Level 7-8 Algebra - Proof

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

   • An assumption
   • An estimation
   • An opinion
   • Evidence that establishes something is true

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

   • Debate
   • Guess
   • Justify
   • Question

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

Quiz written by Hilary Wilson