Questions on Integration and Vector Algebra

Integration is another aspect of calculus. It is sometimes called anti-differentiation because it is the reverse of differentiation. You can attempt up to 22 questions on differentiation by clicking on this link.

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What is Vector Algebra?

A Vector is a quantity having both magnitude and direction. And since you can’t talk about Vector without mentioning Scalar, it would be good to note that Scalar is a quantity that has magnitude but one direction. (kindly use the comment box below to ask a question).

Questions on Integration

  1. The gradient of a curve passing through the point (3,1) is given by:

dy/dx = x2 – 4x + 3

Find the equation of the curve and the area enclosed by the curve, the maximum and minimum ordinates and the x-axis.

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  1. The marginal revenue of a firm is found to be 15 – 4q. Determine the revenue function if from past sales the revenue was N1,250 when 28 units of the product were sold.


  1. If the marginal cost of producing a product in a firm is:

MC = 5q2 – 7q + 20,

Find the total variable cost of producing the first 100 units of the product in the firm.


  1. Determine the customer’s surplus of a commodity at a price of N15 given that the demand function is p = 24 – q2.


  1. If the demand function for a product is p = 155 – 3q and the supply function is p = 7q – 20


  • The equilibrium price and quantity.
  • The consumer’s surplus.
  • The producer’s surplus.

Questions on Vector Algebra

  1. A security firm decides to sell four of its stocks. If the shares are 200, 150, 300 and 250 for stocks A, B, C, and D respectively and the selling price per share N200 for A, N100 for B, N300 for C and N250 for stock D. Calculate the total receipts from the stocks.
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  1. Raphael Investment Limited decides to sell three of its stock. 300 shares of stock P, 400 shares of stock Q and 200 shares of stock R were sold. The selling price per share was N10, N8, and N5 respectively. Determine the total amount received from the sales of the stock.


  1. If A = 3i – 2J + k and  B = 2i + 3J – 4k


  • A . B and angle between the vectors A and B
  • A x B
  • |A| and |B|
  • Hence find the angle between the vectors.


  1. Find the vector product of the following:
  • A = 2i + J and       b = I -3J + K
  • (8,4,2) and       (6,4,-3)


  1. If r = 3i – 2J + k
  • Find the magnitude r
  • Find the unit vector in the direction of r
  • Calculate the direction cosine of r.
See Also:  22 Questions on Differentiation


  1. Show that p and q are perpendiculars where:

P = 3i – 4 J + 5k     and

q = 2i + J + 2k

Other Mathematics Questions

  1. Co-ordinate Geometry
  2. Permutation and Combination
  3. Set Theory
  4. Empirical Probability
  5. Integration & Vector Algebra
  6. Differentiation

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