When faced with algebra in KS3 Maths you will often have to find the value represented by a letter. This can take quite a bit of working out but the best method to help you is trial and improvement.

Trial and Improvement involves intelligent guesswork. You use this method in algebra to work out the value of a letter when there is no obvious other way. The first thing to do is make an intelligent guess as to a letter's value. For example, If x^{2} = 64 then 5 is too low a value for x and 10 is too high. Let's guess that x = 7. Next we work out the problem using our estimated value. 7^{2} = 49 so 7 is too low. How about 8? Well 8^{2} = 64: success!

OK, so not all variables are as easy as that to find but you get the idea. Have a bash at the following quiz to ease you into the process. Take your time and read each question carefully before submitting your answers. Good luck!

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

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

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?

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

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

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

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

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.

x^{2} + x^{3} = 80, what is the value of x?

2

3

4

5

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

9.

x^{3} - 2x = 115, what is the value of x?

3

5

7

9

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

10.

x^{2} + 4x + 7 = 14x - 9, which of the following is a possible value of x?

3

4

6

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

The next step is:

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