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| Formula |
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| A formula is formed by using: |
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| (a) mathematical symbols and variables |
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| (b) given conditions, and |
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| (c) simplification. |
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| Some well known formulae are listed below: |
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| Area of a rectangle A = l x b |
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| A = Area |
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| l = Length |
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| b = Breadth |
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| Perimeter of a rectangle P = 2(l + b) |
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| P = Perimeter |
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| Volume of a cuboid V = l x b x h |
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| V = Volume |
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| h = height |
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Simple interest  |
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| P = Principal |
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| T = Time |
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| R = Rate percent per annum |
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| In an n-sided polygon, the number of diagonals d, which can be drawn from one vertex, is 3 less than the number of sides of the polygon. Write this as a formula. Express d in terms of n. |
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| Number of diagonals = d |
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| Number of sides of a polygon = n |
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 the required formula is = d = n -3 |
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| The sum of the reciprocal of x and the reciprocal of y equals the reciprocal of m. Express this as a formula. |
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Reciprocal of  |
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Reciprocal of  |
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Reciprocal of  |
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The required formula is  |
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| The average weight of each of 'p' boys and 'q' girls is x kg and y kg respectively. Frame a formula for the average weight of (p + q) students. |
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| Average weight of each of 'p' boys = x kg |
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 Their total weight = px kg |
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| Average weight of each of 'q' girls = y kg |
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| Their total weight = qy kg |
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 Total weight of [p + q] students = [px + qy] kg |
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 Average weight of [p + q] students  |
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| A number of two digits p and q in that order is 7 greater than the number formed by reversing the digits. |
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| The ten's digit is p and the unit's digit is q. |
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| Then the number is 10p + q. |
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| The number formed by reversing the digits = 10q + p |
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 (10p + q) - (10q + p) = 7 |
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| A man walks for 'a' hours at x km/hr and then cycles a distance of 'b' kilometres at y km/hr. Write down an expression for his average speed in km/hr for the whole journey. |
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| Distance Time Speed |
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| (1) ? a x |
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| (2) b ? y |
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| In the first case, the man walks at x km/hr for 'a' hours, so he covers a distance of (xa) kilometres. In the second case, he cycles for 'b' kilometres at a speed of y km/hr, so he takes (b/y) hours. |
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 the total distance he covers = (xa + b) and |
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the total time he takes  |
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 Average speed  |
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