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1. |
Find the coordinates of the midpoint of the segment that has endpoints at (-4, 7) and (2, -11). |
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A. |
(-2, -1) |
B. |
(-1, -2) |
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C. |
(-2, -4) |
D. |
(-4, -2) |
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Hint |
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2. |
If rectangle ABCD has vertices A(0, 0), B(a, 0), and C(a, b), find the coordinates of D. |
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A. |
(a, 0) |
B. |
(0, b) |
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C. |
(0, -b) |
D. |
(0, 3) |
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Hint |
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3. |
Write the equation of a circle that passes through the origin and has its center at (–3, –2). |
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A. |
(x + 3)2 + (y + 2)2 = 13 |
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B. |
(x + 3)2 + (y + 2)2 = 5 |
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C. |
(x – 3)2 + (y + 2)2 = 10 |
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D. |
(x – 3)2 + (y – 2)2 = 13 |
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Hint |
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4. |
Write the equation of the circle that is tangent to the line with equation
x + y = –3 and has its center at (4, –1). |
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A. |
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B. |
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C. |
(x – 4)2 + (y + 1)2 = 18 |
D. |
(x + 4)2 + (y – 1)2 = 18 |
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Hint |
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5. |
For the equation  , find the coordinates of the foci of the ellipse. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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6. |
Write the equation x2 + 2y2 + 2x + 4y - 1 = 0 in standard form. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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7. |
Find the vertex of the parabola with equation y2 = 4x + 20. |
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A. |
(0, 5) |
B. |
(-5, 0) |
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C. |
(5, 0) |
D. |
(0, -5) |
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Hint |
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8. |
Find parametric equations for the equation y = x2 + 5. |
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A. |
x = t, y = t2 + 5, -2 < t < 2 |
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B. |
x = t, y = t2 + 5,  |
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C. |
x = t2 + 5, y = t, |
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D. |
x = t, y = t2 + 5,  |
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Hint |
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9. |
Find the angle  of rotation for the graph of the equation
x2 - xy - y2 - 2x - 2y + 6 = 0. Round to the nearest degree. |
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A. |
-27° |
B. |
30° |
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C. |
-13° |
D. |
52° |
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Hint |
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10. |
Graph the system of inequalities  and  . |
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A. |
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B. |
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C. |
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D. |
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Hint |
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11. |
Find the equation of the asymptotes of the hyperbola with a graph of  |
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A. |
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B. |
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C. |
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D. |
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Hint |
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12. |
Find the equation of the asymptotes of a hyperbola with graph of  |
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A. |
y - 6 =  (x + 4) |
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B. |
y - 6 =  (x + 4) |
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C. |
y - 6 =  (x + 4) |
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D. |
y - 6 =  (x + 4) |
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Hint |
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13. |
Write the equation of a parabola in standard form if the general form of the equation is 6x2 + 12x - y + 8 = 0 |
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A. |
(x - 1) 2 = 6(y - 2) |
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B. |
(x - 1) 2 =  (y + 2) |
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C. |
(x + 1) 2 = (y - 2) |
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D. |
(x + 1) 2 = 6(y - 2) |
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Hint |
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14. |
Identify the conic section with equation
4(x + 4) 2 - 3(y + 3) 2 = 12. |
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A. |
parabola |
B. |
hyperbola |
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C. |
circle |
D. |
ellipse |
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Hint |
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15. |
Find the equation of the graph  after it is rotated 60° about the origin. |
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A. |
15(x')2 + 10 x'y' + 31(y')2 = 36 |
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B. |
15(x')2 - 10x'y' + 31(y')2 = 144 |
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C. |
21(x')2 + 10x'y' - 31(y')2 = 36 |
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D. |
21(x')2 + 10x'y' + 31(y')2 = 144 |
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Hint |
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16. |
Which set of inequalities represents the graph? |
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A. |
x2 + y2  2;
x2 + y2  6 |
B. |
x2 + y2 4;
x2 + y2 36 |
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C. |
x2 + y2 2;
x2 + y2 6 |
D. |
x2 + y2 4;
x2 + y2 36 |
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Hint |
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