GED and HiSET mathematics — algebra

Algebra on these tests is mostly a matter of turning a situation into a line of symbols, doing something ordinary to it, and turning it back. These twelve run that route in both directions.

They begin where most candidates find the ground firmest: a phone plan with a twenty-dollar monthly fee and five dollars a gigabyte, written as 20 + 5g — with one of the wrong options putting the fee and the rate the other way round, which is the mistake that actually happens. Then an expression evaluated at a value, a two-step equation, and an equation with the unknown on both sides.

The middle of the set is about reading a relationship rather than solving one. A tank holds a hundred gallons and drains four gallons a minute, so the water left after m minutes is 100 − 4m: the rate of change is minus four, and the minus is doing real work, because the quantity being described is the water left rather than the water removed. The hundred is where that quantity starts. And a rental formula, C = 45d + 0.30m, is turned around to give the miles — take off the daily charge first, then divide by the rate per mile, which is undoing the two operations in the reverse of the order they were done.

The rest: an inequality from a shift that has to clear a hundred and twenty dollars, and which whole numbers of hours satisfy it; two expressions tested for equivalence under the distributive law; a sequence 5, 8, 11, 14 and the rule that generates it; ten tasks at two different rates adding to three hundred and twenty dollars, which is a system of two conditions solved together; and one question that asks only which of four values satisfies an equation, since substituting is a real method and not a lesser one.

Everything is in plain text — x, digits and the ordinary signs — with no notation to decode, and every money amount is written in words. Each solution was checked by substituting it back into its own equation.

Zestly is an independent study tool. It is not affiliated with GED Testing Service, which owns the GED test, or with the HiSET program, and it is not a test centre.

• Write an expression for a described charge, keeping the fixed part and the rate in their places
• Evaluate an expression at a given value
• Solve a two-step equation and one with the unknown on both sides
• Rearrange a formula to make another letter the subject, undoing operations in reverse order
• Form an inequality from a requirement and say which whole numbers satisfy it
• Read a rate of change and a starting value out of a described situation, including what a negative rate means
• Recognize equivalent expressions under the distributive law and state the rule behind a sequence
• Solve two conditions together as a system, and test a value by substitution

Written for this exercise, in plain-text algebra with money spelled out. From the bank: "A van rental is billed by the formula C = 45d + 0.30m, where C is the total cost in dollars, d is the number of days and m is the number of miles driven. Rearranged to give the number of miles, which of these is correct?" The answer is (C - 45d) / 0.30 — the daily charge comes off first, and only then does the mileage rate divide.