MCV 4U Calculus Practice (Practice Exam)

1. Evaluate the following limits:

a) b)

c) d)

2. Determine the derivative of using first principles.

3. Differentiate the following functions:

a) b)

c) d)

e) f)

g) h)

i) j)

4. Determine the equation of the tangent to

a) at the point ( -1, 8).

b) at the point (0, ln2)

5. The cost, in dollars, of water consumed by a factory is given by the function , where w is the water consumption, in litres. Determine the cost

and the rate of change of the cost when the consumption is 2000 L.

6. The position of a braking car at any time t is given by the function

Determine the acceleration and position of the car when the velocity is 22m/s.

7. Determine the equation of the tangent to at .

8. Find the coordinates of all local extrema, the points of inflection, the intervals of increase and decrease, and the concavity for the following functions:

a) b)

9. The concentration of a certain medicine t hours after injection into the bloodstream is given by . Determine when the maximum concentration of the drug in the bloodstream occurs.

10. Determine the equation of the line perpendicular to at x = 0.

11. The perimeter of an isosceles triangle is 36 cm. Find the length of the sides of the triangle of maximum area.

12. If and evaluate

Answers:

1. a) 5 b) 0 c) ¼ d) 2/5 2. 3. a) b)

c) d) e)

f) g) h) i)

j)

4. a) 32x + 2y – 1 = 0 b) x – 2y + 2ln2 = 0 5. $19.47; $0.0011/L 6. s(3) = 21 m, a(3) = 12 m/s2

7.

8 . a) Max (-2, 4), Min (2/3, 59/27) POI: (-2/3, 115/27) concave down x<-2/3, concave up x>-2/3

b) Max (1, 1/e2), Min (0, 0), POI (0.29, 0.047), (1.71, 0.096), concave down (0.29, 1.71) concave up x < 0.29, x > 1.71

9. 10. 4x + 2ey –e2 = 0 11.. 12cm, 12 cm, 12 cm (equilateral)

12.