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) .

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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