**Q3: **

Find the equation of the tangent to that has gradient .

- A
- B
- C
- D

**Q4: **

Do the curves and intersect orthogonally at the origin?

- Ayes
- Bno

**Q5: **

At a point on the curve with , , the tangent makes an angle of with the positive -axis. Find the equation of the tangent at that point.

- A
- B
- C
- D

**Q6: **

Find the points on the curve at which the tangent is parallel to the axis.

- A ,
- B
- C
- D ,

**Q7: **

Find the points that lie on the curve at which the tangent is parallel to line .

- A ,
- B ,
- C ,
- D ,

**Q8: **

A tangent to forms an isosceles triangle when taken with the positive - and -axes. What is the equation of this tangent?

- A
- B
- C
- D

**Q9: **

The point lies on the curve . Find and the equation of the tangent to the curve at this point.

- A , equation of the tangent:
- B , equation of the tangent:
- C , equation of the tangent:
- D , equation of the tangent:

**Q10: **

The tangent at to the curve makes a positive angle with the positive -axis. Find this angle.

- A
- B
- C
- D
- E

**Q11: **

Determine the points on a curve at which the tangent to the curve is perpendicular to the straight line .

- A
- B
- C
- D

**Q12: **

Find the equation of the tangent to the curve at the point .

- A
- B
- C
- D

**Q13: **

Find the equation of the tangent to the curve at the point.

- A
- B
- C
- D

**Q14: **

Find the equations of the tangent lines of the curves and at the intersection points, and state whether the curves intersect orthogonally or not.

- A , , , , intersect orthogonally
- B , , , , do not intersect orthogonally
- C , , , , do not intersect orthogonally
- D , , , , intersect orthogonally

**Q15: **

The two curves and intersect orthogonally. Find all the possible values of .

- A
- B25
- C50
- D

**Q16: **

Determine the gradient of the tangent to at its intersection with the -axis.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q17: **

At a point on the curve with , , the tangent makes an angle of with the positive -axis. Find the equation of the normal at that point.

- A
- B
- C
- D

**Q18: **

Find the area of the triangle bounded by the -axis, the tangent, and the normal to the curve at the point to the nearest thousandth.

**Q19: **

Find the equation of the normal to the curve of the function at .

- A
- B
- C
- D

**Q20: **

Find the equation of the normal to the curve at the point .

- A
- B
- C
- D
- E

**Q21: **

The tangent at to the curve makes a positive angle with the positive -axis. Find this angle.

- A
- B
- C
- D
- E

**Q22: **

Find the equation of the tangent to the curve at .

- A
- B
- C
- D

**Q23: **

At the point , determine the equation of the normal to the curve represented by the equation .

- A
- B
- C
- D

**Q24: **

Find the points of where the angle between the tangent and the positive -axis has cosine .

- A ,
- B ,
- C ,
- D ,

**Q25: **

Find the equation of the tangent to the curve at .

- A
- B
- C
- D