**Q1: **

Find the slope of the tangent to the astroid , in terms of .

- A
- B
- C
- D
- E

**Q2: **

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

- A
- B
- C
- D
- E

**Q3: **

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

- A
- B
- C
- D
- E

**Q4: **

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

- A
- B
- C
- D
- E

**Q5: **

Find an equation of the tangent to the curve , at the point corresponding to the value .

- A
- B
- C
- D
- E

**Q6: **

Find the equation of the tangent to the curve , at the point corresponding to the value .

- A
- B
- C
- D
- E

**Q7: **

Find an equation of the tangent to the curve , at the point corresponding to the value .

- A
- B
- C
- D
- E

**Q8: **

Find an equation of the tangent to the curve , at the point corresponding to the value .

- A
- B
- C
- D
- E

**Q9: **

Given that , and , determine the equation of the tangent to the curve at .

- A
- B
- C
- D

**Q10: **

Determine the equation of the normal to the curve , at .

- A
- B
- C
- D

**Q11: **

Find the equation of the normal to the curves and at .

- A
- B
- C
- D

**Q12: **

A curve is defined by the parametric equations and .

Find the two equations of the tangents to curve on the point at .

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

Find all possible points on where the tangent is horizontal.

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

Find all possible points on where the tangent is vertical.

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

**Q13: **

Consider the curve , .

Find all points on this curve where the tangent is horizontal.

- A , , ,
- B ,
- C
- D ,
- EThere are no horizontal tangents.

Find all points on this curve where the tangent is vertical.

- A ,
- B
- C , , ,
- D ,
- EThere are no vertical tangents.

**Q14: **

Consider the curve , .

Find all points on this curve where the tangent is horizontal.

- A
- B ,
- C , , ,
- D ,
- Eno horizontal tangents.

Find all points on this curve where the tangent is vertical.

- A ,
- B
- C , , ,
- D ,
- Eno vertical tangents.

**Q15: **

A cycloid curve is given by the equations and .

Find the tangent to the cycloid at the point where .

- A
- B
- C
- D
- E

Find all points on the curve where the tangent is horizontal.

- A where is an integer
- B where is an integer
- C , where is an integer
- D where is an integer
- E , where is an integer

Find all points on the curve where the tangent is vertical.

- A , where is an integer
- B where is an integer
- C where is an integer
- D , where is an integer
- E where is an integer

**Q16: **

Find all possible equations of the tangents to the curve , that pass through the point .

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

**Q17: **

Find the value of at which the curve , has a vertical tangent.

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

**Q18: **

Determine the equation of the tangent to the curve , at .

- A
- B
- C
- D

**Q19: **

Consider the curve , .

Find all points on this curve where the tangent is horizontal.

- A , ,
- B ,
- C ,
- D
- EThere are no horizontal tangents.

Find all points on this curve where the tangent is vertical.

- A ,
- B ,
- C , ,
- D
- EThere are no vertical tangents.

**Q20: **

Consider the curve , .

Find all points on this curve where the tangent is horizontal.

- A
- B
- C ,
- D ,
- EThere are no horizontal tangents.

Find all points on this curve where the tangent is vertical.

- AThere are no vertical tangents.
- B
- C
- D ,
- E ,

**Q21: **

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

- A
- B
- C
- D
- E

**Q22: **

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

- A
- B
- C
- D

**Q23: **

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

- A
- B
- C
- D

**Q24: **

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

- A
- B
- C
- D

**Q25: **

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

- A
- B
- C
- D