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1. Consider the curve with equation x

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IB Questionbank Mathematics Higher Level 3rd edition 1

1. Consider the curve with equation x

2

+ xy + y

2

= 3.

(a) Find in terms of k, the gradient of the curve at the point (−1, k).

(5)

(b) Given that the tangent to the curve is parallel to the x-axis at this point, find the value of k.

(1) (Total 6 marks)

2. A curve C is defined implicitly by xe

y

= x

2

+ y

2

. Find the equation of the tangent to C at the point (1, 0).

(Total 7 marks)

3. Find the gradient of the tangent to the curve x

3

y

2

= cos (πy) at the point (−1, 1).

(Total 6 marks)

4. Find the equation of the normal to the curve x

3

y

3

– xy = 0 at the point (1, 1).

(Total 7 marks)

(2)

IB Questionbank Mathematics Higher Level 3rd edition 2

5. Find the gradient of the normal to the curve 3x

2

y + 2xy

2

= 2 at the point (1, –2).

(Total 6 marks)

6. Find the equation of the normal to the curve 5xy

2

– 2x

2

=18 at the point (1, 2).

(Total 7 marks)

7. Show that the points (0, 0) and ( 2 π ,  2 π ) on the curve e

(x + y)

= cos (xy) have a common tangent.

(Total 7 marks)

8. Find the gradient of the curve e

xy

+ ln(y

2

) + e

y

= 1 + e at the point (0, 1).

(Total 7 marks)

Cytaty

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