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

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This algebra quiz helps to show you how important it is to be exact in math. 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.

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

Math: Middle School: Grades 6, 7 and 8 Quiz - 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

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

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

In math 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. Math 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

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!