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
- 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.
- 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.
- 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.
- Determine the customer’s surplus of a commodity at a price of N15 given that the demand function is p = 24 – q2.
- 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
- 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.
- 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.
- 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.
- Find the vector product of the following:
- A = 2i + J and b = I -3J + K
- (8,4,2) and (6,4,-3)
- If r = 3i – 2J + k
- Find the magnitude r
- Find the unit vector in the direction of r
- Calculate the direction cosine of r.
- Show that p and q are perpendiculars where:
P = 3i – 4 J + 5k and
q = 2i + J + 2k
Other Mathematics Questions
- Co-ordinate Geometry
- Permutation and Combination
- Set Theory
- Empirical Probability
- Integration & Vector Algebra