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  • Direct and Inverse Proportions | Study

  • Electricity | Assess

  • Exponents and Powers | Assess

  • Exponents and Powers | Assess

  • Exponents and Powers | Study

  • GRAVITATION | Study

  • HERON’S FORMULA | Assess

  • Light | Assess

  • Light | Study

  • Direct and Inverse Proportions | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Variations: If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation. (Scroll down till end of the page) Study Tools Audio, readmore

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    Variations: If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation. (Scroll down till end of the page)

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    Direct Variation or Direct Proportion:

    Extra:

    Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains

    constant. That is if

    =k [k is a positive number, then x and y are said to vary directly.

    In such a case if y1, y2 are the values of y corresponding to the values x1, x of x

    respectively then = .

    If the number of articles purchased increases, the total cost also increases. More than money deposited in a bank, more is the interest earned.

    Quantities increasing or decreasing together need not always be in direct proportion, same in the case of inverse proportion.

    When two quantities x and y are in direct proportion (or vary directly), they are

    written as

    . Symbol

    stands for ‘is proportion to’.

    Inverse Proportion: Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant. That is, if xy

    = k, then x and y are said to vary inversely. In this case if y1, y2 are the values of y

    corresponding to the values x1, x2 of x respectively then

    x1, Y1 = x2, y2 or

    =

    When two quantities x and y are in inverse proportion (or vary inversely), they are

    written as x

    . Example: If the number of workers increases, time taken to finish

    the job decreases. Or If the speed will increase the time required to cover a given distance decreases.

     

    1. Distance and Time

    Time (hours)Distance (km)Formula
    00

    d=60× t 

    160 
    2120 
    3180

     

    2. Cost of Groceries

    Number of ApplesTotal Cost ($)Formula
    00C=2n  ⇒  
    12 
    24 
    510

     

    3. Cooking Ingredients

    Number of ServingsAmount of Flour (cups)Formula
    00F=0.5s
    42 
    63 
    84

     

    4. Speed and Fuel Consumption

    Distance (km)Fuel Consumed (liters)Formula
    00F=d15
    151 
    302 
    453

     

    5. Salary and Hours Worked

    Hours WorkedTotal Earnings ($)Formula
    00E=15h
    115 
    575 
    10150 
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    • Electricity | Assess

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      • Exponents and Powers | Assess

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          • Exponents and Powers | Study

            Mind Map Overal Idea Content Speed Notes Quick Coverage Exponents are used to express large numbers in shorter form to make them easy to read, understand, compare and operate upon. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Expressing Large Numbers in the Standard Form: Any number can be readmore

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            Exponents are used to express large numbers in shorter form to make them easy to read, understand, compare and operate upon. (Scroll down till end of the page)

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            Expressing Large Numbers in the Standard Form: Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of a number is called its standard form or scientific motion. Very large numbers are difficult to read, understand, compare and operate upon. To make all these easier, we use exponents, converting many of the large numbers in a shorter form. The following are exponential forms of some numbers?

            Here, 10, 3 and 2 are the bases, whereas 4, 5 and 7 are their respective exponents. We also say, 10,000 is the 4th power of 10, 243 is the 5th power of 3, etc. Numbers in exponential form obey certain laws, which are: For any non-zero integers a and b and whole numbers m and n,

            (g) (–1) even number = 1 (–1) odd number = – 1

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            • GRAVITATION | Study

              Mind Map Overal Idea Content Speed Notes Quick Coverage Content Study Tools Content … Key Terms Topic Terminology Term: Important Tables Topic Terminology Term: Assessments Test Your Learning readmore

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              • HERON’S FORMULA | Assess

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                • Light | Assess

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                  • Light | Study

                    Mind Map Overal Idea Content Speed Notes Quick Coverage Light: It is the natural agent that stimulates sight and makes things visible. Light travels along straight line. Any polished or a shining surface acts as a mirror. An image which can be obtained on a screen is called a real image. (Scroll down till end readmore

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                    Light: It is the natural agent that stimulates sight and makes things visible.

                    Light travels along straight line.

                    Any polished or a shining surface acts as a mirror.

                    An image which can be obtained on a screen is called a real image. (Scroll down till end of the page)

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                    It is formed by light rays that actually pass through the screen.

                    An image which cannot be obtained on a screen is called a virtual image.

                    It is formed by light rays that seem to pass through the screen.

                    The image formed by a plane mirror is erect.

                    It is virtual and is of the same size as the object.

                    The image is at the same distance behind the mirror as the object is in front of it.

                    In an image formed by a mirror, the left side of the object is seen on the right side in the image, and right side of the object appears to be on the left side in the image.

                    A concave mirror can form a real and inverted image.

                    When the object is placed very close to the mirror, the image formed is virtual, erect and magnified.

                    A Convex mirror is the mirror that curves out; the reflecting surface is convex.

                    Image formed is virtual, upright and diminished. Image formed by a convex mirror is erect, virtual and smaller in size than the object.

                    A Concave lens is the lens that is thinner at the center than at the edges.

                    It is a diverging lens.

                    Image formed is virtual, erect and diminished.

                    A convex lens can form real and inverted image.

                    When the object is placed very close to the lens, the image formed is virtual, erect and magnified.

                    When used to see objects magnified, the convex lens is called a magnifying glass.

                    White light is composed of seven colors.

                    Properties of Light:

                    1. Rectilinear Propagation of Light: It is the property of light by which it travels in a straight line in any direction.

                    The direction of path in which light make a ray.

                    2. Reflection of Light: It is the bouncing back of light after striking the surface of an object.

                    Shiny smooth surfaces reflect almost all the light.

                    3. Dispersion: It is the phenomenon of splitting of white light into its seven colors. White

                    light is mixture of: Violet, Indigo, Blue, Green, Yellow, Orange and Red (VIBGYOR) colors.

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