Algebra Homework
Clare Briggs
Clare Briggs is a famous cartoonist who lived from 1875 to 1930. Poems by Wilbur Nesbitt.
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Oh, and I was hoping for an example of a problem.
“See? This is the math we *USED* to teach!”
There’s a page from a math book from the 1920s here. Impenetrable at first glance but, nope, you can do these in your head.
Even if it’s been decades.Report
oh, wait
maybe you can only do #14 in your headReport
Most of the problems are amenable to a change of variable and the quadratic formula. Then once you realize that most of the answers are going to be small integers, or at least based on small integers, you can solve a number of them in your head by just trying small integers to see which work.Report
While I can sing the Quadratic to the tune of “Pop Goes the Weasel”, I can’t do it in my head anymore.
Sigh.Report
No, but for the first problem, you can run through small integers in your head and find that 1 and 4 work (so also -1 and -4). For the second, 2 and 3 work (also -2 and -3). For number eight, you chunk through the numbers that have integral fourth roots (1, 16, 81, 196, etc) to find that 196 works.
I always told my calculus students that if they were working one of my test problems and the algebra suddenly became unmanageable, they should back up because they had made a mistake. I wasn’t testing whether they could do overly complicated algebraic manipulation.Report
I don’t think you need the quadratic formula for any of these. There are enough moving parts that you’d probably want scratch paper, but these all seem fairly easily factorable.Report