KS3 Maths Quiz
You can never work out the exact area of a circle.

# Level 7-8 Algebra - Proof

Mathematics is all about logic, especially in algebra, and KS3 Maths is no different. Logic is all about using things we know to work out whether something is true or false. In other words, proof.

Proof is evidence that establishes something is true. If you can find a simple proof that precisely describes all cases of a particular situation it can save having to check a lot of different values. There are many mathematical proofs, for example 2 is a factor in all even numbers, any square number has an odd number of factors or the angles of any triangle always add up to 180o. Once we know these proofs, we can use them in many other situations.

This quiz helps to show you how important it is to be exact in maths. You'll be asked to use proofs to prove or disprove certain claims. Take your time and read each question carefully before you choose your answers. And don't forget the helpful comments after each question - they can make all the difference. Good luck!

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1. When x is an integer, 2x - 1 will always be an odd number, regardless of the value of x; what is the proof?
Any whole number multiplied by 2 will become an even number. Any even number minus 1 will become an odd number
2. The word horse has 5 letters beginning with the letter H and so does the name Henry which proves Henry is a horse. Why is this statement false?
Look at the equivalent French spelling: horse = cheval (6 letters, starting with C). This sort of silly reasoning is called a fallacy. Maths proofs have to be much more precise
3. To prove a result is the same as to ....... the result?
In maths being asked to 'justify' a result is the same as being asked to 'prove' a result
4. Which of the following is a correct definition of 'proof'?
It's just the same whether in mathematics or in a court of law
5. If one of the angles in a triangle is 90° the other two angles must add up to 90°. What fact is used to prove the truth of this statement?
The first two statements are only true of an isosceles right angled triangle. A proof must be true in all cases
6. You can never work out the exact area of a circle; what is the proof?
People claim to have worked out Pi to a million decimal places but still it is not ABSOLUTELY accurate!
7. With the exception of the number 2, all prime numbers are odd numbers; what is the proof?
The rule is 'A prime number can be divided only by itself and 1'. If a number can be divided exactly by 2 then it is NOT a prime number
8. Simon says that if a number is not prime it will always have an even number of factors. Which of these statements proves that he is wrong?
The square root of a square number is said to be a repeated factor. The 5 factors of 16 are: 1, 2, 4, 8 and 16
9. 345,345,345,345 when doubled will be an even number; what is the proof?
The result of multiplying any whole number by 2 is a number which has 2 as a factor. By definition any number which has 2 as a factor is even
10. Sam says that the sum of two prime numbers is always even. How could you prove if he is right or wrong?
Only one counter example is needed to prove that he is wrong. Since 2 is the only even prime number, any other prime added to 2 will give an odd number. 2 + 11 = 13

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