Evaluate
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Evaluate
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Write the following in the form , where and are integers to be found.
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Solve the following equations, giving your answer in exact form.
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Show that
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Solve the equation
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A square has side length
Show that the perimeter of the square is .
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Write the following in the form , where and are integers to be found.
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Solve the equation
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Write down the value of
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Show that
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Express 42 as a product of its prime factors.
Hence, or otherwise, show that
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Sketch the graph of , marking clearly the coordinates of any points where the graph intersects the coordinate axes and stating the equation of any asymptotes.
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Evaluate
Evaluate
giving your answer in the form , where is an integer to be found.
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Solve the following equations, giving your answers in exact form.
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By writing , show that
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Write the following as a single logarithm
Write the following in the form , where a and b are integers to be found.
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The diagram below shows the length of three sides of a triangle, with each side measured in centimetres.
Work out the perimeter of the triangle, giving your answer in the form 2 , where is an integer to be found.
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Show that
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Solve the equation
Solve the equation
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On the same axes, sketch the graphs of and .
Label any points of intersection between each graph and the coordinate axes.
Write down the equations of any asymptotes.
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Solve the equation
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Evaluate
Evaluate
giving your answer in the form .
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Solve the equation
Solve the equation
giving your answer to 3 significant figures.
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Solve the following equations, giving your answers in exact form.
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Simplify
giving your answer in the form , where and are integers to be found.
Write
as a single logarithm.
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Solve the equation
giving your answers in the form .
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Solve the equation
giving your answer in the form , where and are integers to be found.
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A ship sets sail from a harbour.
After some time, the ship’s position is east of the harbour and north of the harbour.
Find the direct distance between the ship and the harbour at this time giving your answer in the form km.
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By writing 5 as , show that
can be written as
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Solve the equation
giving your answers correct to 3 significant figures.
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Solve the equation
giving your answer correct to 3 significant figures.
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Evaluate
Evaluate
giving your answer in the form .
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Solve the equation
giving your answers in the form , where and are rational numbers to be found.
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Solve the following equations, giving your answers correct to 3 significant figures.
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Show that
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Write the following as a single logarithm
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On the same axes, sketch the graphs of and
On each graph, label any points where the graph intersects the coordinate axes.
Write down the equations of any asymptotes for each graph.
Explain the significance of the line .
.
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Show that can be written in the form
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Α triangle is drawn inside a circle such that one side of the triangle is the diameter and all three vertices of the triangle lie on the circumference.
The radius of the circle is cm.
The two smallest angles in the triangle are and respectively where .
Find all three sides of the triangle, giving your answers in the form .
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How many real solutions does the equation have? Justify your answer.
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Without using a calculator, show that
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