SQQM1023 Managerial Mathematics Final Exam 2019-2020 PDF

# CONFIDENTIAL ## SQQM1023 MANAGERIAL MATHEMATICS ### FINAL EXAMINATION #### FIRST SEMESTER 2019/2020 SESSION **COURSE CODE / NAME:** SQQM1023 / MANAGERIAL MATHEMATICS **DATE:** 6 JANUARY 2020 (MONDAY) **TIME:** 2:30 – 4:30 PM (2 HOURS) **VENUE:** TE/DTSO ### INSTRUCTIONS: 1. This examination p...

# CONFIDENTIAL ## SQQM1023 MANAGERIAL MATHEMATICS ### FINAL EXAMINATION #### FIRST SEMESTER 2019/2020 SESSION **COURSE CODE / NAME:** SQQM1023 / MANAGERIAL MATHEMATICS **DATE:** 6 JANUARY 2020 (MONDAY) **TIME:** 2:30 – 4:30 PM (2 HOURS) **VENUE:** TE/DTSO ### INSTRUCTIONS: 1. This examination paper contains FIFTEEN (15) questions in ELEVEN (11) printed pages, excluding the cover page. 2. Answer ALL QUESTIONS in the space provided. 3. You are NOT ALLOWED to take the examination paper out of the hall. 4. Total marks is 80. **MATRIC NO:** (in words) (in numbers) **IDENTIFICATION CARD NO.:** **LECTURER:** **GROUP:** **TABLE NO.:** ### DO NOT OPEN THIS EXAMINATION PAPER UNTIL INSTRUCTED # CONFIDENTIAL ## FOR LECTURER USE ONLY | CLO | QUESTION NO. | ALLOCATED MARKS | STUDENT'S MARKS | |---|---|---|---| | CLO1 (6M) | 1 (a),(b) | 2 | | | | 7 (a)-(d) | 4 | | | CLO2 (20M) | 15 (i)-(iii) | 7 | | | | 16 (i)-(v) | 13 | | | | 2 | 3 | | | CLO3 (22M) | 3 (i), (ii) | 5 | | | | 4 | 2 | | | | 5 (i) – (iv) | 10 | | | | 6 | 2 | | | | 8 (a), (b) | 4 | | | CLO4 (32M) | 9 | 4 | | | | 10 | 4 | | | | 11 | 5 | | | | 12 | 5 | | | | 13 | 4 | | | | 14 | 6 | | | **TOTAL** | | **80** | | # CONFIDENTIAL ## SQQM1023 MANAGERIAL MATHEMATICS ### QUESTION 1 (2 MARKS) Find the domain of the followings: a) $y = \frac{2x}{\sqrt{x-1}}$ (1 mark) b) $y = \frac{1}{x(x-2)}$ (1 mark) ### QUESTION 2 (3 MARKS) Find the linear function, f(x), such that its slope is -2 and f(2) = -7. ### QUESTION 3 (5 MARKS) The profit function for the sales (in RM) of a healthcare product is given by P(q) = 4q - 800, where q is the quantity sold. i. Find the break-even quantity. (2 marks) ii. Find the revenue function if the cost function is C(q) = 5.5q + 800. (3 marks) ### QUESTION 4 (2 MARKS) A parabola given by y = 2ax² +ax+1 intersects the straight line by y = 1-ax at point (-1,2). Find the value of a. ### QUESTION 5 (10 MARKS) The marketing research department for a company that manufactures and sells notebook computers established the following demand function: p(x) = 2000-60x, where p is the price of a notebook computer in RM, and x is the quantity, in thousands, of the notebook produced by the company. The total cost of producing these notebook computers is represented by C'(x) = 4000+500x. i. Find the total profit function. (2 marks) ii. Determine the break-even points. (4 marks) iii. Determine the output that will produce the maximum profit. (2 marks) iv. What is the maximum profit? (2 marks) ### QUESTION 6 (2 MARKS) Use the appropriate logarithmic properties, show that ln 25 + ln(2/3)=0. ### QUESTION 7 (4 MARKS) Given that $f(x) = \begin{cases} 4, x≤1 \\ x², x>1 \end{cases}$ find the following limits, i. $\lim_{x\to2} f(x)$. (1 mark) ii. $\lim_{x\to1-} f(x)$. (1 mark) iii. $\lim_{x\to1+} f(x)$. (1 mark) iv. $\lim_{x\to1} f(x)$. (1 mark) ### QUESTION 8 (4 MARKS) Differentiate a) y=(3+2x²)³ (2 marks) b) y = e³x ln(2x) (2 marks) ### QUESTION 9 (4 MARKS) Given $f(x) = \frac{x³}{x⁴+1}$, find f'(-1 1/2). ### QUESTION 10 (4 MARKS) If critical point of the function f(x, y) = 2x² + y²-ax-by+11 is (1, 1). Find the values of a and b. ### QUESTION 11 (9 MARKS) Evaluate the following integral. a) $\int \frac{(1+lnx)²}{x}dx$ (5 marks) b) $\int \frac{xe^{5x} - 3}{x}dx$ (4 marks) ### QUESTION 12 (5 MARKS) Based on FIGURE 1, find the area of the region enclosed by the curve y = x² and the line y = x. #### FIGURE 1: A diagram was included. It shows the graphs of y = x^2 and y = x. The graphs intersect at (0,0) and (1,1). ### QUESTION 13 (6 MARKS) The supply function of a certain product is given by p = 20q + 100 where p is price and q is quantity. If the market equilibrium point is (10, 300), find the producer's surplus. ### QUESTION 14 (7 MARKS) Given matrices B = [3 2], C = [2 1 9], and D = [4 5 1 4 1], [1 -1], [3 2 7] Perform each of the following operations. If the resulting matrix does not exist, state the reason. i. 2B-C (2 marks) ii. C+D (2 marks) iii. DTB (3 marks) ### QUESTION 15 (13 MARKS) Given the system of linear equations: $\begin{cases} x + 2y + 2z = 5 \\ y+3z = 3 \\ 2x+2z = 2 \end{cases}$ i. Write the above system in matrix form, AX = B. ii. Find determinant for matrix A. (2 marks) iii. Find cofactor for matrix A. (5 marks) iv. Find inverse of matrix A. (2 marks) v. Using the inverse of A in (iv), find the values of x, y, and z in the equation, $\begin{cases} x + 2y+2z = 5 \\ y+3z = 3 \\ 2x+2z = 2 \end{cases}$ (3 marks) ## ~ END OF QUESTIONS ~