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    Application of Quadratic Equation in Real Context

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    MCH
    This document contains 3 word problems involving quadratic equations. 1) The first problem involves finding the quadratic equation, solving it, and calculating the area of two shapes - a trapezium and a right-angled triangle - where side lengths are related to variables. 2) The second problem relates the ages of 3 people on 2 dates and derives a quadratic equation from their relationships, solves it, and finds one of the ages. 3) The third problem derives a quadratic equation from a rotated square shape, solves it, and calculates the perimeter and area of the resulting 16-sided shape.

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    Application of Quadratic Equation in Real Context

    Uploaded by

    MCH
    45 views3 pages
    This document contains 3 word problems involving quadratic equations. 1) The first problem involves finding the quadratic equation, solving it, and calculating the area of two shapes - a trapezium and a right-angled triangle - where side lengths are related to variables. 2) The second problem relates the ages of 3 people on 2 dates and derives a quadratic equation from their relationships, solves it, and finds one of the ages. 3) The third problem derives a quadratic equation from a rotated square shape, solves it, and calculates the perimeter and area of the resulting 16-sided shape.

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    210813_application of Quadratic Equation in Real Context

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    This document contains 3 word problems involving quadratic equations. 1) The first problem involves finding the quadratic equation, solving it, and calculating the area of two shapes - a trapezium and a right-angled triangle - where side lengths are related to variables. 2) The second problem relates the ages of 3 people on 2 dates and derives a quadratic equation from their relationships, solves it, and finds one of the ages. 3) The third problem derives a quadratic equation from a rotated square shape, solves it, and calculates the perimeter and area of the resulting 16-sided shape.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    45 views3 pages

    Application of Quadratic Equation in Real Context

    Uploaded by

    MCH
    This document contains 3 word problems involving quadratic equations. 1) The first problem involves finding the quadratic equation, solving it, and calculating the area of two shapes - a trapezium and a right-angled triangle - where side lengths are related to variables. 2) The second problem relates the ages of 3 people on 2 dates and derives a quadratic equation from their relationships, solves it, and finds one of the ages. 3) The third problem derives a quadratic equation from a rotated square shape, solves it, and calculates the perimeter and area of the resulting 16-sided shape.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    CAMBRIDGE SECONDARY 3

    MODERNLAND

    APPLICATION OF QUADRATIC EQUATION IN REAL


    CONTEXT
    1. (a)
    2x + 4

    x+2 x NOT TO
    SCALE

    x2 – 40

    The diagram shows a trapezium.


    Two of its angles are 90o.
    The lengths of the sides are given in terms of x.
    The perimeter is 62 units.

    (i) Write down a quadratic equation in x to show this information. Simplify your equation. [2]

    (ii) Solve your quadratic equation. [2]

    (iii) Write down the only possible value of x. [1]

    (iv) Calculate the area of the trapezium. [2]

    (b)

    2y – 1
    y NOT TO
    SCALE

    y+2

    The diagram shows a right-angled triangle.


    The lengths of the sides are given in terms of y.

    (i) Show that 2y2 – 8y – 3 = 0. [3]


    (ii) Solve the equation 2y2 – 8y – 3 = 0, giving your answers to 2 decimal places. [4]
    (iii) Calculate the area of the triangle. [2]

    0580/04, 0581/04 Jun 2006


    2. (a) On 1st January 2000, Ashraf was x years old.
    Bukki was 5 years older than Ashraf and Claude was twice as old as Ashraf.

    (i) Write down in terms of x, the ages of Bukki and Claude on 1st January 2000. [2]
    (ii) Write down in terms of x, the ages of Ashraf, Bukki and Claude on 1st January 2002. [1]
    (iii) The product of Claude’s age and Ashraf’s age on 1st January 2002 is the same as the square of
    Bukki’s age on 1st January 2000.
    Write down an equation in x and show that it simplifies to x2 – 4x – 21 = 0. [4]
    (iv) Solve the equation x2 – 4x – 21 = 0. [2]
    (v) How old was Claude on 1st January 2002? [1]

    (b) Claude’s height, h metres, is one of the solutions of h2 + 8h – 17 = 0.

    (i) Solve the equation h2 + 8h – 17 = 0.


    Show all your working and give your answers correct to 2 decimal places. [4]
    (ii) Write down Claude’s height, to the nearest centimetre. [1]

    0580/4,0581/4/O/N02
    3. A'

    xc
    m
    xc

    m
    A x cm x cm B
    P Q

    12 cm

    D' B'

    D C

    C'

    An equilateral 16-sided figure APA′QB …… is formed when the square ABCD is rotated 45° clockwise
    about its centre to position A′B′C′D′.
    AB = 12 cm and AP = x cm.

    (a) (i) Use triangle PA′Q to explain why 2x2 = (12 – 2x)2. [3]
    (ii) Show that this simplifies to x2 – 24x + 72 = 0. [3]
    (iii) Solve x2 – 24x + 72 = 0. Give your answers correct to 2 decimal places. [4]

    (b) (i) Calculate the perimeter of the 16-sided figure. [2]


    (ii) Calculate the area of the 16-sided figure. [3]

    0580/4, 0581/4 Jun02

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