre per second. Find the rate, per second, at which the area of the circle is increasing at the time when the radius is 8 millimetres. Give your answer as a multiple of .
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The diagram shows the graph of , where ,
Write down the maximum value of when .
Find, in terms of , the combination of transformations that would map the graph of onto the graph of , .
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In the expansion of the coefficient of the term is 216.
In the expansion of the coefficient of the term is 4860.
Find the possible values of and .
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The curve C has equation . The point P lies on C.
Find an expression for .
Show that an equation of the normal to C at point P is .
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Show that .
Hence, or otherwise, solve the equation tan3 tan2 tan for , giving your answers to 1 decimal place where appropriate.
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The th term of a geometric progression is given by .
Calculate, giving your answers as exact values
The sum to infinity of the progression starting with the seventh term.
The sum to infinity of the progression whose th term is given by , where is defined as above.
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A circle has equation
The lines l1 and l2 are both tangents to the circle, and they intersect at the point (5, 0).
Find the equations of l1 and l2, giving your answers in the form .
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The circle sector is shown in the diagram below.
The angle at the centre is radians , and the radii and are each equal to cm
Additionally, is parallel to , so that and .
In the case when cm, show that the area of the shaded shape is given by sin .
.
Show that for small values of , the area of is approximately .
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The functions f(x) and g(x) are defined as follows
Find
(i) fg(x)
(ii) gf(x)
Write down and state its domain and range.
The graphs of f(x) and are drawn on the same axes.
Describe the transformation that would map one graph onto the other.
Find the coordinates of the point where the graphs of y = f(x) and meet.
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A curve has the equation .
Find expressions forand .
Determine the coordinates of the local minimum of the curve.
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The diagram below shows the graphs of
Find the area of the shaded region, .
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