What is trial and improvement?

Answer 1

If you are asked to solve an equation where there is no exact answer, you might need to use trial and improvement. You need a calculator to do this.

If you are asked to give the solution to an equation to a given number of decimal places (d.p.) or significant figures (s.f.), you can be sure there is no exact solution. In this case, you might be asked to solve it through a method of trial and improvement. The question should indicate the degree of accuracy required (1 d.p., 2 s.f. etc).

Example:

An equation such as y² + 2y = 40 does not have an exact solution: the answer is a decimal number. Find the answer correct to 1 decimal place.

y² + 2y = 40

You need to work out what y is.

Let's start with y = 5:

5 × 5 + 2 × 5 = 25 + 10 = 35 - too small!

y = 6?

6 × 6 + 2 × 6 = 36 + 12 = 48 - too big!

So the answer lies between 5 and 6.

y = 5.5?

5.5 × 5.5 + 2 × 5.5 = 30.25 + 11 = 41.25 - too big!

y = 5.4?

5.4 × 5.4 + 2 × 5.4 = 29.16 + 10.8 = 39.96 - too small!

So the answer lies between 5.4 and 5.5, but must be closer to 5.4

y = 5.4 (1 d.p.)

So y = 5.4

I think it is on both an higher and foundation tier exam, so revise just in case. Your teacher will keep you noticed.