RE-PREC2111 PRE-CALCULUS

 RE-PREC2111 PRE-CALCULUS

PREVIEW:

The x’y’-coordinate system has been rotated θ degrees from the xy-coordinate system. The coordinates of a point in the xy-coordinate system are given. Find the coordinates of the point in the rotated coordinate system. a.Θ = 90 o , (0, 3) Select one: a. (-3, 0) b. (0, -3) c. (-3, 0) d. (3, 0) Feedback The correct answers are: (-3, 0), (0, -3), (3, 0), (-3, 0) Question 2 Correct Mark 1.00 out of 1.00 Flag question Question text Find the standard equation of the parabola which satisfies the given condition: Vertex (-8, 3), directrix x = -10.5 Select one: a. (y - 3) 2  = 10(x + 8) b. (y - 3) 2  = -10(x + 8) c. (y + 3) 2  = 10(x + 8) d. (y - 3) 2  = 10(x - 8) Feedback The correct answer is: (y - 3) 2  = 10(x + 8) Question 3 Correct Mark 1.00 out of 1.00 Flag question Question text The x’y’-coordinate system has been rotated θ degrees from the xy-coordinate system. The coordinates of a point in the xy-coordinate system are given. Find the coordinates of the point in the rotated coordinate system. b. Θ = 30 o , (1, 3) Select one: a. b. c. d. Feedback The correct answers are: , , , Question 4 Correct Mark 1.00 out of 1.00 Flag question Question text Find the specified nth term in the expansion of the binomial. (x + y) 10 , n = 4 Select one: a. 120x 7 y 3 b. 60x 7 y 3 c. 120x 3 y 7 d. 30x 8 y2 Feedback Your answer is correct. The correct answer is: 120x 7 y 3 Question 5 Correct Mark 1.00 out of 1.00 Flag question Question text What is the standard form of the equation of the circle x 2  + y 2  + 10x - 4y - 7 = 0? Select one: a. (x - 5) 2  + (y - 2) 2  = 6 2 b. (x - 5) 2  + (y + 2) 2  = 6 2 c. (x + 5) 2  + (y + 2) 2  = 6 2 d. (x + 5) 2  + (y - 2) 2  = 6 2 Feedback Your answer is correct. The correct answer is: (x + 5) 2  + (y - 2) 2  = 6 2 Question 6 Correct Mark 1.00 out of 1.00 Flag question Question text Find the standard equation of the hyperbola which satisfies the given condition: asymptotes y=43x+13 and y=−43x+413,a vertex (−1,7)y=43x+13 and y=−43x +413,a vertex (−1,7) Select one: a. (x−5)236−(y−7)264=1(x−5)236−(y−7)264=1 b. (x+2)216−(y−4)220=8(x+2)216−(y−4)220=8 c. (x−4)226−(y−8)264=1(x−4)226−(y−8)264=1 d. (x−6)240−(y−4)22=4(x−6)240−(y−4)22=4 Feedback The correct answer is: (x−5)236−(y−7)264=1(x−5)236−(y−7)264=1 Question 7 Correct Mark 1.00 out of 1.00 Flag question Question text In order to graph a circle one must graph all the points that are equidistant from: Select one: a. two points, one inside and one outside the circle. b. a single point at the center. c. a single point outside the circle. d. one point and one line, like a parabola. Feedback Your answer is correct. The correct answer is: a single point at the center. Question 8 Correct Mark 1.00 out of 1.00 Flag question Question text Use any method to solve the system. 3x – 5y = 7 2x + y = 9 Select one: a. (0, 2) b. (2, 1) c. (8, 2) d. (4, 1) Feedback The correct answer is: (4, 1) Question 9 Correct Mark 1.00 out of 1.00 Flag question Question text What kind of symmetry does a circle have? Select one: a. Horizontal b. Vertical c. Radial d. All of the answer choices are correct. Feedback Your answer is correct. The correct answer is: All of the answer choices are correct. Question 10 Correct Mark 1.00 out of 1.00 Flag question Question text Find the equation in standard form of the ellipse whose foci are F 1  (-8,0) and F 2  (8,0), such that for any point on it, the sum of its distances from the foci is 20. Select one: a. b. c. d. Feedback The correct answer is: Question 11 Correct Mark 1.00 out of 1.00 Flag question Question text Find the standard equation of the parabola which satisfies the given condition: Vertex (-4, 2), focus (-4, -1) Select one: a. (x + 4) 2  = -12(y - 2) b. (x + 4) 2  = -12(y + 2) c. (x + 4) 2  = 12(y - 2) d. (x - 4) 2  = -12(y - 2) Feedback The correct answer is: (x + 4) 2  = -12(y - 2) Question 12 Correct Mark 6.00 out of 6.00 Flag question Question text Give the coordinates (enclose the coordinates in parentheses) of the foci, vertices, and covertices of the ellipse with equation Foci Vertices Covertices (-12, 0) (12, 0) (-13, 0) (13, 0) (0, -5) (0, 5) Question 13 Correct Mark 1.00 out of 1.00 Flag question Question text Find the sum using the formulas for the sums of powers of integers. Answer: Feedback The correct answer is: -3402 Question 14 Correct Mark 1.00 out of 1.00 Flag question Question text Find the sum using the formulas for the sums of powers of integers. Answer: Feedback The correct answer is: 120 Question 15 Correct Mark 1.00 out of 1.00 Flag question Question text Find the center point of the following circle x 2  + y 2  + 8x + 4y - 3 = 40. Select one: a. (-4, -2) b. (4, 2) c. (2, 4) d. (-2, -4) Feedback Your answer is correct. The correct answer is: (-4, -2) Question 16 Correct Mark 1.00 out of 1.00 Flag question Question text Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form. a. xy + 1 = 0 Select one: a. b. c. d. Feedback The correct answer is: Question 17 Correct Mark 1.00 out of 1.00 Flag question Question text Two control towers are located at points Q(-500, 0) and R(500, 0), on a straight shore where the x-axis runs through (all distances are in meters). At the same moment, both towers sent a radio signal to a ship out at sea, each traveling at 300 m/µs. The ship received the signal from Q 3 µs (microseconds) before the message from R.

 

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