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PrerequisiteInfo1

# PrerequisiteInfo1 - MTH 154 Pr e r e q u isit e s T h e f o...

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MTH 154 Prerequisites The following is a listing and partial description of aspects of prerequisite courses that will be issues in Calculus I. Of course, you need to be able to use this material in modeling real problems (what we used to call setting up word problems) and solving problems rather than just memorizing and regurgitating it. Geometry Pythagorean Theorem Similar Triangles Cartesian Plane Distance formula: d ° (x 1 , y 1 ), (x 2 , y 2 ) ¢ = q (x 2 x 1 ) 2 + (y 2 y 1 ) 2 Midpoint formula: the midpoint of the line segment from (x 1 , y 1 ), to (x 2 , y 2 ) is µ x 1 + x 2 2 , y 1 + y 2 2 Standard form for the equation of a circle with radius r and center (h, k) : point (x, y) is on the circle a (x h) 2 + (y k) 2 = r 2 . General form for the equation of a circle is: Ax 2 + Ay 2 + Bx + Cy + D = 0 , where A 0 . Graphs of Equations Test for symmetry about the x -axis: replacing y with y yields an equivalent equation. Test for symmetry about the y -axis: replacing x with x yields an equivalent equation. Test for symmetry with respect to the origin: replacing x with x and replacing y with y yields an equivalent equation. Lines in the Plane • Definition of slope of a line: the slope m of a non-vertical line passing through points (x 1 , y 1 ) and (x 2 , y 2 ), is m = y x = y 2 y 1 x 2 x 1 . Note: the fact that the line is non-vertical implies that x 1 x 2 . A vertical line has NO slope (not 0 slope). Point-slope formula for a line: an equation of line passing through the point (x 1 , y 1 ) and having slope m is: y y 1 = m(x x 1 ).

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