Calculus, 2ADV C4 2020 HSC 30
The diagram shows two parabolas `y = 4x - x^2` and `y = ax^2`, where `a > 0`. The two parabolas intersect at the origin, `O`, and at `A`.
- Show that the `x`-coordinate of `A` is `4/(a + 1)`. (2 marks)
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- Find the value of `a` such that the shaded area is `16/3`. (4 marks)
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Calculus, 2ADV C4 2017 HSC 14d
Calculus, 2ADV C4 SM-Bank 1 MC
The diagram below is the graph of `y = x^2 - x - 6`
What is the correct expression for the area bounded by the `x`-axis and the graph `y = x^2 - x - 6` between `0 <= x <= 4`?
(A) `A = int_0^4 x^2 - x - 6\ dx`
(B) `A = |\ int_0^3 x^2 - x - 6\ dx\ | + int_3^4 x^2 - x - 6\ dx`
(C) `A = int_0^3 x^2 - x - 6\ dx + |\ int_3^4 x^2 - x - 6\ dx|`
(D) `A = |\ int_0^4 x^2 - x - 6\ dx\ |`
Calculus, 2ADV C4 2015 HSC 16a
The diagram shows the curve with equation `y = x^2-7x + 10`. The curve intersects the `x`-axis at points `A and B`. The point `C` on the curve has the same `y`-coordinate as the `y`-intercept of the curve.
- Find the `x`-coordinates of points `A and B.` (1 mark)
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- Write down the coordinates of `C.` (1 mark)
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- Evaluate `int _0^2 (x^2-7x + 10)\ dx.` (1 mark)
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- Hence, or otherwise, find the area of the shaded region. (2 marks)
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Calculus, 2ADV C4 2015 HSC 7 MC
Calculus, 2ADV C4 2005 HSC 8b
Calculus, 2ADV C4 2014 HSC 12d
Calculus, 2ADV C4 2012 HSC 13b
The diagram shows the parabolas `y = 5x - x^2` and `y = x^2 - 3x`. The parabolas intersect at
the origin `O` and the point `A`. The region between the two parabolas is shaded.
- Find the `x`-coordinate of the point `A` (1 mark)
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- Find the area of the shaded region. (3 marks)
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