Solve the inequalities:
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Solve the inequalities:
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Solve the inequalities:
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Write down the solutions to .
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Sketch the graph of , clearly showing the coordinates of the points where the graph intercepts the
-axis.
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Hence, or otherwise, solve the inequality .
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Find the discriminant for the quadratic function .
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Write down the number of real solutions to the equation .
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On the axes below, show the region bounded by the inequalities
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Sketch the graph of and hence solve the inequality
.
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Write down, in terms of , the discriminant of
.
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Hence find the values of for which the equation
has two real and distinct solutions.
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Write down the three inequalities that define the region shown in the diagram below.
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The total cost to a company manufacturing cables is
pence.
The total income from selling all cables is
pence.
What is the minimum number of cables the company needs to sell in order to recover their costs?
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The equation , where
is a constant, has no real roots.
Find the possible value(s) of k.
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Solve the inequality , giving your answer in set notation.
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Solve the inequality .
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Solve the inequality .
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Solve the inequality .
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The equation , where
is a constant, has two distinct real roots.
Find the possible value(s) of k.
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On the axes below show the region satisfied by the inequalities
Label this region R.
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Find the values of that satisfy the inequalities
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Solve the inequality , giving your answer in set notation.
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The cross section of a tunnel is in the shape of the region defined by the inequalities
On the axes below show the region satisfying the inequalities
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Given that and
are in metres write down the height and the maximum width of the tunnel.
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Write down the inequalities that define the region R shown in the diagram below.
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The total cost to a company manufacturing cables is
pence.
The total income from selling all cables is
pence.
What is the minimum number of cables the company needs to sell in order to recover their costs?
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A stone is projected vertically upwards from ground level.
The distance above the ground, m at
seconds after launch, is given by
How long does the stone remain m above the ground?
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Solve the inequality .
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Solve the inequality .
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The equation , where