smc-975-10-Quadratic

Calculus, 2ADV C4 2024 HSC 14

The curves and intersect at two points, as shown in the diagram.

Find the -coordinates of the points of intersection of the two curves. (1 mark)

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Find the area enclosed by the two curves. (3 marks)

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b.

Calculus, 2ADV C4 2022 HSC 16

The parabola meets the line at the points and as shown in the diagram.

Find the area enclosed by the parabola and the line. (3 marks)

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Calculus, 2ADV C4 2020 HSC 30

The diagram shows two parabolas and , where . The two parabolas intersect at the origin, , and at .

Show that the -coordinate of is . (2 marks)

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Find the value of such that the shaded area is . (4 marks)

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♦ Mean mark part (b) 48%.

b.

Calculus, 2ADV C4 2017 HSC 14d

The shaded region shown is enclosed by two parabolas, each with -intercepts at and .

The parabolas have equations and , where .

Given that the area of the shaded region is 8, find the value of . (3 marks)

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Calculus, 2ADV C4 SM-Bank 1 MC

The diagram below is the graph of

What is the correct expression for the area bounded by the -axis and the graph between ?

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Calculus, 2ADV C4 2015 HSC 16a

The diagram shows the curve with equation . The curve intersects the -axis at points . The point on the curve has the same -coordinate as the -intercept of the curve.

Find the -coordinates of points (1 mark)

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Write down the coordinates of (1 mark)

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Evaluate (1 mark)

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Hence, or otherwise, find the area of the shaded region. (2 marks)

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i.

ii.

iii.

iv.

♦ Mean mark 49%.

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Calculus, 2ADV C4 2015 HSC 7 MC

The diagram shows the parabola meeting the line at and .

Which expression gives the area of the shaded region bounded by the parabola and the line?

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Calculus, 2ADV C4 2005 HSC 8b

The shaded region in the diagram is bounded by the circle of radius 2 centred at the origin, the parabola , and the -axis.

By considering the difference of two areas, find the area of the shaded region. (3 marks)

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Calculus, 2ADV C4 2014 HSC 12d

The parabola and the line intersect at the origin and at the point .

Find the -coordinate of the point . (1 mark)

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Calculate the area enclosed by the parabola and the line. (3 marks)

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ii.




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Calculus, 2ADV C4 2012 HSC 13b

The diagram shows the parabolas and . The parabolas intersect at

the origin and the point . The region between the two parabolas is shaded.

Find the -coordinate of the point (1 mark)

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Find the area of the shaded region. (3 marks)

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MARKER’S COMMENT: Less errors were made in part (ii) by students who simplified the definite integral before integrating, as shown in the worked solution.

ii.





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