IBDP Maths AA SL Predicted Paper 2 - IB Maths AA Predicted Papers

Question 1

The diagram shows the curve $y=\dfrac{2x-3}{4x^{2}+1}$ . Point P lies on the curve where the tangent has gradient $2$ .

Part a

[3]

Find the coordinates of P, given that $x_{P}>0$ .

Part b

[2]

Find the equation of the tangent at P. Give your answer correct to $3$ significant figures.

Part c

[1]

State the horizontal asymptote of the curve.

[6]

The diagram shows sector AÔB of a circle with centre O, radius $(3x+1)\text{ cm}$ and angle AÔB $=2$ radians.

Part a

[3]

Given that the area of the sector is less than $(44x-7)\text{ cm}^{2}$ , find the set of possible values of $x$ .

Part b

[2]

For $x=1$ , find the length of arc AB.

[5]

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