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Math: Middle School: Grades 6, 7 and 8 Quiz - Algebra - Trial and Improvement (Questions)

This Math quiz is called 'Algebra - Trial and Improvement' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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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.

Have a bash at the following Math quiz to ease you into the process.

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
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Math: Middle School: Grades 6, 7 and 8 Quiz - 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
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
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
9. x3 - 2x = 115, what is the value of x?
[ ] 3
[x] 5
[ ] 7
[ ] 9
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
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