PRECALCULUS 3rd Trimester
Intersection of Curves (b) Assignment #3B-2
Calculate (x,y) coordinates of points of intersection (NO DECIMALS):
1.) 2.)
3.) 4.)
5.) 6.)
7.) 8.)
PRECALCULUS 3rd Trimester
Intersection of Curves (c) Assignment #3B-3
Calculate (x,y) coordinates of points of intersection (NO DECIMALS):
1.) y = x2 + 4 2.) y = x2 + 15
y = 6x - 4 y = -8x
3.) y = x2 + 5 4.) y = 3x2 + 4
y = 6x - 4 y = -10x + 1
5.) y = 5x2 - 12x
y = 15x - 10
6.) y = 6/x 7.) y = x + 1
y = 5x + 7 y = 16/(x+1)
8.) y = 3x + 1 9.) y = 2/(x-1)
y = 26/(x-2) y = 3x - 2
10.) y = 8/(x+2)
y = 6x - 1
PRECALCULUS 3rd Trimester
Intersection of Curves (d) Assignment #3B-4
Calculate coordinates of points of intersection (using quadratic formula):
1.) y = x2 - 8 2.) y = 9x2 + 2
y = 3x + 7 y = 5x + 3
3.) y = -3x2 + 9 4.) y = 8x - 14
6x + 4y = 3 y = -5/x
5.) y = 3x - 2 6.)
y = 2/(x-5)
7.) 8.)
PRECALCULUS 3rd Trimester
Lines - Point-Slope Form Assignment #3C-1
Write equation of line in point-slope form: y-y0 = m(x-x0) Line passes through the given points (NO DECIMALS):
1.) (2,1) and (5,10) 2.) (-4,4) and (4,8)
3.) (5,7) and (9,1) 4.) (-6,3) and (-1,-1)
5.) (3,21/3) and (6,5) 6.) (-2,-2) and (4,23/4)
7.) (11/2,2) and (3,-11/5) 8.) (31/3,-1) and (5,22/5)
9.) (-2,1/3) and (21/4,21/6) 10.) (32/3,31/4) and (41/4,12/5)
PRECALCULUS 3rd Trimester
Lines - General Form (Ax + By = C) Assignment #3C-2
1-4 Find y-intercept point & x-intercept point for line (NO DECIMALS):
1.) 2x + 5y = 6 3.) -3x + 4y = 20
3.) 4x - (2/5)y = -3/2 4.) (-5/3)x + 3y = 7/4
5-6 Find slope “m” and y-intercept “b” for given line (NO DECIMALS):
5.) 5x + 6y = 12 6.) -4x + 7y = 9
7-8 Find slope “m” and y-intercept “b” for given line (NO DECIMALS):
7.) (5/2)x - 4y = 7/3 8.) 5x + (-9/4)y = 2/5
9-10 Express equation of line in general form, with whole-number constants
9.) y = (¾)x - 1/2 10.) y = (-11/5)x + 3/4
11-12 Find equation of line (in general form, with whole-number constants) which passes through the given points:
11.) (-2,9) and (4,6) 12.) (3,2) and (8,10)
PRECALCULUS 3rd Trimester
Parallel Lines Assignment #3C-3
1-7 Find equation of line l2 which is PARALLEL to line l1
Express equations of lines in slope-intercept form (y = mx + b).
1.) l1: y = 2x + 1 2.) l1: y = (-5/7)x + 3
l2 contains (3,1) l2 contains (-2,3)
3.) l1: 4x + 3y = 7 4.) l1: (-2/5)x + 3y = 5
l2 contains (-4,2) l2 contains (3,4)
5.) l1 contains (3,-1) and (6,7) l2 contains (2,1)
6.) l1 contains (2,33/10) and (41/4,11/2) l2 contains (3,-3)
7.) l1 contains (-1,12/3) and (11/2,23/4) l2 contains (-2,4)
PRECALCULUS 3rd Trimester
Perpendicular Lines Assignment #3C-4
1-7 Find equation of line l2 which is PERPENDICULAR to line l1
Express equations of lines in slope-intercept form (y = mx + b).
1.) l1: y = -4x + 4 2.) l1: y = (7/4)x - 2
l2 contains (6,-1) l2 contains (5,-2)
3.) l1: 5x - 4y = 11 4.) l1: 3x + (8/3)y = 1
l2 contains (3,-2) l2 contains (-3,1)
5.) l1 contains (-2,7) and (3,1) l2 contains (-2,3)
6.) l1 contains (-1,31/2) and (11/2,13/4) l2 contains (5,-3)
7.) l1 contains (15/6,-2) and (31/3,13/5) l2 contains (4,-2)
PRECALCULUS 3rd Trimester
Distance Assignment #3C-5
1-2 Line l1 & point P are given: find distance from P to l1
1.) l1: y = 4x - 5 P = (-3,1)
2.) l1: y = -1.4x + 3 P = (2,5)
3.) Triangle ABC. Vertices: A = (-2,7), B = (4,-3), C = (7,5) Find line containing each altitude: lA, lB, lC are lines containing altitudes from vertices A, B, C. (Altitude: segment from vertex perpendicular to opposite side (or extension)) For each of the 3 pairs of altitudes, find point of intersection.
PRECALCULUS 3rd Trimester
Area of Triangles Assignment #3C-6
1-2 The 3 vertices of triangle ABC are given. Find length AB. Find length of altitude from C to side (or extension) Find area of triangle.
1.) A = (-2,3), B = (5,-1), C = (3,6)
2.) A = (-3,-1), B = (2,1), C = (5,6)
PRECALCULUS 3rd Trimester
Circles (a) Assignment #3D-1
1.) Find equation of circle with center at (5,-1) and passing through (-2,4)
2.) Find equation of circle: (-3,7) and (8,2) are endpoints of a diameter.
3.) Circle given by: x2 + y2 + 4x - 10y - 30 = 0
Calculate coordinates (h,k) of center. Calculate radius “r”
4.) Find equation of circle with center at (5,4) and tangent to the y-axis.
5.) Find equation of circle: center at (2,3) and tangent to line y = (1/3)x - 4
PRECALCULUS 3rd Trimester
Circles (b) Assignment #3D-2
1.) A = (-3,4) & B = (3,4) lie on circle x2 + y2 = 25 C = (0,0) is center
of circle. Calculate CA, CB, AB, and ÐACB
2.) A = (-3,4), B = (3,4), & D = (-4,-3) lie on circle x2 + y2 = 25
Calculate DA, DB, AB, and ÐADB
3.) A = (-2,3) & B = (2,3) lie on circle x2 + y2 = 13 C = (0,0) is center
of circle. Calculate CA, CB, AB, and ÐACB
Calculate area of region bounded by segment CA, segment CB, and arc AB
4-5 A=(0,10), B=(8,6) on circle x2 + y2 = 100 Center of circle at C=(0,0)
4.) Calculate CA, CB, AB, ÐACB, and area of triangle ACB
5.) Calculate area of region bounded by segments CA & CB and arc AB
6.) Calculate area of region between the given circle and line:
x2 + y2 = 36 y = 13 - 2x
PRECALCULUS 3rd Trimester
Ellipses Assignment #3D-3
All ellipses have foci on x-axis and center at (0,0)
1.) Find equation of ellipse with a vertex at (8,0) and one focus at (7,0)
2.) Find equation of ellipse which contains points (9,0) and (0,5)
Calculate positions of foci.
3.) Find equation of ellipse which contains points (15,0) and (10,5)
Calculate length of semi-minor axis.
4.) Find equation of ellipse which contains points (-8,5) and (0,7)
Calculate length of semi-major axis.
5.) Find equation of ellipse with eccentricity e = 0.4 and focus at (7,0)
Calculate length of semi-major axis and length of semi-minor axis.
6.) Ellipse’s equation: 8x2 + 15y2 - 50 = 0 Calculate length of
semi-major axis, length of semi-minor axis, and eccentricity.
7-8 Orbits of planets and comets are ellipses with sun at one focus.
7.) Earth: e = 0.0167 , semi-major axis = 1.50 x 1011 m
Calculate greatest and smallest distance of earth from sun
8.) Halley’s Comet: e = 0.96 , semi-major axis = 2.69 x 1012 m
Calculate greatest and smallest distance of comet from sun
PRECALCULUS 3rd Trimester
Hyperbolas Assignment #3D-4
All hyperbolas have foci on x-axis and center at (0,0)
1.) Find equation of hyperbola with a vertex at (8,0) and a focus at (12,0)
Find equations of asymptotes.
2.) Find equation of hyperbola with a vertex at (4,0) and a focus at (12,0)
Find equations of asymptotes.
3.) Find equation of hyperbola which contains points (3,0) and (7,2)
Calculate positions of foci. Find equations of asymptotes.
4.) Find equation of hyperbola which contains points (3,0) and (4,11)
Calculate positions of foci. Find equations of asymptotes.
5.) Find equation of hyperbola with eccentricity e = 3.5 and focus at (15,0)
Calculate positions of vertices. Find equations of asymptotes.
6.) Find equation of hyperbola with eccentricity e = 1.2 and focus at (15,0)
Calculate positions of vertices. Find equations of asymptotes.
7.) Hyperbola’s equation: 18x2 - 7y2 - 30 = 0
Calculate positions of vertices & foci.
8.) A rectangular hyperbola has asymptotes given by: y = x and y = -x
Calculate equation of rectangular hyperbola with focus at (5,0)
PRECALCULUS 3rd Trimester
Polar & Rectangular Coordinates (a) Assignment #3E-1
Convert to polar coordinates: x = r·cos(q) and y = r·sin(q)
Simplify using identities: sin2q + cos2q = 1 and cos2q - sin2q = cos(2q)
1.) x = -3 2.) x2 + y2 = 16
3.) 2y = -x 4.) y2 - x2 = 4
5.) (x-1)2 + y2 = 1 6.) 2x + 5y = 6
7.) x2 + (y-5)2 = 25 8.) x2 + 4y2 = 2
PRECALCULUS 3rd Trimester
Polar & Rectangular Coordinates (b) Assignment #3E-2
Convert to rectangular coordinates.
1.) r·cos(q) = 5 2.) r = 6·sin(q)
3.) q = p/4 4.) r2(4·sin2(q)-9·cos2(q)) = 36
5.) r(sin(q)-2·cos(q)) = 6 6.) r(sin(q)+r·cos2(q)) = 1
7.) r = 8·sin(q) - 2·cos(q) 8.) r = tan(q)
PRECALCULUS 3rd Trimester 2007-2008
Limits (at finite points) Assignment #1-10
1.) 2.)
3.) 4.)
5.) 6.)
7.) 8.)
9.) 10.)
11.) 12.)
13.) 14.)
15.) 16.)
17.) 18.)
19.) 20.)
PRECALCULUS 3rd Trimester 2007-2008
Limits (at infinity) Assignment #1-11
1.) 2.)
3.) 4.)
5.) 6.)
7.) 8.)
9.) 10.)
11.) 12.)
13.) 14.)
15.) 16.)