University of the Philippines, Manila College of Arts and Sciences Department of Physical Sciences and Mathematics MATHEMA MATHEMATICS TICS 11: College Algebra Second Departmental Exam September 11, 2013
I. Write TRUE if the given statement is always accurate; otherwise write FALSE.
(2 points each )
1. A system system of two quadratic equations equations in two two variables ariables may have have infinitely infinitely many solutions. 2. If a, b
∈ R and a nd c > 0, then (x − a)
2
= c has two real solutions.
3. If r1 and r2 are the two roots of a quadratic equation, then it is impossible for r1 to be rational and r2 be irrational. 4. If ax2 + bx + c = 0 has the same solution set as cx2 + bx + a = 0, then a = c . 5. If two two nonvertical nonvertical lines intersect at exactly one point, then the product of their slopes is negative.
− 5) + (y + 7) = √ 19. 7. The graphs of 11x − 2y = 3 and 2x = 11y − 3 are perpendicular to each other. 6. The point (7 , 3) is inside the circle ( x
−
2
2
8. If the sum of the roots of a quadratic quadratic equation equation is zero, then the verte vertex x of the parabola is on the y -axis. 9. The solut solution ion set of 3x + 5 =
| |
| −2x is empty.
10. If V ( ( 1, 2) is the vertex of the parabola y = ax 2 + bx + c and a nd b2
−
− 4ac > 0, then a > 0.
II. Give only your FINAL ANSWER to each of the following problem.
(2 points each )
1. Find the distance distance between between the points (3, 2) and ( 3, 2).
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2. Given Given A(0, 1), B (1, 1) and C (3 (3, y), find the value of y so that A, B and C are collinear.
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4x2 + 9 3. Give Give the set containing containing the x-intercept(s) of y = 2 . 3 x
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4. Find the slope-interc slope-intercept ept form of the equation of the line that is parallel parallel to 3 x whose x-intercept is also the x-intercept of the line 2 x 3y + 6 = 0.
−
− y + 1 = 0 and and
5. One endpoint endpoint of a line segment segment has coordinate coordinate ( 1, 2). If the midpoint of the line segment has coordinate (3, 0), find the coordinate of the other end.
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6. Determine Determine the value value of k so that the graph of y = 2x2 + kx one point.
− 2 intersects the x-axis at exactly
7. If y varies jointly as x and z , and y = 5 when x = 2 and z = = 4, find the value of y when x = e and z = = π .
necessary equation(s) equation(s) to solve solve the following following word problems. problems. Define properly properly the III. III. SET UP UP the necessary variable(s) that will answer the question. (3 points each ) 1. A total total of of 20, 000 pesos is invested in two funds paying 9% and 11% simple interest. If the annual interest from the two funds is 1500 pesos, how much is invested at each rate? 2. How many gallons of distilled water must be mixed with 30 gallons of an 80% sulfuric acid solution so that the resulting solution contains 50% sulfuric acid? 3. Neil can complete complete a certain certain typing typing job in 6 hours, while Therese Therese can accomplish accomplish the same job in 5 hours. One day, they worked together for 2 hours, but then Neil had to leave to help another typist typist on a different different job. For how many more hours did Therese Therese have to work work alone to finish the typing job after Neil had left?
IV. Show your COMPLETE SOLUTION for each of the following problem.
1. Solve Solve for for x a. b.
∈ R in each of the following:
|x − 1| + |x − 1| − 1 = 2 x + 1 −2x − 3 2x + 1 + = − 4x − 3 2x − 5x + 3 2x − x − 1
3+
4x2
2
(5 points )
2
2
(7 points )
2
2. Solve Solve for the points points of intersec intersection tion of x2 + y 2 + 4x 6y 12 = 0 and y = x2 + 4 x 6. Graph Graph the equations together and label the coordinates of the important points including the points of intersection. (15 points )
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*****END OF EXAM***** Total Points: Points: 70 “Rest if you must, but don’t quit.”
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