The Spache Readability Formula is designed to categorize reading materials for grades 1-3. For a passage of text, the variables are S, the number of sentences, W, the number of words, and U, the number of unfamiliar words (words not on a specific list). The formula (as revised) for the grade level is

Grade level = 0.121

W

S

+ 0.082U + 0.659

b) What is the maximum possible number of sentences?

(c) What is the minimum number of sentences that would put this passage at the second-grade level?

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For maximum number of sentences; we Maximise Grade level = 0.121w/s + 0.082U + 0.659 with respect to s, number of sentences change in Grade/ Change in S = (-0.121w)/(s^2) = 0 thus s = For minimum number of sentences we integrate the fxn to get; s = 1, One sentence

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