SEMESTER EXAM GUIDE MATHEMATICS IV
NOTE: Remember that answered phone is required to submit review. On Monday 18 will review progress with their guide and clarify doubts
SOLVE WHAT IS ASKED
1. Find the distance between pairs of points whose coordinates are:
a) (4, 1), (3, -2)
b) (-7, 4), (1, -11)
2. Find the perimeter of the triangles whose vertices are
a) (0.5), (-3,4), (0, -3)
b) (-2.5) (4.3), (7 , -2)
3. Prove that triangles given by the coordinates of its vertices isosceles
a) (2, 4), (5, 1), (6, 5)
b) (6, 7), (-8, -1), (-2, -7)
4. Demonstrate, by the distance formula, the following points are collinear
(0, 4), (3, -2) (-2, 8)
5. Find the coordinates of the midpoints, the segment bounded by the following
a) (-2.3) (-6, 1)
b) (1, 2), (-3, 10)
6. Find the slope and angle of inclination of the lines through the following
a) (1.3) (7.1)
b) (-5.3) (2, -3)
7. Find one of the interior angles of triangles whose vertices are
a) (4.2), (0.1), (6, -1)
b) (-3, -1), (4.4), (-2.3)
8. Find areas of polygons, the coordinates of the vertices are:
a) (0.4), (-8.0), (-1, -4)
b) (1.5), (-2.4 ), (-3, -1), (2, -3), (5.1)
9. Find equations of lines that meet the following conditions
a) P (0, -3), m = -2
b) P (0.4), m = 1 / 3
c) (2, -3) and (4.2)
d) (-4.1) and (5, -3)
e) a = 5, b = 1
f) a = 7, b = -5
g) m = -4 , b = 5
h) m = 2, b = 3
10 Find the equation of two lines through A, one parallel and one perpendicular to the line that corresponds to the given equation:
a) A (7, 0), 9x + y - 3 = 0
b) A (-4, 0), 4x + 3y - 2 = 0
11. Find the distance from the line at any given point
a) x + y -3 = 0, (4, 5)
b) 3x + y - 10 = 0, (-3, -1)
12. In the triangle of vertices A (-5.6), B (-1, -4), C (3.2), Find a) the equations of the medium and the point of intersection of the same b) their bisectors and
intersection point 13. Find the equations of the altitudes of the triangle whose vertices are A (-5.6), B (-1, -4), C (3.2), and their point of intersection
14. Find the equation of the circle:
b) center point (0.5) and radius 5
c) center point (-4.2) and diameter 8
d) center point (4, -1 ) and passing through the point (-1.3)
e) across the segment joining the points (-3.5) (7, -3)
15. Find the center and radius of the circles below. Determine if each of them is real, imaginary or reduced to a point.
a) x2 + y2-8x + 10y - 12 = 0
b) 2x2 + 2y2 - x = 0
16. A circle has its center at point C (0, -2) and is tangent to the line 5x - 12y + 2 = 0. Halle its equation
17. Find the equation of the circle whose radius is 5 and whose center is the point of intersection of lines
3x - 2y - 24 = 0 and 2x + 7y + 9 = 0
18. Write the equation of the parabola with vertex at the origin and satisfies the condition in each case
a) focus on (-4.0)
b) focus on the axis and passes through (2.8)
c) opens to the right and straight length is 16
lada 19. Find the coordinates of the focus, the coordinates of the extreme right side and the equation of the guideline in each case
a) y2 =-16x b) x2 = 12y
20. Write the equation of the parabola, which satisfies the following conditions
a) vertex (0.3), focus (4.3)
b) vertex (5, -2), focus (-2, -2)
c) vertex (4, -1), right side 8, is opened to the right
21. Determine for each equation of the parabola the coordinates of the vertex, focus, and the extreme right side
a) y2 + 12x - 48 = 0
b) and 2 - 8y + 6x + 16 = 0
c) x2 - 8x + 6y - 8 = 0
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