1. Learning How to Find a Solution Using Trial and Improvement

2. Example A solution to the equation x 3 + 2x – 5 = 0 Lies between 1 and 2 So try 1.5 first For 1 mark

3. x 3 + 2x – 5 = 0 Remember we are seeing what happens if x = 1.5 (1.5) 3 + 2 (1.5) - 5 Try 1.5 before moving to next slide

4. x 3 + 2x – 5 = 0 (1.5) 3 + 2(1.5) – 5 = Remember x = 1.5 Is 1.5 too big or too small? 3.375 + 3 - 5 = 1.375 Compare 1.375 with 0 1.375 is bigger than 0 so the value 1.5 is too big! We need to try a smaller value, try 1.4

5. x 3 + 2x – 5 = 0 Remember we are seeing what happens if x = 1.4 (1.4) 3 + 2 (1.4) - 5 Try 1.4 before moving on to the next slide

6. x 3 + 2x – 5 = 0 (1.4) 3 + 2(1.4) – 5 = Remember x = 1.4 Is 1.4 too big or too small? 2.744 +2.8 - 5 = 0.544 Compare 0.544 with 0 0.544 is bigger than 0 so the value 1.4 is too big! We need to try a smaller value, try 1.3 We need an answer less than 0 1 mark for trying a 2nd value for x

7. x 3 + 2x – 5 = 0 Remember we are seeing what happens if x = 1.3 (1.3) 3 + 2 (1.3) - 5 Try 1.3 before moving on to the next slide

8. x 3 + 2x – 5 = 0 (1.3) 3 + 2(1.3) – 5 = 0 Remember x = 1.3 Is 1.3 too big or too small? 2.197 +2.6 - 5 = -0.203 Compare with 0 -0.203 is less than 0 so the value 1.3 is too small! The answer is either x = 1.3 or x = 1.4 We need an answer less than 0 1 mark for finding a + and -ve answer

9. x 3 + 2x – 5 = 0 What happens if x = 1.35 (1.35) 3 + 2 (1.35) - 5 1 mark for trying 1.35 We halfway between 1.3 and 1.4 need to ty the value Try 1.35 before moving on to the next slide

10. x 3 + 2x – 5 = 0 (1.35) 3 + 2(1.35) – 5 x = 1.3 or x = 1.4 we are trying 1.35 Is 1.35 too big or too small? 2.46 + 2.7 - 5 = 0.16 Compare with 0 0.16 is bigger than 0 so the value 1.35 is too big The answer is the smaller choice! x = 1.3 to 1dp 1 mark for answer So is the answer 1.3 or 1.4 ?