CBSE Class 8 Annual Assessment

Chapter 5: Algebra Play

Summary

Algebra Play uses algebra to explain and invent number tricks and puzzles. Think-of-a-number tricks always land on a fixed value because the chosen number \(x\) cancels out — for example, doubling, adding \(4\), halving and subtracting \(x\) always gives \(2\). A date trick encodes month \(M\) and day \(D\) as \(100M + 165 + D\), so subtracting \(165\) recovers the date. Number pyramids, where each cell is the sum of the two below it, are decoded with letter-numbers: a three-row pyramid has top value \(a + 2b + c\). Algebra grids and calendar tricks (a \(2\times2\) calendar block sums to \(4a + 16\)) are solved by setting up and solving equations. The chapter shows how to make the largest product from given digits by using the largest as the multiplier, and proves divisibility tricks — the difference of a two-digit number and its reverse, \((10a+b)-(10b+a) = 9(b-a)\), is always divisible by \(9\); cycling the digits of \(abc\) yields a sum divisible by \(37\). Word problems on ages, animals and coins are modelled and solved with linear equations.

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