Lesson A1

A1 Mathematical proof, disproof and contradiction Quiz: AQA Maths, Unit 1

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson A1, Mathematical proof, disproof and contradiction: 20 multiple choice questions for the AQA Maths (7357), Unit 1: Proof, written with Revision Ninja.

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The 20 questions

  1. Which method of proof tests every individual case in a finite set of possibilities?

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

  2. What is the primary purpose of a counter-example in mathematics?

    • Simplifying an equation
    • Disproving a statement
    • Finding a limit
    • Proving a statement

  3. What is the initial assumption made in a proof by contradiction?

    • Statement is false
    • Statement is true
    • Statement is zero
    • Statement is undefined

  4. Which number has a classic proof of irrationality by contradiction?

    • 22/7
    • 0.75
    • sqrt(9)
    • sqrt(2)

  5. In proving that sqrt(2) is irrational, what contradiction is reached?

    • p and q are odd
    • p and q are prime
    • p and q share factors
    • p and q are negative

  6. What initial assumption is used in Euclid's proof that primes are infinite?

    • Only odd primes
    • Infinitely many primes
    • Finitely many primes
    • No prime numbers

  7. What is the smallest positive integer n that disproves 'n^2 + n + 1 is prime for every positive integer n'?

    • 3
    • 4
    • 5
    • 2

  8. What is the smallest non-negative integer n for which n^2 + n + 41 is not prime?

    • 40
    • 39
    • 10
    • 20

  9. Which number is a counter-example to the statement that all primes are odd?

    • 1
    • 9
    • 2
    • 3

  10. Which expression algebraically represents a general odd integer for integer k?

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

  11. How many individual cases must be checked to prove a statement for n = 1, 2, 3, 4 by exhaustion?

    • Infinite
    • 4
    • 1
    • 3

  12. Which calculation gives a rational sum, disproving that the sum of two irrationals is always irrational?

    • sqrt(2) + sqrt(3)
    • sqrt(2) + 0
    • sqrt(2) + sqrt(2)
    • sqrt(2) + (-sqrt(2))

  13. What is assumed about integers p and q when writing sqrt(3) = p/q at the start of a proof?

    • No common factors
    • Both are prime
    • Both are even
    • p is greater than q

  14. Which value of x serves as a counter-example to the claim that sqrt(x^2) = x?

    • -3
    • 3
    • 9
    • 0

  15. Which shape is a counter-example to the statement that every quadrilateral with equal diagonals is a rectangle?

    • Parallelogram
    • Isosceles trapezium
    • Kite
    • Rhombus

  16. To prove that if n^2 is even then n is even by contradiction, what is assumed?

    • n is prime
    • n^2 is odd
    • n is even
    • n is odd

  17. Assuming x + 1/x < 2 for x > 0 leads to which impossible statement?

    • (x - 1)^2 < 0
    • (x - 1)^2 > 0
    • (x + 1)^2 < 0
    • x^2 + 1 = 0

  18. What is a logical progression of steps from known facts to a conclusion called?

    • Proof by contradiction
    • Deductive proof
    • Proof by exhaustion
    • Counter-example

  19. What is the truth value of a universal statement after a valid disproof?

    • True
    • Sometimes true
    • False
    • Undetermined

  20. Which method of proof is used to show that the square root of 2 is irrational?

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

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