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 180^{o}. 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!

1.

Sam says that the sum of two prime numbers is always even. How could you prove if he is right or wrong?

Check a few sums

Find a sum which is odd

Do some reverse calculations

Find a sum which is even

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

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?

The similarity in spelling is accidental

No one would call a horse Henry

Henry's name starts with a capital letter

You can't mix humans with animals

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.

With the exception of the number 2, all prime numbers are odd numbers; what is the proof?

2 is a factor in all even numbers

2 is the next number after 1

4 divided by 2 gives a whole number

Exponents of 2 always give an even number

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

4.

Which of the following is a correct definition of 'proof'?

An assumption

An estimation

An opinion

Evidence that establishes something is true

It's just the same whether in mathematics or in a court of law

5.

When x is an integer, 2x - 1 will always be an odd number, regardless of the value of x; what is the proof?

2 - 1 = an odd number

2 + 1 = an odd number

2x = an even number and one less will be an odd number

Any term with a - sign in it produces an odd number

Any whole number multiplied by 2 will become an even number. Any even number minus 1 will become an odd number

6.

You can never work out the exact area of a circle; what is the proof?

Pi is required to work it out and its exact value is unknown

The area of a circle is infinite

The theorem of Pythagoras doesn't work with circles

There are no formulae for circular areas

People claim to have worked out Pi to a million decimal places but still it is not ABSOLUTELY accurate!

7.

To prove a result is the same as to ....... the result?

Debate

Guess

Justify

Question

In maths being asked to 'justify' a result is the same as being asked to 'prove' a result

8.

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?

Two sides of the triangle are equal

The other two angles must both be 45°

The angles of any triangle add up to 180°

All triangles have three angles

The first two statements are only true of an isosceles right angled triangle. A proof must be true in all cases

9.

345,345,345,345 when doubled will be an even number; what is the proof?

All numbers over 1,000 are even numbers

Doubling any number results in an even number

Each 4 has a 3 on one side and a 5 on the other side

Repeated sequences result in even numbers

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.

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?

All prime numbers have two factors

Many numbers have 3 as a factor

Any square number has an odd number of factors

That's just the way it is

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