1.1.1 Structure of mathematical proof and methods of proof Quiz: Pearson Edexcel Maths, Unit 1

The 20 questions

1. What do we call a mathematical statement that has been proven true?

   • Conjecture
   • Axiom
   • Theorem
   • Hypothesis

2. What term describes an unproven mathematical statement that is believed to be true?

   • Lemma
   • Corollary
   • Theorem
   • Conjecture

3. Which proof method demonstrates a statement is true for all cases by systematically checking every possibility?

   • Exhaustion
   • Deduction
   • Induction
   • Contradiction

4. What proof method assumes the negation of the statement to arrive at a logical absurdity?

   • Contradiction
   • Exhaustion
   • Counterexample
   • Induction

5. What single example is sufficient to disprove a universal mathematical conjecture?

   • Counterexample
   • Base case
   • Contradiction
   • Anomalous root

6. What is the primary method of proof used in A-level maths to move logically from known facts?

   • Estimation
   • Deduction
   • Observation
   • Induction

7. Which proof type is specifically used to prove statements involving positive integers n?

   • Contradiction
   • Exhaustive testing
   • Exhaustion
   • Mathematical induction

8. In proof by induction, what is the first explicit value of n you must test?

   • n = 2
   • n = 1
   • n = k
   • n = 0

9. When testing a general algebraic statement, how do we write an even integer algebraically?

   • 2n - 3
   • 2n
   • 2n + 1
   • n^2

10. How do we algebraically represent an odd integer where n is an integer?

    • 3n
    • 2n + 1
    • n^2 + 1
    • 2n

11. To prove the sum of two even numbers is even, what expression should you add?

    • m + n
    • 2m + 2n + 1
    • 4m + 2n
    • 2m + 2n

12. What is the assumption made about n in the inductive step of mathematical induction?

    • Assume false for n = k
    • Assume true for n = k
    • Assume true for n = k + 1
    • Assume true for n = 1

13. After assuming a statement is true for n = k, what value of n must you prove it for next?

    • n = k + 2
    • n = k + 1
    • n = k - 1
    • n = 2k

14. To disprove that all prime numbers are odd, what single number is the counterexample?

    • 2
    • 9
    • 3
    • 1

15. What foundational self-evident truth in mathematics requires no proof?

    • Theorem
    • Axiom
    • Lemma
    • Corollary

16. What do we call a minor proved result used primarily as a stepping stone to a larger theorem?

    • Conjecture
    • Axiom
    • Corollary
    • Lemma

17. What term describes a proposition that follows easily from the proof of another theorem?

    • Lemma
    • Corollary
    • Conjecture
    • Axiom

18. When using proof by contradiction, what is your ultimate goal to reach?

    • A counterexample
    • A contradiction
    • A positive integer
    • A factorization

19. If you show a statement holds for all integers between 1 and 4 by testing each, what proof method is this?

    • Contradiction
    • Exhaustion
    • Deduction
    • Induction

20. What expression represents the square of any odd integer?

    • 4k^2 + 4k + 1
    • 4k^2 + 1
    • 2k^2 + 1
    • 2k + 1

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