Trial and ImprovementLearning Objective:- to use trial and improvement (grade

C) to find an estimate for solutions to complex equations (grade B)

Key words: trial and improvement, estimate, equation

Tracking B

Challenge: Can you find an estimate for each of the following?

a)29.6 x 3.41b)12.1 x 456c)292 ÷ 2.13d)292 ÷ 2.93e)29.3 x4.67

12.3

Challenge...

A man buys a bag of fruit for £4.45. It contains a pineapple, two apples, three bananas and four oranges. The following information is displayed at the fruit stall:

• 1 orange and 1 apple costs 80p• 2 oranges and 1 apple costs £1.30• 1 apple and 1 banana costs 55p

How much does the pineapple cost?

x2 + x = 9

What does this mean?

Why do I need to solve it?

How can I solve it?

What if I don’t know how to start the problem?

Success CriteriaGrade D: I can substitute numbers into

an equation

Grade C: I can use trial and improvement to find an estimate for a solution

Grade B: I know how to check that my answer to the trial and

improvement is the best estimate

What is the best estimate for...

29 x 10.12

Type your answer in...

What is the best estimate for...

√106

Type your answer in...

What is the best estimate for...

29 x 2.34 15

Type your answer in...

x3 + x2 + x = 258

a) x = 3b) x = 4c) x = 5d) x = 6e) x = 7f) x = 8

Which answer is it and

why?

x3 + x2 + x = 26

a) x = 2.3b) x = 2.4c) x = 2.5d) x = 2.6e) x = 2.7f) x = 2.8

Which is the best answer

and why?

Trial and Improvement

Sometimes equations are too hard for us to solve (because they include a cubed expression, have more than one unknown etc)

In these cases, we use trial and improvement to find an estimate for the solution.

The equation x3 + x2 = 230has a solution between x = 5 and x = 6Use trial and improvement to find this solution.Give your answer correct to 1 decimal place.You must show ALL your working out.

4 marks

x3 + x2 = 230

To get full marks you must:a) try some answers between the two solutionsb) try some answers to a greater number of decimal places than the question asksc) prove beyond doubt that your answer is the

closest (by using midpoints!)

The answer lies between x = 5 and x = 6.

Use trial and improvement to find an approximate solution to

2x3 + x = 35

The answer lies between 2 and 3Give your answer to 1 decimal place

Try it for yourself...

Page Exercise

Try this one (grade A)

2x5 – 3x3 + x = 3.7xx

The answer lies between 1 and 4.

Give your answer to 1 decimal place.