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AQA A Level Further Maths

Topic questions Pure mathematics Graphs & curve sketching

Graphs & curve sketching

7 questions · 59 marks · about 1 hour

Graphs and curve sketching questions

TopicGraphs & curve sketching

AQA 7367 Graphs and curve sketching 7 questions

Paper 2 June 2024, Question 15 7 marks

The diagram shows the line y = 5 – x

Figure for question 15
(a)

On the diagram above, sketch the graph of y = │x2 – 4x│, including all parts of the graph where it intersects the line y = 5 – x

(You do not need to show the coordinates of the points of intersection.)

[3]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Find the solution of the inequality

│x2 – 4x│> 5 – x

Give your answer in an exact form.

[4]
Reveal mark scheme Mark scheme for question 15(b)

Paper 2 June 2024, Question 16 9 marks

The function f is defined by

Question 16, shown as an image

where a and b are constants.

The graph of y = f(x) has asymptotes x = –2 and y = 3

(a)

Write down the value of a and the value of b

[2]
Reveal mark scheme Mark scheme for question 16(a)
(b)

The diagram shows the graph of y = f(x) and its asymptotes.

The shaded region R is enclosed by the graph of y = f(x), the x-axis and the y-axis.

Figure for question 16
(b)(i)

The shaded region R is rotated through 360° about the x-axis to form a solid.

Find the volume of this solid.

Give your answer to three significant figures.

[3]
Reveal mark scheme Mark scheme for question 16(b)(i)
(b)(ii)

The shaded region R is rotated through 360° about the y-axis to form a solid.

Find the volume of this solid.

Give your answer to three significant figures.

[4]
Reveal mark scheme Mark scheme for question 16(b)(ii)

Paper 1 June 2022, Question 9 14 marks

Roberto is solving this mathematics problem:

Figure for question 9

Roberto’s solution is as follows:

Figure for question 9
(a)

Sketch the curve C1

Figure for question 9
[2]
Reveal mark scheme Mark scheme for question 9(a)
(b)

Explain what Roberto has done wrong.

[2]
Reveal mark scheme Mark scheme for question 9(b)
(c)

Find the area enclosed by C1

[2]
Reveal mark scheme Mark scheme for question 9(c)
(d)

P and Q are distinct points on C1 for which r is a maximum. P is above the initial line.

Find the polar coordinates of P and Q

[2]
Reveal mark scheme Mark scheme for question 9(d)
(e)
Question 9, shown as an image

T maps C1 onto a curve C2

(e)(i)

T maps P onto the point Pmaths symbol

Find the polar coordinates of Pmaths symbol

[4]
Reveal mark scheme Mark scheme for question 9(e)(i)
(e)(ii)

Find the area enclosed by C2

Fully justify your answer.

[2]
Reveal mark scheme Mark scheme for question 9(e)(ii)

Paper 2 June 2022, Question 7 8 marks

Figure for question 7
(a)

Find the value of a and the value of b

[2]
Reveal mark scheme Mark scheme for question 7(a)
(b)

Solve the inequality

Question 7, shown as an image

Fully justify your answer.

[6]
Reveal mark scheme Mark scheme for question 7(b)

Paper 1 November 2021, Question 7 7 marks

The diagram below shows the graph of y maths symbol f (x) (maths symbol 4 maths symbol x maths symbol 4)

The graph meets the x-axis at x maths symbol 1 and x maths symbol 3

The graph meets the y-axis at y maths symbol 2

Figure for question 7
(a)
Figure for question 7
[2]
Reveal mark scheme Mark scheme for question 7(a)
(b)
Question 7, shown as an image

Show any axis intercepts and asymptotes.

Figure for question 7
[3]
Reveal mark scheme Mark scheme for question 7(b)
(c)

Sketch the graph of y maths symbol f (maths symbolxmaths symbol) on the axes below.

Show any axis intercepts.

Figure for question 7
[2]
Reveal mark scheme Mark scheme for question 7(c)

Paper 1 November 2020, Question 9 13 marks

The function f is defined by

Question 9, shown as an image
(a)

Find the interval (a, b) in which f (x) does not take any values.

Fully justify your answer.

[5]
Reveal mark scheme Mark scheme for question 9(a)
(b)

Find the coordinates of the two stationary points of the graph of y maths symbol f (x)

[2]
Reveal mark scheme Mark scheme for question 9(b)
(c)

Show that the graph of y maths symbol f (x) has an oblique asymptote and find its equation.

[2]
Reveal mark scheme Mark scheme for question 9(c)
(d)
Figure for question 9
[4]
Reveal mark scheme Mark scheme for question 9(d)

Paper 2 June 2019, Question 2 1 mark

Which of the straight lines given below is an asymptote to the curve

Question 2, shown as an image

where a is a non-zero constant?

Circle your answer.

Question 2, shown as an image
[1]
Reveal mark scheme Mark scheme for question 2

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Further Maths starter pack

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