PRE-CALCULUS I REVIEW ASSIGNMENT |
QUESTIONS
1) Solve these inequalities:
a) 7 2 - 5x < 9 | b) 3 + 7x 2x - 9 | c) | d) |
e) | f) | g) | 7 - x | [ 5 | h) | 5 - 2x | > 4 |
i) x^{ 2} - 9x < - 20 |
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2) Write the equation of the line: (leave answers in point/slope form)
a) through (-1, -6) with slope of -1/3.
b) through (2, -7) and (-3, -11).
c) through (-6, 4), parallel to the X-axis.
d) through (3, 3), parallel to the Y-axis.
e) through the x-intercept of 2x + 3y - 8 = 0 and parallel to -x + 3y + 1 = 0.
f) through the y-intercept of x + 2y - 16 = 0 perpendicular to 3x + 2y - 7 = 0.
g) that is the right bisector of the line segment joining (-3, 2) and (1, 14).
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3) Write the equation of the circle:
a) center (0,0) radius 3.
b) center (-1, -4) radius 6.
c) center (2, -1) radius the distance from (2, 3) to (-1, 7).
d) radius 4, tangent to the negative X-axis and the line x = -7. (4 answers) (a diagram helps)
e) with (-1, 2) and (5, 8) as endpoints of a diameter.
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4) Find the center and radius of the follwing circles:
a) (x - 2)^{2} + (y - 1)^{2} = 16 | b) x^{ 2} + y^{ 2} - 6x - 8y + 9 = 0 |
c) x^{ 2} + y^{ 2} + 4x + 2y + 5 = 0 | d) x^{ 2} + y^{ 2} - x + 2y + 1/4 = 0 |
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SOLUTIONS
1) Inequalities
a) -7/5 < x -1 | b) x - 12/5 | c) 2 < x < 3 | d) -8 < x < 0 or x > 4 |
e) x - 4 or - 1 < x < 5 | f) x < 2 | g) 2 [ x [ 12 | h) x < ½ or x > 9/2 |
i) 4 < x < 5 |
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2) Lines and their Equations
a) | b) or | c) y = 4 |
d) x = 3 | e) | f) u y = 2/3 x + 8 |
g) |
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3) Circles and their Equations
a) x^{ 2} + y^{ 2} = 9 | b) (x + 1)^{ 2} + (y + 4)^{ 2} = 36 | c) (x - 2)^{ 2} + (y + 1)^{ 2} = 25 |
d) (x + 3)^{ 2} + (y - 4)^{ 2} = 16 (x + 3)^{ 2} + (y + 4)^{ 2} = 16 (x + 11)^{ 2} + (y + 4)^{ 2} = 16 (x + 11)^{ 2} + (y - 4)^{ 2} = 16 |
e) (x - 2)^{ 2} + (y - 5)^{ 2} = 18 |
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4) Center and Radius of Circle
a) ctr (2, 1) r = 4 | b) ctr (3, 4) r = 4 | c) ctr (-2, -1) r = 0 | d) ctr (½, -1) r = 1 |
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