Accuplacer: Math 2023/2024 Study Guide

Define - "ordered pairs" Correct Answer = (x, y) = a single point on a coordinate plane Define - "origin" Correct Answer = (0,0) = the point where two axes meet Explain - "quadrants" Correct Answer = when the two axes (x and y) cross they form 4 quadrants Explain what - "the distance" means Define - "distance formula" for a line(s) Correct Answer = "distance" - the length between two points on a plane - (x1, y1), (x2, y2) * does not have to be forming a line *distance is ALWAYS positive = (Distance (d) = "square root" all over - [( x2-x1)^2 + (y2-y1)^2] Explain what - "the midpoint" means Define - "midpoint formula" for a line(s) Correct Answer = "midpoint" - the middle point between two points on a plane - (x1, y1), (x2, y2) - that are forming one line *remember - "MidPOINT" = Midpoint (M) = [(x1+x2)/2] , [(y1+y2)/2] Coordinate Plane = ______________ demential. Correct Answer = 2D Describe/Define what a "one demential (1D) line" is In a 1D line, what two things need to be accounted for and explain how we can do this Correct Answer = a horizontal or vertical line = (x=0) - horizontal - (look at the location of (x) on the coordinate plane) = (y=0) - vertical - (look at the location of (y) on the coordinate plane) = Distance and Midpoint: = horizontal = (D = ("absolute value" X2-x1)) = (M = (x1+x2)/2) = vertical = (D = ("absolute value" y2-y1)) = (M = (y1+y2)/2) Define/Explain - "slope" of a line Correct Answer = (m)=(rise/run)=(change in y/change in x) = (y2-y1/x2-1) When looking at a graphed line - how can we immediately know if the slope is negative or positive Correct Answer = (-) "negative slope" = (line starts in Q3 - the line ends in Q1) = (+) "positive slope" = (lines starts in Q1 - the line ends in Q4) Horizontal Lines have ____________ slope. Correct Answer = (0) Vertical Lines have ____________ slope. Correct Answer = "undefined", "no slope", "infinite" Give the - Standard Form of a Linear Equation Describe how to quickly find the - "slope" and "y - intercept" of this specific equation Correct Answer = (Ax + By = C) *rule: A or B can NOT = (0) *rule: A can NOT be "negative" (-) = "slope" = (-A/B) = "y-intercept" = (C/B) Give the - Standard Form of a Quadratic Equation Correct Answer = (ax^2 + bx + c = 0) Give the - General Form of a line - and describe what it essential means Correct Answer = (Ax + By +C = 0) *rule: A can NOT = (0) = "some expression" [= (0)] - expression ALWAYS equals 0