GED and HiSET mathematics — lines, slope and functions

Linear relationships run through a large part of both high-school equivalency math tests. The GED Mathematical Reasoning test gives you the slope formula, the slope-intercept form and the point-slope form on its formula sheet, and the HiSET Mathematics test gives algebraic concepts — including functions and their graphs — its largest share of questions. Knowing where a formula is printed is not the same as knowing when to use it, and that is what this material trains.

The twelve quiz questions each practice a different skill. You find a slope from a line drawn on a grid through two marked points, and a rate from two real data pairs: a plumber's bill after two hours and after five. You read the slope and the y-intercept of a phone plan written as $y=0.10x+25$ and say what each number means in dollars and minutes. You build the equation of a line from a rate and one known job, and from two known prices for a car rental. You evaluate $f(x)=2x^2-3x+10$ at a negative input, where the signs are the whole difficulty. You decide which table fails to be a function, fill in a missing value in a linear table, pick a parallel line, find a perpendicular slope, read both intercepts of $3x + 4y = 12$, and compare two moving companies, one described by an equation and one by a table, to see whose charge rises faster per hour.

Wrong options are built from the mistakes people actually make: run over rise instead of rise over run, $-3(-2)$ written as $-6$, a fixed fee counted as part of the hourly rate, a repeated output mistaken for a repeated input. The explanation after each answer says which mistake produces which wrong option.

The flashcards collect the forms of a line, the definition of a function, the vertical line test, the slope rules for parallel and perpendicular lines, and how to find each intercept.

The written work asks you to show and explain your steps on paper: finding a slope and an equation from two bills, interpreting a starting value, testing a table, checking whether two lines are parallel or perpendicular, and comparing two rates. The oral exam asks one question at a time about the same skills and expects you to explain your reasoning aloud, the way you would explain a bill or a pay rate to someone else.

The material is independent practice written by Zestly, based on the published content of the GED and HiSET mathematics tests; it is not produced or endorsed by GED Testing Service or ETS.

• Find the slope of a line from two points, from a graph, or from two real data pairs, and state its units
• Interpret the slope and y-intercept of y = mx + b in a real situation
• Write the equation of a line from a slope and a point, or from two points
• Evaluate function notation, including at negative inputs
• Decide whether a table represents a function and complete a linear table
• Recognize parallel and perpendicular lines from their slopes and find the intercepts of a line in standard form
• Compare rates of change of two linear functions given in different forms

Practice material written by Zestly, based on the published content of the GED Mathematical Reasoning test (algebraic problem solving; the slope, slope-intercept and point-slope formulas as printed on the GED Mathematics Formula Sheet, GED Testing Service, 2014 test) and the HiSET Mathematics test (algebraic concepts: linear functions and their graphs).