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Maths Quiz - Level 5-6 Algebra - Trial and Improvement (Questions)

Practise solving equations through estimation and refinement. Trial and improvement helps you find unknown values by testing, adjusting, and checking your answers in KS3 Maths.

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Fascinating Fact:

A recipe for 10 people uses 650 grams of pasta. Scaling to 16 people can be checked by trials, 1,000 grams gives 62.5 grams per person, which is sensible.

In KS3 Maths, trial and improvement is used when equations are difficult to solve exactly. You test different numbers, substitute them into the equation, and adjust until you get close to the correct answer.

Key Terms

Estimate: An educated guess used to start solving a problem.
Trial: A value you test in an equation to see how close it comes to the correct answer.
Refinement: Adjusting your trials to get closer to the correct value step by step.

Frequently Asked Questions (Click to see answers)

What is trial and improvement in KS3 Maths?

Trial and improvement is a method where you test values in an equation to find one that fits. You start with a guess, check the result, and refine it until accurate.

When is trial and improvement used?

It’s used when equations can’t be solved easily by algebraic methods, for example when the solution isn’t a whole number or includes powers or decimals.

How can I check my trial and improvement answer?

Substitute your answer back into the original equation. If both sides are almost equal, your answer is correct or very close to it.

Try These Related Quizzes

1.

You are given a value for x within an equation and told that you need to work out the answer by trial and improvement. What is the first thing you do?

[ ]	Try to remember formulas that might help
[ ]	Multiply x by six different numbers
[ ]	Make an intelligent guess at the value of x
[ ]	Move on to the next question

2.

After you have made an intelligent guess at the value of x what do you do next?

[ ]	Assume that you guessed correctly
[ ]	Guess another value for x
[ ]	Guess another three values for x
[ ]	Put your guessed value into the equation in place of x

3.

After you have put your guessed value into the equation in place of x what do you do next?

[ ]	Work out the equation using your guessed value
[ ]	Sing a hymn
[ ]	Dance a jig
[ ]	Recite a poem

4.

When you work out the equation using your guessed value, you find that your value is too high so what do you do next?

[ ]	Make another guess that is higher than your first
[ ]	Make another guess that is lower than your first
[ ]	Make three more guesses that are higher
[ ]	Make three more guesses that are lower

5.

You are told that Louise has some sisters and, within an equation, the number of sisters she has is represented by x. What would be a good first guess for the value of x?

[ ]	0
[ ]	2
[ ]	10
[ ]	20

6.

Within an equation, the boiling point of a solution is represented by x. What would be a good first guess for the value of x?

[ ]	50 degrees C
[ ]	75 degrees C
[ ]	100 degrees C
[ ]	200 degrees C

7.

You are told that the value of x lies somewhere between 300 and 400, and you are given an equation containing x. What would be a good first guess for x?

[ ]	301
[ ]	302
[ ]	350
[ ]	399

8.

x² + x³ = 80, what is the value of x?

[ ]	2
[ ]	3
[ ]	4
[ ]	5

9.

x³ - 2x = 115, what is the value of x?

[ ]	3
[ ]	5
[ ]	7
[ ]	9

10.

x² + 4x + 7 = 14x - 9, which of the following is a possible value of x?

[ ]	3
[ ]	4
[ ]	6
[ ]	8

You can find more about this topic by visiting BBC Bitesize - Equations with one unknown

Maths Quiz - Level 5-6 Algebra - Trial and Improvement (Answers)

1.

You are given a value for x within an equation and told that you need to work out the answer by trial and improvement. What is the first thing you do?

[ ]	Try to remember formulas that might help
[ ]	Multiply x by six different numbers
[x]	Make an intelligent guess at the value of x
[ ]	Move on to the next question

Choose a number which you think is likely to be close to the real value

2.

After you have made an intelligent guess at the value of x what do you do next?

[ ]	Assume that you guessed correctly
[ ]	Guess another value for x
[ ]	Guess another three values for x
[x]	Put your guessed value into the equation in place of x

Work the answer out. This will tell you whether your guess was too low, too high or exactly right

3.

After you have put your guessed value into the equation in place of x what do you do next?

[x]	Work out the equation using your guessed value
[ ]	Sing a hymn
[ ]	Dance a jig
[ ]	Recite a poem

We expect you got that one right!

4.

When you work out the equation using your guessed value, you find that your value is too high so what do you do next?

[ ]	Make another guess that is higher than your first
[x]	Make another guess that is lower than your first
[ ]	Make three more guesses that are higher
[ ]	Make three more guesses that are lower

Make one guess at a time and go through all the processes again. Gradually you will narrow it down to the correct answer

5.

You are told that Louise has some sisters and, within an equation, the number of sisters she has is represented by x. What would be a good first guess for the value of x?

[ ]	0
[x]	2
[ ]	10
[ ]	20

We know that Louise has SOME sisters so we know that 0 sisters is impossible. It is not likely that she has 10 sisters and even less likely that she has 20!

6.

Within an equation, the boiling point of a solution is represented by x. What would be a good first guess for the value of x?

[ ]	50 degrees C
[ ]	75 degrees C
[x]	100 degrees C
[ ]	200 degrees C

100 degrees C is the boiling point of water and would make a good starting point

7.

You are told that the value of x lies somewhere between 300 and 400, and you are given an equation containing x. What would be a good first guess for x?

[ ]	301
[ ]	302
[x]	350
[ ]	399

Going to the midway point is usually a good idea - depending on the answer you will then know in which half the answer is

8.

x² + x³ = 80, what is the value of x?

[ ]	2
[ ]	3
[x]	4
[ ]	5

2 would be too low and 5 too high so 3 and 4 are good numbers to begin with

9.

x³ - 2x = 115, what is the value of x?

[ ]	3
[x]	5
[ ]	7
[ ]	9

3 would be too low and 9 too high. I hope you chose 5 or 7 as your original estimate

10.

x² + 4x + 7 = 14x - 9, which of the following is a possible value of x?

[ ]	3
[ ]	4
[ ]	6
[x]	8

Each time that you make a guess, record the guess. Then by a process of trial and error you will find the correct answer