Lesson OT1.1-OT1.5

OT1.1-OT1.5 Mathematical argument, language and proof Quiz: AQA Further Maths, Unit 1

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson OT1.1-OT1.5, Mathematical argument, language and proof: 20 multiple choice questions for the AQA Further Maths (7367), Unit 1: Overarching themes, written with Revision Ninja.

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The 20 questions

  1. In the expression 3x^2 + 5x - 7, which term is the constant term?

    • 3
    • 5x
    • 3x^2
    • -7

  2. Which word names a letter such as x whose value can change within an expression or equation?

    • variable
    • constant
    • coefficient
    • index

  3. Which statement correctly defines a function f from set A to set B?

    • Each element of A is mapped to exactly one element of B
    • Each element of B is mapped to exactly one element of A
    • Each element of B is mapped to at least one element of A
    • Each element of A is mapped to at least one element of B

  4. For f(x) = sqrt(x - 2) with real outputs, what is the domain of f?

    • x >= 2
    • x <= 2
    • x > 0
    • All real x

  5. For f(x) = x^2 with domain all real numbers, what is the range of f?

    • y > 0
    • y >= 0
    • y <= 0
    • All real y

  6. If A = {1, 2, 3} and B = {2, 3, 4, 5}, what is A intersection B?

    • {4, 5}
    • {1, 2, 3, 4, 5}
    • {2, 3}
    • {1, 4, 5}

  7. If A = {1, 2, 3} and B = {2, 3, 4, 5}, how many elements does A union B contain?

    • 5
    • 4
    • 2
    • 6

  8. Which symbol means is an element of in set notation?

    • ∩
    • ∪
    • ⊆
    • ∈

  9. Which statement is true for all sets A and B?

    • A is a subset of the intersection of A and B
    • The union of A and B is a subset of A
    • A minus B is always equal to B minus A
    • The intersection of A and B is a subset of A

  10. Which value of n shows that the statement n^2 is always greater than n is false for natural numbers n?

    • n = 4, since 4^2 = 16 is greater than 4
    • n = 3, since 3^2 = 9 is greater than 3
    • n = 2, since 2^2 = 4 is greater than 2
    • n = 1, since 1^2 = 1 is not greater than 1

  11. Which approach correctly disproves the claim that every prime number is odd?

    • Show that 9 is not prime
    • Prove that 11 is odd
    • Check that 3, 5 and 7 are all odd
    • Exhibit the prime number 2, which is even

  12. A student claims sin(A + B) = sin A + sin B. Which choice of A and B shows the claim is false?

    • A = 90 degrees and B = 0, so both sides equal 1 and the two results agree
    • A = 30 degrees and B = 60 degrees, since sin 90 = 1 but sin 30 + sin 60 is about 1.37
    • A = 45 degrees and B = 0, so both sides equal sin 45 and the two results agree
    • A = 0 and B = 0, so both sides are 0 and the claim holds for these values

  13. Which of these is an identity rather than an equation?

    • x^2 = 9 holds only when x = 3 or x = -3, so it restricts x to two values
    • (x + 1)^2 = 0 only when x = -1, which is a condition that holds for one value
    • (x + 1)^2 = x^2 + 2x + 1 for all real x
    • 2x + 3 = 11 holds only when x = 4, and it is not true for other values

  14. For f(x) = 2x + 1, what is f(3)?

    • 7
    • 5
    • 6
    • 9

  15. Which proof method establishes a result for all integers n >= 1 by checking n = 1 and showing that truth at n = k implies truth at n = k + 1?

    • Proof by contradiction
    • Mathematical induction
    • Direct substitution
    • Proof by exhaustion

  16. For the function g(x) = 1/(x - 3), what is the domain?

    • All real x except x = 3
    • x > 0
    • x >= 3
    • All real x except x = -3

  17. The function f: x -> x^2 is applied to the set {-2, -1, 0, 1, 2}. What is the range?

    • {1, 4}
    • {0, 1, 2, 4}
    • {0, 1, 4}
    • {-2, -1, 0, 1, 2}

  18. A student solves x^2 = 4 by taking square roots, obtaining x = 2, and concludes that 2 is the only solution. Which statement identifies the error?

    • The student omitted the negative root x = -2
    • Square roots cannot be taken of both sides of an equation
    • The value x = 2 is wrong because 2^2 is not 4
    • The equation x^2 = 4 has no real solutions

  19. If A is a subset of B, what is A union B?

    • A
    • The complement of B
    • The empty set
    • B

  20. Let f(x) = x^3 - 3x for all real x. Which statement about the range of f is correct?

    • The range is y >= 0, since the cubic is never negative
    • The range is -2 <= y <= 2, since the graph has a maximum at 2 and a minimum at -2
    • The range is y >= -2, since the minimum value of f is -2
    • The range is all real numbers, since the cubic term dominates for large positive and negative x

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