KS3 algebra proof - being exact with mathematical calculations

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Maths Quiz - Level 7-8 Algebra - Proof (Questions)

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!

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

[ ]	An assumption
[ ]	An estimation
[ ]	An opinion
[ ]	Evidence that establishes something is true

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

[ ]	Debate
[ ]	Guess
[ ]	Justify
[ ]	Question

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

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

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

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 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

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

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

10.

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

Maths Quiz - Level 7-8 Algebra - Proof (Answers)

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

[ ]	An assumption
[ ]	An estimation
[ ]	An opinion
[x]	Evidence that establishes something is true

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

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

[ ]	Debate
[ ]	Guess
[x]	Justify
[ ]	Question

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

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

[x]	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

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

[ ]	All numbers over 1,000 are even numbers
[x]	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

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
[x]	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

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°
[x]	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

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?

[x]	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

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
[x]	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

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
[x]	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

10.

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

[x]	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!