Lesson 1.01

1.01 Methods of proof Quiz: OCR Maths, Unit 1

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.01, Methods of proof: 20 multiple choice questions for the OCR Maths (H240), Unit 1: Proof, written with Revision Ninja.

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The 20 questions

  1. Which method of proof assumes the statement is false to reach an impossible result?

    • Proof by induction
    • Proof by contradiction
    • Proof by deduction
    • Proof by exhaustion

  2. How many counter-examples are needed to disprove a general mathematical statement?

    • One
    • All possible cases
    • Two
    • Infinitely many

  3. What does the logical statement "P if and only if Q" mean?

    • P implies Q only
    • Two-way implication
    • One-way implication
    • No implication

  4. Which method of proof involves testing every possible individual case separately?

    • Proof by exhaustion
    • Proof by induction
    • Proof by deduction
    • Proof by contradiction

  5. What starting assumption begins the proof that root 2 is irrational?

    • Root 2 is integer
    • Root 2 is rational
    • Root 2 is imaginary
    • Root 2 is negative

  6. Which number is irrational?

    • sqrt(16)
    • 0.75
    • sqrt(3)
    • 22/7

  7. Which value of n is a counter-example to n^2 + n + 11 being prime?

    • n = 3
    • n = 1
    • n = 11
    • n = 2

  8. Which algebraic argument proves that the sum of an even integer and an odd integer is odd?

    • 2m + 2n + 2 = 2(m + n + 1), which is even
    • (2m)(2n + 1) = 2m(2n + 1), which is even
    • 2m + 2n = 2(m + n), which is even
    • 2m + (2n + 1) = 2(m + n) + 1, which is odd

  9. How many cases are tested to prove a statement for integers modulo 2?

    • 3
    • 2
    • 1
    • 4

  10. What initial assumption is made for proof by contradiction that primes are infinite?

    • Prime numbers are odd
    • Finitely many primes
    • No prime numbers
    • Only one prime

  11. Which statement is the converse of 'if x > 2 then x^2 > 4'?

    • If x <= 2 then x^2 <= 4
    • If x > -2 then x^2 > 4
    • If x^2 > 4 then x > 2
    • If x > 2 then x^2 <= 4

  12. Which is the algebraic form of the square of an odd integer?

    • (2n + 1)^2 = 4n^2 + 1 = 2(2n^2) + 1, which is odd
    • (2n + 1)^2 = 4n^2 + 4n + 2 = 2(2n^2 + 2n + 1), which is even
    • (2n + 1)^2 = 4n^2 + 4n + 1 = 2(2n^2 + 2n) + 1, which is odd
    • (2n + 1)^2 = 2(2n + 1) + 4n^2, which is even

  13. How many cases are tested when using proof by exhaustion modulo 3?

    • 3
    • 6
    • 2
    • 1

  14. Is the statement "if x^2 < 9 then x < 3" true or false for real x?

    • Negatives only
    • Always false
    • Positives only
    • Always true

  15. If p^2 = 2q^2 for integers p and q, what property must p have?

    • Odd
    • Even
    • Irrational
    • Prime

  16. What statement is the negation of "all integers satisfy n^2 > n"?

    • No n^2 > n
    • All n^2 <= n
    • Some n^2 > n
    • Some n^2 <= n

  17. Which is a valid counter-example to 'if n is prime then 2^n - 1 is prime'?

    • n = 11, since 2^11 - 1 = 2047 = 23 x 89
    • n = 5, since 2^5 - 1 = 31 is prime
    • n = 2, since 2^2 - 1 = 3 is prime
    • n = 3, since 2^3 - 1 = 7 is prime

  18. Why is checking x = 2 insufficient to prove that x^2 = 4 implies x = 2?

    • Misses x = -2
    • Equation is invalid
    • x = 2 is false
    • Ignores x = 0

  19. How many counter-examples are required to disprove a universal mathematical claim?

    • 2
    • All cases
    • 1
    • 0

  20. Which statement is logically equivalent to the implication "P implies Q"?

    • Contrapositive
    • Converse
    • Inverse
    • Negation

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