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Trial and Improvement: Solving Equations with Formulas

Use trial and improvement method to solve equations and find the values within a certain range. Explore examples with decimal points and negative numbers.

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Trial and Improvement: Solving Equations with Formulas

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  1. Mathsercise-C Using Formulae Ready? Here we go!

  2. Use Trial and Improvement to solve.. x3 + 2x = 50 to 1 d.p (x lies between 3 and 4) Big/small x3 + 2x x Question 2 3 27 + 6 = 33 Too small 4 64 + 8 = 72 Too big 3.5 Very close! 42.875 + 7 = 49.875 Now choose a number between 3 and 4 3.6 Too big 46.656 + 7.2 = 53.856 3.55 Too big 44.7389 + 7.1 = 51.8389 Answer The answer is 3.5 to 1 d.p because the real answer lies between 3.5 and 3.55! You may be tempted to stop now, but you must go to one more decimal place to prove the answer to 1 d.p 1 Using Formulae

  3. Use Trial and Improvement to solve.. ½x3 - x = 90 to 1 d.p (x lies between 5 and 6) Big/small ½x3 - x x Question 3 Too small 5 62.5 – 5 = 57.5 Too small 5.5 83.1875 – 5.5 = 77.6875 Too small 5.7 92.5965 – 5.5 = 87.0965 Too Big 5.8 97.556 – 5.5 = 92.056 Now lets try 5.7 5.75 95.0547 – 5.5 = 89.5547 We know that the answer lies between 5 and 6, so now try 5.5 Answer These are very close, so now try 5.75 This is just under 90, so the real answer must lie between 5.75 and 5.8 or 5.8 to 1 d.p 2 Using Formulae

  4. Just substitute the values, but be careful with the -4….look at the signs when multiplying! Find the value of…. a) t2 – 4t when t = 3 Question 4 32 – 4x3 = - 3 9 - 12 b) p2 – 3p when p = -4 Answer (-4)2 – (3x-4) = 28 16 – (-12) 3 Using Formulae

  5. Just substitute the values, but be careful with the -2….look at the signs when multiplying! Another common mistake is that ½ x ½ is not 1!! If P = q2 – 5q…… a) Find P when q = -2 Start P = (-2)2 – (5x-2) P = 14 P = 4 + 10 Answer b) Find P when q = ½ P = (½)2 – (5x½) 4 Using Formulae P = ¼ – 2.5 P = -2.25

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