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    IB Math AAHL
    /
    Transformations & asymptotes
    /

    Video

    Video Reviews

    Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Transformations & asymptotes

    Video Reviews

    Watch comprehensive video reviews for Transformations & asymptotes, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    HL content

    The video will automatically pause when it reaches a problem.

    Inequalities of functions

    AHL 2.15

    Inequalities of the form

    g(x)≥f(x)

    can be solved either algebraically or with technology.


    It is crucial to remember that when multiplying both sides of an inequality by a negative number, the inequality changes direction:

    −x<1⇒x>−1


    Example

    Solve the inequality

    x3−x2+x−7>2x2−x−7

    Subtracting the RHS:

    x3−3x2+2x>0
    x(x−2)(x−1)>0


    Now we make a table of signs:

    xxx−1x−2Product​]−∞,0[−−−−​]0,1[+−−+​]1,2[++−−​]2,+∞[++++​


    So the solution is 0<x<1 or 2<x.

    Inequalities of functions

    AHL 2.15

    Inequalities of the form

    g(x)≥f(x)

    can be solved either algebraically or with technology.


    It is crucial to remember that when multiplying both sides of an inequality by a negative number, the inequality changes direction:

    −x<1⇒x>−1


    Example

    Solve the inequality

    x3−x2+x−7>2x2−x−7

    Subtracting the RHS:

    x3−3x2+2x>0
    x(x−2)(x−1)>0


    Now we make a table of signs:

    xxx−1x−2Product​]−∞,0[−−−−​]0,1[+−−+​]1,2[++−−​]2,+∞[++++​


    So the solution is 0<x<1 or 2<x.

    HL content