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Questions and Answers
What is the domain of the function $y = \frac{2x}{\sqrt{x-1}}$?
What is the domain of the function $y = \frac{2x}{\sqrt{x-1}}$?
The domain is $x \geq 1$.
What is the domain of the function $y = \frac{1}{x(x-2)}$?
What is the domain of the function $y = \frac{1}{x(x-2)}$?
The domain is $x \neq 0$ and $x \neq 2$.
Find the linear function $f(x)$ with a slope of -2 and $f(2) = -7$.
Find the linear function $f(x)$ with a slope of -2 and $f(2) = -7$.
The function is $f(x) = -2x + -3$.
What is the break-even quantity for the profit function $P(q) = 4q - 800$?
What is the break-even quantity for the profit function $P(q) = 4q - 800$?
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Using logarithmic properties, simplify the expression ln 25 + ln(2/3) to show it equals 0.
Using logarithmic properties, simplify the expression ln 25 + ln(2/3) to show it equals 0.
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What is the revenue function given the cost function $C(q) = 5.5q + 800$?
What is the revenue function given the cost function $C(q) = 5.5q + 800$?
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For the function $f(x)$, what is the value of $ ext{lim}_{x o 2} f(x)$?
For the function $f(x)$, what is the value of $ ext{lim}_{x o 2} f(x)$?
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How do you find the value of $a$ in the equation $y = 2ax^{2} + ax + 1$ given it intersects with $y = 1 - ax$ at point $(-1,2)$?
How do you find the value of $a$ in the equation $y = 2ax^{2} + ax + 1$ given it intersects with $y = 1 - ax$ at point $(-1,2)$?
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What is the total profit function if the demand function is $p(x) = 2000 - 60x$ and total cost function is $C'(x) = 4000 + 500x$?
What is the total profit function if the demand function is $p(x) = 2000 - 60x$ and total cost function is $C'(x) = 4000 + 500x$?
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Calculate the derivative of the function $y=(3+2x²)^{3}$.
Calculate the derivative of the function $y=(3+2x²)^{3}$.
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What are the values of a and b if the critical point of the function $f(x, y) = 2x² + y² - ax - by + 11$ is (1, 1)?
What are the values of a and b if the critical point of the function $f(x, y) = 2x² + y² - ax - by + 11$ is (1, 1)?
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Determine the point at which maximum profit occurs based on the total profit function derived.
Determine the point at which maximum profit occurs based on the total profit function derived.
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What is the area of the region enclosed by the curves $y = x^2$ and $y = x$?
What is the area of the region enclosed by the curves $y = x^2$ and $y = x$?
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Find the producer's surplus given the supply function $p = 20q + 100$ at the market equilibrium point (10, 300).
Find the producer's surplus given the supply function $p = 20q + 100$ at the market equilibrium point (10, 300).
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What is the result of the matrix operation $2B - C$ where $B = [3, 2]$ and $C = [2, 1]$?
What is the result of the matrix operation $2B - C$ where $B = [3, 2]$ and $C = [2, 1]$?
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Express the system of linear equations in matrix form, AX = B, and state the dimensions of matrix A.
Express the system of linear equations in matrix form, AX = B, and state the dimensions of matrix A.
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Study Notes
Course Information
- Course Code: SQQM1023
- Course Name: Managerial Mathematics
- Date: 6 January 2020 (Monday)
- Time: 2:30 PM – 4:30 PM (2 hours)
- Venue: TE/DTSO
- Total Marks: 80
- Number of Questions: 15
- Number of Pages: 11 (excluding cover page)
Instructions
- Answer all questions in the provided space
- Do not remove the examination paper from the hall
- The examination paper contains 15 questions across 11 pages
Question Breakdown (CLO/Marks)
- CLO1 (6 marks): Questions 1(a),(b) and 7(a)-(d)
- CLO2 (20 marks): Questions 15(i)-(iii) and 16(i)-(v)
- CLO3 (22 marks): Questions 3(i), (ii), 5(i) - (iv), 6
- CLO4 (32 marks): Questions 9, 10, 11, 12, 13, 14
Question Details (Example)
- Question 1: Find the domain of the following functions.
- Question 2: Find the linear function, f(x), with a slope of -2 and f(2) = -7.
- Question 3: Find the break-even quantity for a profit function. Calculate the revenue function given the cost function.
- Question 4: Determine the value of 'a' for a parabola given a point of intersection with a straight line.
- Question 5: Determine the total profit function given the demand function and total cost function. Calculate break-even points and maximum output.
- Question 6: Show that using logarithmic properties.
- Question 7: Calculate the limits of a piecewise function.
- Question 8: Differentiate the given functions.
- Question 9: Find the value given a specific function.
- Question 10: Find the values of 'a' and 'b' based on a given critical point
- Question 11: Evaluate the given integral
- Question 12: Find the enclosed area between a curve and a line (graphical information required)
- Question 13: Calculate the producer's surplus
- Question 14: Perform matrix operations (2B-C, and C+D).
- Question 15: Express a linear equation in matrix format, determine the determinant and inverse of the matrix. Calculate the values of x, y, and z
Additional Notes
- Pages contain detailed questions, including specific function forms and specific values
- Figures, graphs, and equations necessary for solving questions are also present.
- The exam covers Managerial Mathematics topics.
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Description
This examination for the Managerial Mathematics course consists of 15 questions across various topics, covering key learning outcomes (CLOs) such as functions, revenue, and cost analysis. Students are required to demonstrate their understanding and application of mathematical principles relevant to managerial decisions. The exam carries a total of 80 marks, structured to evaluate both theoretical knowledge and practical skills.
