**Q1: **

If the rate of change in the area of a metallic plate with respect to time due to heating is given by the relation where the area is in square meters, and the time is in minutes, find the area of the plate just before heating, given that when minutes, approximating the result to the nearest two decimal places.

- A
46.14 m
^{2} - B
62.07 m
^{2} - C
71.93 m
^{2} - D
59.64 m
^{2}

**Q2: **

Suppose that and when . Find in terms of .

- A
- B
- C
- D
- E

**Q3: **

Find the function of the curve whose first derivative is and the function equals 7 when equals .

- A
- B
- C
- D

**Q4: **

Find the function of the curve whose first derivative is and the function equals when equals 1.

- A
- B
- C
- D

**Q5: **

Find the function of the curve whose first derivative is and the function equals 2 when equals 2.

- A
- B
- C
- D

**Q6: **

Determine the function if and .

- A
- B
- C
- D
- E

**Q7: **

Determine the function if and .

- A
- B
- C
- D
- E

**Q8: **

Determine the function if and .

- A
- B
- C
- D
- E

**Q9: **

Find the equation of the curve through the point with the property that the slope of the normal to the curve at is .

- A
- B
- C
- D

**Q10: **

Determine the function if , , and .

- A
- B
- C
- D
- E

**Q11: **

Determine the function if , , and .

- A
- B
- C
- D
- E

**Q12: **

Find the function on which satisfies , , and .

- A
- B
- C
- D
- E

**Q13: **

Determine the function satisfying , , and .

- A
- B
- C
- D
- E

**Q14: **

Determine the function satisfying , , and .

- A
- B
- C
- D
- E

**Q15: **

The product of the gradient of a tangent to a curve and the square of its -coordinate is 3. Find the equation of the curve given the curve passes through the point .

- A
- B
- C
- D

**Q16: **

A group of laborers are digging a hole, where the rate of change of the volume of the sand removed in cubic meters with respect to the time in hours is given by the relation . Calculate the volume of the sand dug out in 5 hours approximated to the nearest hundredth, if needed.

- A
100.00 m
^{3} - B
77.50 m
^{3} - C
80.00 m
^{3} - D
87.50 m
^{3}

**Q17: **

The rate of change of the volume of a gas, in cubic metres, with respect to its pressure is given by , where is a constant. Find the relationship between the volume of the gas and the pressure when and .

- A
- B
- C
- D

**Q18: **

Determine if .

- A
- B
- C
- D
- E

**Q19: **

Find the equation of the curve passing though the point given the gradient of the tangent at any point is . Then find the tangents at the points on the curve which intersect with the line .

- Athe curve: , the tangents: and
- Bthe curve: , the tangents: and
- Cthe curve: , the tangents: and
- Dthe curve: , the tangents: and

**Q20: **

The function satisfies for some constants and . If the graph of has an inflection at and a local minimum value at , what is ? If the graph also has a local maximum, identify it.

- A , local maximum value:
- B , local maximum value:
- C , local maximum value:
- D , local maximum value:

**Q21: **

The equation of the tangent to a curve at is . Find the equation of the curve given .

- A
- B
- C
- D

**Q22: **

The gradient at each point of a curve is inversely proportional to . The gradient is 8 when and . Determine in terms of .

- A
- B
- C
- D

**Q23: **

Given that , and when , find the relation between and .

- A
- B
- C
- D

**Q24: **

Determine the function if , , and .

- A
- B
- C
- D
- E

**Q25: **

Determine the function , if , when , , and .

- A
- B
- C
- D
- E