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Subject: Maths

Topic: C3

C3 EXAM PRACTICE QUESTIONS

To improve your C3 Exam performance, attempt our C3 Exam questions, then view our C3 Exam Solutions and work on your weaknesses.

 

Question

For the curve with equation

 C3 EXAM PRACTICE QUESTIONS

Find the values of  C3 EXAM PRACTICE QUESTIONS and  C3 EXAM PRACTICE QUESTIONS

Solution

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Question

Differentiate with respect to  C3 EXAM PRACTICE QUESTIONS,

(a)    C3 EXAM PRACTICE QUESTIONS

(b)   C3 EXAM PRACTICE QUESTIONS

Solution

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Question

(a) Prove the identity

 C3 EXAM PRACTICE QUESTIONS

 

(b) Solve the equation

 C3 EXAM PRACTICE QUESTIONS  for   C3 EXAM PRACTICE QUESTIONS

Solution

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Question

(a) Differentiate  C3 EXAM PRACTICE QUESTIONS with respect to  C3 EXAM PRACTICE QUESTIONS

(b) Use your answer from part (a) to differentiate with respect to  C3 EXAM PRACTICE QUESTIONS

 C3 EXAM PRACTICE QUESTIONS

Solution

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Question

(i) Using the chain rule and an appropriate substitution differentiate  C3 EXAM PRACTICE QUESTIONS with respect to  C3 EXAM PRACTICE QUESTIONS

(ii) Hence show that

 C3 EXAM PRACTICE QUESTIONS

Solution

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Question

Differentiate with respect to  C3 EXAM PRACTICE QUESTIONS,

i.    C3 EXAM PRACTICE QUESTIONS

ii.    C3 EXAM PRACTICE QUESTIONS

simplify your answer where possible.

Solution

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Question

Show that

(a)   C3 EXAM PRACTICE QUESTIONS

(b)   C3 EXAM PRACTICE QUESTIONS

Solution

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Question

(a) Differentiate   C3 EXAM PRACTICE QUESTIONS with respect to  C3 EXAM PRACTICE QUESTIONS and simplify where possible.

(b) show that

 C3 EXAM PRACTICE QUESTIONS

Solution

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Question

show that

 C3 EXAM PRACTICE QUESTIONS

Solution

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Question

A curve has equation

 C3 EXAM PRACTICE QUESTIONS

(a) Using the product rule for differentiation find  C3 EXAM PRACTICE QUESTIONS,

and hence the coordinates of the turning points of  C3 EXAM PRACTICE QUESTIONS

(b) Determine the nature of these turning points.

(c) Given that the equation of the tangent to  C3 EXAM PRACTICE QUESTIONS at the point where  C3 EXAM PRACTICE QUESTIONS

can be expressed in the form  C3 EXAM PRACTICE QUESTIONS find  C3 EXAM PRACTICE QUESTIONS and  C3 EXAM PRACTICE QUESTIONS

Solution

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Question

The curve shown in the figure has equation

 C3 EXAM PRACTICE QUESTIONS

C3graph1 300x218 C3 EXAM PRACTICE QUESTIONS

 

(a) Clearly from the figure the curve has three turning points. Find them all.

(b) Using your answer from part (a) find  C3 EXAM PRACTICE QUESTIONS.

(c) Hence determine the nature of the turning points of  C3 EXAM PRACTICE QUESTIONS

Solution

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Question

A curve has equation

 C3 EXAM PRACTICE QUESTIONS

(a) show that in the interval   C3 EXAM PRACTICE QUESTIONS  there is a root  C3 EXAM PRACTICE QUESTIONS to the equation  C3 EXAM PRACTICE QUESTIONS

(b) show that  C3 EXAM PRACTICE QUESTIONS can be written in the form

 C3 EXAM PRACTICE QUESTIONS

(c) Hence using an appropriate iterative formula for  C3 EXAM PRACTICE QUESTIONS and an appropriate value for

 C3 EXAM PRACTICE QUESTIONS find the values of  C3 EXAM PRACTICE QUESTIONS and  C3 EXAM PRACTICE QUESTIONS to  C3 EXAM PRACTICE QUESTIONS decimal places.

(d) Find, to  C3 EXAM PRACTICE QUESTIONS decimal places, the coordinates of the turning points of  C3 EXAM PRACTICE QUESTIONS

Solution

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Question

(a) Express   C3 EXAM PRACTICE QUESTIONS   in terms of  C3 EXAM PRACTICE QUESTIONS

(b) Prove the identity

 C3 EXAM PRACTICE QUESTIONS

Solution

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Question

(a) Solve, for  C3 EXAM PRACTICE QUESTIONS the equation

 C3 EXAM PRACTICE QUESTIONS

(b) Show that

 C3 EXAM PRACTICE QUESTIONS

Solution

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Question

(a) Show that

 C3 EXAM PRACTICE QUESTIONS

(b) Solve, for  C3 EXAM PRACTICE QUESTIONS the equation

 C3 EXAM PRACTICE QUESTIONS

giving your answer/s to one decimal place.

Solution

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Question

(a) By writing  C3 EXAM PRACTICE QUESTIONS show that

 C3 EXAM PRACTICE QUESTIONS

(b) Show that

 C3 EXAM PRACTICE QUESTIONS

Solution

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Question

 C3 EXAM PRACTICE QUESTIONS

Given that  C3 EXAM PRACTICE QUESTIONS can be expressed in the form  C3 EXAM PRACTICE QUESTIONS

where  C3 EXAM PRACTICE QUESTIONS and  C3 EXAM PRACTICE QUESTIONS

(a) Find the values of  C3 EXAM PRACTICE QUESTIONS and  C3 EXAM PRACTICE QUESTIONS to  C3 EXAM PRACTICE QUESTIONS decimal places.

(b) Hence solve

 C3 EXAM PRACTICE QUESTIONS  for  C3 EXAM PRACTICE QUESTIONS

(c) Write down the maximum value of  C3 EXAM PRACTICE QUESTIONS and the smallest possible value of  C3 EXAM PRACTICE QUESTIONS for which this occurs.

Solution

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Question

 C3 EXAM PRACTICE QUESTIONS

(a) By expressing  C3 EXAM PRACTICE QUESTIONS in the form  C3 EXAM PRACTICE QUESTIONS where  C3 EXAM PRACTICE QUESTIONS and  C3 EXAM PRACTICE QUESTIONS

solve  C3 EXAM PRACTICE QUESTIONS for  C3 EXAM PRACTICE QUESTIONS

(b)  i.  Write down the maximum value of  C3 EXAM PRACTICE QUESTIONS

ii. Find the smallest negative value of  C3 EXAM PRACTICE QUESTIONS for which this maximum occurs.

Solution

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Question

The figure shows a sketch of the curve  C3 EXAM PRACTICE QUESTIONS with equation  C3 EXAM PRACTICE QUESTIONS

Graph2 300x219 C3 EXAM PRACTICE QUESTIONS

(a) Find   C3 EXAM PRACTICE QUESTIONS.

(b) Hence find the coordinates of the turning points of  C3 EXAM PRACTICE QUESTIONS

(c) Show that

 C3 EXAM PRACTICE QUESTIONS

and hence determine the nature of the turning points.

Solution

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Question

Differentiate the following functions with respect to  C3 EXAM PRACTICE QUESTIONS and simplify where possible.

(a)   C3 EXAM PRACTICE QUESTIONS

(b)   C3 EXAM PRACTICE QUESTIONS

Solution

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Question

 C3 EXAM PRACTICE QUESTIONS

(a) Show that there lies a root of  C3 EXAM PRACTICE QUESTIONS  in the interval   C3 EXAM PRACTICE QUESTIONS

(b) Show that  C3 EXAM PRACTICE QUESTIONS  is equivalent to   C3 EXAM PRACTICE QUESTIONS

(c) Use the iterative formula   C3 EXAM PRACTICE QUESTIONS

to calculate the values of   C3 EXAM PRACTICE QUESTIONS and  C3 EXAM PRACTICE QUESTIONS to five decimal places.

Solution

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Question

The figure shows the curve with equation    C3 EXAM PRACTICE QUESTIONS

which intersects the  C3 EXAM PRACTICE QUESTIONS-axis at point  C3 EXAM PRACTICE QUESTIONS and has two turning points.

graph3 300x218 C3 EXAM PRACTICE QUESTIONS

 

(a) Find the coordinates of the turning points of the curve.

Let point  C3 EXAM PRACTICE QUESTIONS have  C3 EXAM PRACTICE QUESTIONS-coordinate  C3 EXAM PRACTICE QUESTIONS To find an approximation to  C3 EXAM PRACTICE QUESTIONS the iterative formula

 C3 EXAM PRACTICE QUESTIONS  is used.

(b) Taking  C3 EXAM PRACTICE QUESTIONS find to five decimal places the values of  C3 EXAM PRACTICE QUESTIONS and  C3 EXAM PRACTICE QUESTIONS

(c) Show that, correct to five decimal places,  C3 EXAM PRACTICE QUESTIONS

Solution

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Question

The function  C3 EXAM PRACTICE QUESTIONS is given by

 C3 EXAM PRACTICE QUESTIONS

(a) Show that

 C3 EXAM PRACTICE QUESTIONS

The function  C3 EXAM PRACTICE QUESTIONS is given by

 C3 EXAM PRACTICE QUESTIONS

(b) Show that  C3 EXAM PRACTICE QUESTIONS

Solution

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Express   C3 EXAM PRACTICE QUESTIONS  as a single fraction in its simplest from.

Solution

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Question

(a) Simplify   C3 EXAM PRACTICE QUESTIONS

(b) Given that   C3 EXAM PRACTICE QUESTIONS

find  C3 EXAM PRACTICE QUESTIONS in terms of  C3 EXAM PRACTICE QUESTIONS

Solution

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Question

(a) Differentiate   C3 EXAM PRACTICE QUESTIONS  with respect to  C3 EXAM PRACTICE QUESTIONS

(b) Find   C3 EXAM PRACTICE QUESTIONS  for   C3 EXAM PRACTICE QUESTIONS

Solution

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Question

Differentiate with respect to  C3 EXAM PRACTICE QUESTIONS

(a)  C3 EXAM PRACTICE QUESTIONS

(b)  C3 EXAM PRACTICE QUESTIONS

simplifying where possible.

Solution

…………………………………………………………………………………………………………………………………………

Question

Differentiate with respect to  C3 EXAM PRACTICE QUESTIONS

(a)  C3 EXAM PRACTICE QUESTIONS

(b)  C3 EXAM PRACTICE QUESTIONS

simplifying where possible.

Solution

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Question

(a) Find   C3 EXAM PRACTICE QUESTIONS  at the point  C3 EXAM PRACTICE QUESTIONS  on the curve with equation  C3 EXAM PRACTICE QUESTIONS

(b) Differentiate  C3 EXAM PRACTICE QUESTIONS  with respect to  C3 EXAM PRACTICE QUESTIONS

Solution

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