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  • Q76
    Lever: Modulus / absolute value behaviourConcept: Integrating greatest-integer (floor) functions

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    [Q92 · Sep · 2025]
  • Q77
    Lever: Modulus / absolute value behaviourConcept: Regions Bounded by Lines & Modulus

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    [Q98 · Sep · 2025]
  • Set · 2 questions
    Let f(x)=∣x∣f(x)=|x|f(x)=∣x∣ and g(x)=[x]−1g(x)=[x]-1g(x)=[x]−1. Let h(x)=f(g(x))g(f(x))h(x)=\frac{f(g(x))}{g(f(x))}h(x)=g(f(x))f(g(x))​.
    • Q78
      Lever: Modulus / absolute value behaviourConcept: Limits of the greatest-integer function

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      [Q57 · Sep · 2023]
    • Q79
      Lever: Modulus / absolute value behaviourConcept: Limits of the greatest-integer function

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      [Q58 · Sep · 2023]
  • Set · 2 questions
    Let f(x)=x−3∣x−3∣+a; x<3f(x)=\frac{x-3}{|x-3|}+a;\ x<3f(x)=∣x−3∣x−3​+a; x<3, a−b; x=3a-b;\ x=3a−b; x=3, x−3∣x−3∣+b; x>3\frac{x-3}{|x-3|}+b;\ x>3∣x−3∣x−3​+b; x>3. f(x)f(x)f(x) is continuous at x=3x=3x=3.
    • Q80
      Lever: Modulus / absolute value behaviourConcept: Finding parameters so f is continuous

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      [Q59 · Sep · 2023]
    • Q81
      Lever: Modulus / absolute value behaviourConcept: Finding parameters so f is continuous

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      [Q60 · Sep · 2023]
  • Set · 2 questions
    Let f(x)=axx+1+b, x<1f(x)=\frac{ax}{x+1}+b,\ x<1f(x)=x+1ax​+b, x<1 and x−1, 1≤x≤2\sqrt{x-1},\ 1\leq x\leq2x−1​, 1≤x≤2.
    • Q82
      Lever: Differentiability at a pointConcept: Finding parameters so f is differentiable

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      [Q63 · Sep · 2023]
    • Q83
      Lever: Modulus / absolute value behaviourConcept: Left-hand and right-hand limits

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      [Q64 · Sep · 2023]
  • Q84
    Lever: Modulus / absolute value behaviourConcept: The chain rule (composite functions)

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    [Q65 · Sep · 2023]
  • Q85
    Lever: Modulus / absolute value behaviourConcept: Below the Axis, Loops & the Factor of 2

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    [Q68 · Sep · 2023]
  • Q86
    Lever: Modulus / absolute value behaviourConcept: One-one, onto, and bijective

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    [Q22 · Apr · 2024]
  • Q87
    Lever: Modulus / absolute value behaviourConcept: Testing a relation defined by a rule

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    [Q23 · Apr · 2024]
  • Q88
    Lever: Modulus / absolute value behaviourConcept: Integrating absolute-value and piecewise functions

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    [Q77 · Apr · 2024]
  • Q89
    Lever: Modulus / absolute value behaviourConcept: Finding the domain (roots, denominators, logs)

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    [Q80 · Apr · 2024]
  • Q90
    Lever: Differentiability at a pointConcept: Continuity vs differentiability

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    [Q87 · Apr · 2024]
  • Q91
    Lever: Modulus / absolute value behaviourConcept: Limits of the greatest-integer function

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    [Q88 · Apr · 2024]
  • Set · 2 questions
    Let f(x)=∣x−1∣f(x)=|x-1|f(x)=∣x−1∣, g(x)=[x]g(x)=[x]g(x)=[x] and h(x)=f(x)⋅g(x)h(x)=f(x)\cdot g(x)h(x)=f(x)⋅g(x) where [⋅][\cdot][⋅] is the greatest integer function.
    • Q92
      Lever: Modulus / absolute value behaviourConcept: Integrating greatest-integer (floor) functions

      Tap an option to check your answer.

      [Q93 · Apr · 2024]
    • Q93
      Lever: Modulus / absolute value behaviourConcept: Integrating greatest-integer (floor) functions

      Tap an option to check your answer.

      [Q94 · Apr · 2024]
  • Q94
    Lever: Modulus / absolute value behaviourConcept: The fractional part {x} = x − [x]

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    [Q71 · Sep · 2024]
  • Q95
    Lever: Modulus / absolute value behaviourConcept: Left-hand and right-hand limits

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    [Q74 · Sep · 2024]
  • Q96
    Lever: Modulus / absolute value behaviourConcept: Floor equations and sums

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    [Q77 · Sep · 2024]
  • Set · 1 question
    Let f(x)=[x]2−[x2]f(x)=[x]^2-[x^2]f(x)=[x]2−[x2], where [⋅][\cdot][⋅] denotes the greatest-integer function.
    • Q97
      Lever: Modulus / absolute value behaviourConcept: Definition, graph, and behaviour at integers

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      [Q83 · Sep · 2024]
  • Q98
    Lever: Modulus / absolute value behaviourConcept: Types of discontinuity (removable, jump, oscillatory)

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    [Q84 · Sep · 2024]
  • Set · 2 questions
    Let f(x)=∣x2−x−2∣f(x)=|x^2-x-2|f(x)=∣x2−x−2∣.
    • Q99
      Lever: Modulus / absolute value behaviourConcept: Integrating absolute-value and piecewise functions

      Tap an option to check your answer.

      [Q91 · Sep · 2024]
    • Q100
      Lever: Modulus / absolute value behaviourConcept: Integrating absolute-value and piecewise functions

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      [Q92 · Sep · 2024]
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