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Expressions, Formulae, and Re-arranging: Learn and Solve Problems!

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  1. Chapter 14 Formulae

  2. Learning Objectives • Write expressions in algebra • Write a formula • Know the difference between expressions & formula • Substitute values into formulae and evaluate • Substitute values into formulae with powers & roots • Re-arrange formulae • Solve problems by re-arranging formulae

  3. Writing Expressions & Formulae • An expression does not have an equal sign • A formula does have an equal sign Examples • A box of matches has 55 matches, write an expression for the total matches in n boxes. • Write a formula for the total perimeter, P, of a shape with sides x – 3, x+ 2 & x

  4. Substituting in Formula Examples • What is the value of A in the formula A = pq – r. when p = -1, q = 5 and r = -2 2. Find H when x = 5 and y = 7 in H = 3(3x – 2)

  5. Formulae with Powers & Roots Examples • Find the value of S = (½p)3, when (a) p = 4 (b) p = -4 • Calculate √(5x) when x = 0.4 • Use the formula v = √(u2 + 2as) to find the value of v when a = -9.8, s = 1.67 and u = 45.3

  6. Re-arranging Formulae • Remember that when moving terms to the other side you do the opposite Examples • Make m the subject in k = 8m/5 • Make x the subject in y = 2x + 8 • Make r the subject in A = 3r2 • Make b the subject in T = a + √b

  7. More Re-arranging Examples 5. Make the bold letters the subject in the following: (a) 3a = 4b/5 (b) 3(x – a) = x (c) e = ½mv2 (d) a(b + x) = b(2a – x)

  8. Solving Problems by Re-arranging • The volume of a cuboid, with length 7.8cm and breadth 5cm, is 136.5cm3. Calculate the height of the cuboid. • V = 4/3πr3. Calculate r when the volume is 3.56×104.

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