Pre-Calculus Practice Problems PDF

Rectangular Coordinates 1. Plot the points in the Cartesian plane. a. (-4,2), (-3,-6), (0,5), (1,-4) b. (1, -1/3), (3/4, 3), (-3,4), (-4/3, -3/2) Find the coordinates of the point. a. The point is located three units to the left of the y-axis and four units above the x-axis. b. The point is loca...

Rectangular Coordinates 1. Plot the points in the Cartesian plane. a. (-4,2), (-3,-6), (0,5), (1,-4) b. (1, -1/3), (3/4, 3), (-3,4), (-4/3, -3/2) Find the coordinates of the point. a. The point is located three units to the left of the y-axis and four units above the x-axis. b. The point is located eight units below the x-axis and four units to the right of the y-axis. c. The point is located five units below the x-axis and the coordinates of the point are equal. Determine the quadrant in which (x,y) is located so that the condition(s) is (are) satisfied. a. x > 0 and y < 0 b. x = -4 and y > 0 c. x < 0 and y > 0 d. x and y > 0 Find the distance between the points. a. (6,-3), (6,5) b. (1,4), (8,4) c. (-3, -1), (2, -1) II. Graphs of Equations 1. Complete the table. Use the resulting solution points to sketch the graph of the equation. a. y = -2x + 5 b. y = 3/4x – 1 Find the x- and y-intercepts of the graph of the equation. a. y = 8 – 3x b. y = 2x3 – 4x2 (6pts) c. y 2 = x + 1 Use the algebraic test to check for symmetry with respect to both axes and the origin. a. x 2 – y = 0 b. y = x4 – x 2 + 3 c. y = x3 Linear Equations in two variables 1. Sketch the lines through the point with the indicated slopes on the same set of coordinate axes. a. Point: (2, 3) Slope: i.) 0 ii.) 1 iii.) 2 iv.) -3 b. Point: (-4, 3) Slope: i.) 3 ii.) -3 iii.) ½ iv.) undefined Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line. a. y = 5x + 3 b. 7x + 6y = 30 c. y – 3 = 0 Plot the points and find the slope of the line passing through the pair of points. a. (-6, -1), (-6, 4) b. (11/2, -4/3), (-3/2, -1/3) c. (4.8, 3.1), (-5.2, 1.6)