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GCSEFurther MathsAQAExam Questions4. CalculusDifferentiation

Differentiation (AQA GCSE Further Maths): Exam Questions

52 mins15 questions

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1
Sme Calculator3 marks

y equals x open parentheses 2 x to the power of 4 – 7 x cubed close parentheses

Work out an expression for the rate of change of y with respect to x.

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2
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y equals 2 x left parenthesis x squared – 5 x right parenthesis

Circle the expression for  fraction numerator d y over denominator d x end fraction

2 left parenthesis 2 x – 5 right parenthesis

6 x squared – 20

3 x squared – 10 x

6 x squared – 20 x

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3
Sme Calculator2 marks

y space equals space x to the power of 6 over 2 space plus space x to the power of 4 over 4

Work out  fraction numerator straight d y over denominator straight d x end fraction

Simplify your answer.

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4
Sme Calculator4 marks

Work out the rate of change of y with respect to x at the point on the curve space y equals x squared left parenthesis x squared – 9 right parenthesis spacewhere  space x equals – 2

You must show your working.

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5
Sme Calculator3 marks

y equals x squared open parentheses x minus 10 close parentheses

Work out   fraction numerator d y over denominator d x end fraction.

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6
Sme Calculator1 mark

On the grid, sketch a graph for which the rate of change of y with respect to x is always zero.

qp7a-2019-paper-2-aqa-gcse-further-maths

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7
Sme Calculator1 mark

On the grid, sketch a graph for which the rate of change of space y spacewith respect to x is always a positive constant.

qp7b-2019-paper-2-aqa-gcse-further-maths

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1
Sme Calculator3 marks

y space equals space 2 x to the power of 10 minus 3 over x squared

Work out fraction numerator straight d y over denominator straight d x end fraction.

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2
Sme Calculator4 marks

y equals fraction numerator 2 x to the power of 7 plus 15 x squared over denominator 3 x end fraction

Work out the value of x when fraction numerator straight d y over denominator straight d x end fraction equals 133.

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3
Sme Calculator3 marks

For the curve   y equals straight f open parentheses x close parentheses,

fraction numerator d y over denominator d x end fraction equals 3 over 2 x minus k x to the power of 4 plus k   where k is a constant.

When x equals negative 2 the gradient of the curve is 12.

Work out the value of k.

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4
Sme Calculator5 marks

A curve has the equation y equals x cubed plus a x squared minus 7 where a is a constant.

The gradient of the curve when x equals 4 is twice the gradient of the curve whenspace x equals negative 1 space

Work out the value of a. You must show your working.

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5
Sme Calculator5 marks

y equals x cubed plus 3 x squared minus 40 x minus 7

Find the two values of x for which the rate of change of y with respect to x is 5.

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1
Sme Calculator6 marks

v equals fraction numerator open parentheses 2 t cubed minus 1 close parentheses squared over denominator 3 t to the power of 7 end fraction

Find the rate of change of v with respect to t at the point when t equals 0.5

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2
Sme Calculator5 marks

y equals p x to the power of 4 plus q x to the power of negative 4 end exponent plus 2 is the equation of a curve, where p and q are integers.

You are given that fraction numerator straight d y over denominator straight d x end fraction equals fraction numerator 28 x to the power of 8 plus 12 over denominator x to the power of 5 end fraction.

Find the values of p and q.

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3
Sme Calculator6 marks

A curve has the equation

y equals x to the power of n plus b x cubed plus c

where n is a positive integer greater than 1, and b and c are integers.

The curve has a y-intercept of negative 5.

The curve passes through the point open parentheses 1 comma space 8 close parentheses, at which the gradient of the curve is 45.

Find the values of n, b and c.

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