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  • Set · 1 question
    A function is defined by f(x)=(x+1)2/3(2x+4)6/3(6x+9)f(x)=(x+1)^{2/3}(2x+4)^{6/3}(6x+9)f(x)=(x+1)2/3(2x+4)6/3(6x+9).
    • Q10426
      NDA Maths strategyConcept: Critical points and the derivative tests

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      [Q46 · Sep · 2023]
  • Set · 2 questions
    Given that 4x2+y2=94x^2+y^2=94x2+y2=9.
    • Q10427
      NDA Maths strategyConcept: AM-GM: the calculus-free shortcut

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      [Q47 · Sep · 2023]
    • Q10428
      Lever: AM-GM / mean inequalities (incl. x + 1/x ≥ 2)Concept: AM-GM: the calculus-free shortcut

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      [Q48 · Sep · 2023]
  • Set · 2 questions
    A function is defined by f(x)=π+sin⁡2xf(x)=\pi+\sin^2 xf(x)=π+sin2x.
    • Q10429
      NDA Maths strategyConcept: Finding the range

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      [Q49 · Sep · 2023]
    • Q10430
      NDA Maths strategyConcept: Finding the range

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      [Q50 · Sep · 2023]
  • Set · 2 questions
    A parabola passes through (1,2)(1,2)(1,2) and satisfies dydx=2yx, x>0,y>0\frac{dy}{dx}=\frac{2y}{x},\ x>0,y>0dxdy​=x2y​, x>0,y>0.
    • Q10431
      NDA Maths strategyConcept: The Latus Rectum

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      [Q51 · Sep · 2023]
    • Q10432
      NDA Maths strategyConcept: The Latus Rectum

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      [Q52 · Sep · 2023]
  • Set · 2 questions
    Let f(x)=ax−1+bx−12f(x)=\dfrac{a^{x-1}+b^{x-1}}{2}f(x)=2ax−1+bx−1​ and g(x)=x−1g(x)=x-1g(x)=x−1.
    • Q10433
      NDA Maths strategyConcept: The 1^∞ form

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      [Q53 · Sep · 2023]
    • Q10434
      NDA Maths strategyConcept: The 1^∞ form

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      [Q54 · Sep · 2023]
  • Set · 2 questions
    Let f(x)=2−x+2+xf(x)=\sqrt{2-x}+\sqrt{2+x}f(x)=2−x​+2+x​.
    • Q10435
      NDA Maths strategyConcept: Finding the domain (roots, denominators, logs)

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      [Q55 · Sep · 2023]
    • Q10436
      NDA Maths strategyConcept: Finding the domain (roots, denominators, logs)

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      [Q56 · Sep · 2023]
  • 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))​.
    • Q10437
      Lever: Modulus / absolute value behaviourConcept: Limits of the greatest-integer function

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      [Q57 · Sep · 2023]
    • Q10438
      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.
    • Q10439
      Lever: Modulus / absolute value behaviourConcept: Finding parameters so f is continuous

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      [Q59 · Sep · 2023]
    • Q10440
      Lever: Modulus / absolute value behaviourConcept: Finding parameters so f is continuous

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      [Q60 · Sep · 2023]
  • Set · 2 questions
    Let I=∫−2π2πsin⁡4x+cos⁡4x1+3x dxI=\int_{-2\pi}^{2\pi}\frac{\sin^4x+\cos^4x}{1+3^x}\,dxI=∫−2π2π​1+3xsin4x+cos4x​dx.
    • Q10441
      NDA Maths strategyConcept: Odd/even symmetry over a symmetric interval

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      [Q61 · Sep · 2023]
    • Q10442
      NDA Maths strategyConcept: Odd/even symmetry over a symmetric interval

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      [Q62 · 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.
    • Q10443
      Lever: Differentiability at a pointConcept: Finding parameters so f is differentiable

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      [Q63 · Sep · 2023]
    • Q10444
      Lever: Modulus / absolute value behaviourConcept: Left-hand and right-hand limits

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      [Q64 · Sep · 2023]
  • Q10445
    Lever: Modulus / absolute value behaviourConcept: The chain rule (composite functions)

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    [Q65 · Sep · 2023]
  • Q10446
    NDA Maths strategyConcept: The chain rule (composite functions)

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    [Q66 · Sep · 2023]
  • Q10447
    NDA Maths strategyConcept: Integrals of periodic functions

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    [Q67 · Sep · 2023]
  • Q10448
    Lever: Modulus / absolute value behaviourConcept: Below the Axis, Loops & the Factor of 2

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    [Q68 · Sep · 2023]
  • Q10449
    NDA Maths strategyConcept: Order and degree of a differential equation

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    [Q69 · Sep · 2023]
  • Q10450
    NDA Maths strategyConcept: Eliminating arbitrary constants

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    [Q70 · Sep · 2023]
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