QTS0103 BUSINESS MATHEMATICS CONTINUOUS ASSESSMENT 1
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BUSINESS MATHEMATICS (QTS0103)
CONTINUOUS ASSESSMENT 1
INDIVIDUAL ASSIGNMENT (30%)
Question 1 (10 marks)
(a) Solve the following inequalities:
(1i) 12x2 + 3x + 1 < 10 [2 marks]
(ii) |3x + 5| < 4 [2 marks]
(b) The function f and g are given by f(x) = −2x2 and g(x) = 3x3 + 2 .
(i) Find the value of f(2). [1 mark]
(ii) Determine the domain of g(x). [1 mark]
(iii) Find g ∘ f(x) [1 mark]
(iv) Find the value of f ∘ g(1). [1 mark]
(c) Find the equation of a line that passes through the point (5, 0) and is perpendicular to the line that passes through the points (- 1, - 1) and (4, 2). [2 marks]
(Total 10 marks)
Question 2 (10 marks)
(a) The demand and supply functions for a product given by p = −0.3x2 + 30 and p = 2x2 + 3x − 20 respectively, where p is the unit price in dollars and x is the quantity demanded in units of a hundred.
(i) Determine the quantity supplied when the unit price is set at $20. Provide your workings to 3 decimal places when relevant. [2 marks]
(ii) Determine the equilibrium price and quantity of the product. [2 marks]
(b) Find the points of intersection(s) of the functions f(x) = x2 + 1 and g(x) = −x2 + x + 3 . Provide your workings and answers to two decimal places when relevant. [2 marks]
(c) A firm produces kitchen gloves at $0.50 per unit and sells at $1.50 per unit. The fixed cost for the firm is $50,000 per month.
(i) Calculate the firm’s monthly breakeven revenue. [2 marks]
(ii) If the firm sells 60,000 units in the month, calculate its profit/loss for the month. [2 marks]
(Total 10 marks)
Question 3 (10 marks)
(a) Find the 10th term of a geometric progression whose 8th term is 192 and the common ratio is 2. [2 marks]
(b) A machine has an original value of $30,000 and is depreciated linearly over 5 years. The scrap value of the system is $500.
(i) Determine the rate of depreciation of the machine. [2 marks]
(ii) Determine an expression giving the book value of the machine at the end of year. [2 marks]
(iii) Using your expression in part (ii), calculate the book value of the machine at
the end of the second year? [1 mark]
(c) The number of waffles sold by a bakery is approximated by the model:
After 10 days, 100 waffles were sold. Determine how many waffles will be sold after 100 days? Provide your workings to 4 decimal places when applicable. [3 marks]
(Total 10 marks)
2024-01-08