Maths Midterm Review Exam
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maths_midterm_review_exam.docx1. Solve the system of linear equations, using the Gauss-Jordan elimination method.
A)
B)
C)
D)
E)
2. Consider the linear programming problem.
Sketch the feasible set for the linear programming problem.
A)
B)
C)
D)
E)
3. Indicate whether the matrix is in row-reduced form.
A) The matrix is in row-reduced form. B) The matrix is not in row-reduced form.
4. Write the equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line.
A)
B)
C)
D)
5. Solve the linear system of equations
A) Unique solution:
B) Unique solution:
C) Infinitely many solutions:
D) No solution
6. Solve the linear system of equations
A) Unique solution:
B) Unique solution:
C) Infinitely many solutions:
D) No solution
7. Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9
A) y = x +
B) y = x -
C) y = - x -
D) y = - x +
E) y is not a linear function of x.
8. Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.
A)
B)
C)
D)
9. Metro Department Store's annual sales (in millions of dollars) during 5 years were
|
Annual Sales, y |
5.8 |
6.1 |
7.2 |
8.3 |
9 |
|
Year, x |
1 |
2 |
3 |
4 |
5 |
Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.
A)
B)
C)
10. If the line passing through the points (2, a) and (5, - 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a?
A) a = -8 B) a = 4 C) a = -4 D) a = 8
11. Maximize
P= 10x + 12y
subject to
A)
B)
C)
D)
E)
12. Solve the linear programming problem by the simplex method.
A) x = 16, y = 0, z = 16, t = 0, u = 80, v = 21, w = 61, P = 180 B) x = 0, y = 16, z = 0, t = 0, u = 80, v = 21, w = 61, P = 96 C) x = 80, y = 16, z = 0, t = 0, u = 0, v = 21, w = 61, P = 68 D) x = 80, y = 0, z = 0, t = 16, u = 80, v = 21, w = 61, P = 174
13. Find the slope of the line that passes through the given pair of points.
(2, 2) and (8, 5)
A)
B)
2
C)
D)
E)
14. Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.
A)
B)
C)
D)
15. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.
A) one and only one solution
B) one and only one solution
C) one and only one solution
D) infinitely many solutions
E) no solution
16. Find the pivot element to be used in the next iteration of the simplex method.
A)
B)
C)
D)
E)
17. Find an equation of the line that passes through the points (1, 4) and ( -7, -4)
A) y = 7x + 7 B) y = x + 3 C) y = 3x - 7 D) y = 3x – 3
18. Find the constants m and b in the linear function f(x) = mx + b so that f(1) = 2 and the straight line represented by f has slope - 1.
A)
B)
C)
D)
19. Solve the linear system of equations
A) Unique solution:
B) Unique solution:
C) Infinitely many solutions:
D) No solution
20. Determine whether the given simplex table is in the final form. If so, find the solution to the associated regular linear programming problem.
A)
B)
C)
D)
E)
21. Solve the system of linear equations using the Gauss-Jordan elimination method.
A) ( 7, –3 ) B) ( 6, –2 ) C) ( 2, –6 ) D) ( –6, 2 ) E) ( –7, –2 )
22. Consider the linear programming problem.
Sketch the feasible set for the linear programming problem.
A)
B)
C)
D)
E)
23. Solve the system of linear equations using the Gauss-Jordan elimination method.
A) ( 0, 2 ) B) ( 8, 2 ) C) ( 4, –6 ) D) ( –2, 4 ) E) ( 4, –2 )
24. Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b.
A)
B)
C)
D)
E) y is not a linear function of x.
25. Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.
A)
B)
C)
D)
E)
