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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!
1 .
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
2 .
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
3 .
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
4 .
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
5 .
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
6 .
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
7 .
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
8 .
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!
9 .
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
10 .
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
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