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. In a function from set A to set B, how many elements of B does each element of A map to?

    • Exactly one
    • At least one
    • Any number
    • At most one

  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. For any two sets A and B, which set is always a subset of A?

    • A union B
    • B backslash A
    • A complement
    • A intersect B

  10. Which natural number n acts as a counterexample to the claim that n^2 > n?

    • n = 4
    • n = 3
    • n = 2
    • n = 1

  11. Which number provides a counterexample to the claim that all prime numbers are odd?

    • 3
    • 9
    • 1
    • 2

  12. Which pair of angles A and B disproves the statement sin(A + B) = sin A + sin B?

    • 0° and 90°
    • 30° and 60°
    • 180° and 0°
    • 0° and 0°

  13. What name is given to a mathematical statement that is true for all values of its variables?

    • Expression
    • Equation
    • Identity
    • Inequality

  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. What solution was omitted when solving x^2 = 4 to get only x = 2?

    • x = -2
    • x = 4
    • x = -4
    • x = 0

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

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

  20. What is the range of the cubic function f(x) = x^3 - 3x for real x?

    • Strictly positive numbers
    • Integers only
    • Non-negative real numbers
    • All real numbers

All AQA Further Maths quizzes