Trial and Improvement

You will Learn to:

- Find a value for x using trial and imrovement

Method

    A trial and improvement question will look like this.

Give x to 1 d.p.

Steps:

1. Draw a table with 4 columns: - Trial - Calculation - Value - High / Low

2. Pick a value that may work. You don’t need need to be too accurate, but don’t be too inaccurate. Let’s try 5.

   Trial	Calculation	Value	High / Low
   x = 5	(5 * 5) + 5 = 25 + 5	30	High

3. 5 was too big. Let’s try 4.

   Trial	Calculation	Value	High / Low
   x = 5	(5 * 5) + 5 = 25 + 5	30	High
   x = 4	(4 * 4) + 4 = 16 + 4	20	Low

4. 4 is too small, 5 is too big. We write: “x Lies between 4 and 5”. We can now go into Single digit Decimals. Start with 4.5 so you know which direction to go in.

Trial	Calculation	Value	High / Low
x = 5	(5 * 5) + 5 = 25 + 5	30	High
x = 4	(4 * 4) + 4 = 16 + 4	20	Low
x lies between 4 and 5
x = 4.5	(4.5 * 4.5) + 4.5 = 24.75	24.75	High

1. Continue in this manner till you find the two numbers that x lies between that are the accuracy that you want, in this case, 1 d.p.

Trial	Calculation	Value	High / Low
x = 5	(5 * 5) + 5 = 25 + 5	30	High
x = 4	(4 * 4) + 4 = 16 + 4	20	Low
x lies between 4 and 5
x = 4.5	(4.5 * 4.5) + 4.5 = 24.75	24.75	High
x = 4.4	(4.4 * 4.4) + 4.4 = 23.76	23.76	Low

1. Again, state that “x lies between 4.4 and 4.5”. Then try halfway between so that you know the answer.

Trial	Calculation	Value	High / Low
x = 5	(5 * 5) + 5 = 25 + 5	30	High
x = 4	(4 * 4) + 4 = 16 + 4	20	Low
x lies between 4 and 5
x = 4.5	(4.5 * 4.5) + 4.5 = 24.75	24.75	High
x = 4.4	(4.4 * 4.4) + 4.4 = 23.76	23.76	Low
x lies between 4.4 and 4.5
Check - Is X closer to 4.4 or 4.5?
x = 4.45	(4.45 * 4.45) + 4.45 = 24.2525	24.2525	High
x = 4.4 (1 d.p.)

Hake sure you work logically and systematically. Don’t just skip numbers. Make sure you write the “check” and “x lies between” parts.