Maths year 11

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    (Original post by RDKGames)
    Factor out the numerator as much as you can, then see how much the denominator can divide it.
    I divide the top and bottom by the same number?

    They mustn't give decimals right?

    Is the final answer a whole number or fraction?

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    (Original post by z_o_e)
    I divide the top and bottom by the same number?

    They mustn't give decimals right?

    Is the final answer a whole number or fraction?

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    Yes you divide the top and bottom by the same number as long as the top and bottom remain whole numbers.

    No decimals.

    The final answer is still a fraction but a simpler one. Smaller numbers.
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    (Original post by RDKGames)
    Yes you divide the top and bottom by the same number as long as the top and bottom remain whole numbers.

    No decimals.

    The final answer is still a fraction but a simpler one. Smaller numbers.
    5 goes into -356

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    (Original post by z_o_e)
    5 goes into -356

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    I have bad tendency to come up with difficult questions, but a challenge is always good! But just remember your normal procedure with surds and you'll get it right. Spoilers are there for hints.

    A right-angled triangle has side length's (2+\sqrt{5}) and (9-2\sqrt{5})

    (i) Find the length of the hypotenuse of this triangle and express it in the form \sqrt{a-b\sqrt{5}} where a and b are integers. BONUS: Express the length of the hypotenuse in the form \sqrt{c} \sqrt{55-c^4\sqrt{5}} where c is an integer.
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    You can sketch the triangle to help and label the sides. How can we work out the hypotenuse? What formula do we know to help us with this?

    For the bonus, it is worth getting the wanted form under the same square root, can you spot any similarities between your answer and this form that you can draw some equations from?
    (ii) Express 4.1% of the triangle's area in the form \frac{A}{B}(c^3+5\sqrt5) where A, B and c are integers.
    Spoiler:
    Show
    How can we find the area? Notice that the value of c is the same as you found it in the first part if you did the bonus.

    Observe the wanted form. There is a fraction, this means can we rewrite 4.1% as a fraction.
    (iii) What is 1.4% of the area you found in part (ii)? Express this in the form (D \cdot 10^{-2c})(c^3+5\sqrt5) where D is a decimal, and c is an integers.
    Spoiler:
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    What can we convert 1.4% into? A fraction can be useful, but what would we multiply this fraction by?

    Remember that something like 1234 can be turned into the scientific notation of 1.234\cdot 10^3
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    (Original post by RDKGames)
    I have bad tendency to come up with difficult questions, but a challenge is always good! But just remember your normal procedure with surds and you'll get it right. Spoilers are there for hints.

    A right-angled triangle has side length's (2+\sqrt{5}) and (9-2\sqrt{5})

    (i) Find the length of the hypotenuse of this triangle and express it in the form \sqrt{a-b\sqrt{5}} where a and b are integers. BONUS: Express the length of the hypotenuse in the form \sqrt{c} \sqrt{55-c^4\sqrt{5}} where c is an integer.
    Spoiler:
    Show
    You can sketch the triangle to help and label the sides. How can we work out the hypotenuse? What formula do we know to help us with this?

    For the bonus, it is worth getting the wanted form under the same square root, can you spot any similarities between your answer and this form that you can draw some equations from?
    (ii) Express 4.1% of the triangle's area in the form \frac{A}{B}(c^3+5\sqrt5) where A, B and c are integers.
    Spoiler:
    Show
    How can we find the area? Notice that the value of c is the same as you found it in the first part if you did the bonus.

    Observe the wanted form. There is a fraction, this means can we rewrite 4.1% as a fraction.
    (iii) What is 1.4% of the area you found in part (ii)? Express this in the form (D \cdot 10^{-2c})(c^3+5\sqrt5) where D is a decimal, and c is an integers.
    Spoiler:
    Show
    What can we convert 1.4% into? A fraction can be useful, but what would we multiply this fraction by?

    Remember that something like 1234 can be turned into the scientific notation of 1.234\cdot 10^3
    These are really hard :/

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    (Original post by z_o_e)
    These are really hard :/

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    Don't be daunted by the looks of it, have a go and spend however much time you need to complete it. Ask whatever you need at each stage, you already know the methods to find what the questions asks for. This tests you on surds, algebra, fractions, and decimals altogether.
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    (Original post by RDKGames)
    Yes you divide the top and bottom by the same number as long as the top and bottom remain whole numbers.

    No decimals.

    The final answer is still a fraction but a simpler one. Smaller numbers.
    So I square the brackets


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    (Original post by z_o_e)
    So I square the brackets


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    Yes. Follow that formula, you know what a and b are. Try not to rush it, and check for any errors.
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    (Original post by RDKGames)
    Yes. Follow that formula, you know what a and b are. Try not to rush it, and check for any errors.
    I got this


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    (Original post by z_o_e)
    I got this


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    Don't give it in decimals. Just expand the brackets and collect like terms.
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    (Original post by RDKGames)
    Don't give it in decimals. Just expand the brackets and collect like terms.


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    That's not what I meant.
    \displaystyle c^2=(2+\sqrt5)^2+(9-2\sqrt5)^2

    \displaystyle =(2+\sqrt5)(2+\sqrt5)+(9-2\sqrt5)(9-2\sqrt5)

    THOSE brackets. First expand the two then add up any common terms.
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    (Original post by RDKGames)
    That's not what I meant.
    \displaystyle c^2=(2+\sqrt5)^2+(9-2\sqrt5)^2

    \displaystyle =(2+\sqrt5)(2+\sqrt5)+(9-2\sqrt5)(9-2\sqrt5)

    THOSE brackets. First expand the two then add up any common terms.
    Like this?


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    (Original post by z_o_e)
    Like this?


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    Yep you expanded that one correctly; so now you know that (2+\sqrt5)^2=9+4\sqrt5, now do the other one.
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    (Original post by RDKGames)
    Yep you expanded that one correctly; so now you know that (2+\sqrt5)^2=9+4\sqrt5, now do the other one.
    Is this correct?


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    (Original post by z_o_e)
    Is this correct?


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    First 3 terms are correct, but check that last one. (-2\sqrt5)(-2\sqrt5) is not -4\sqrt5
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    (Original post by RDKGames)
    First 3 terms are correct, but check that last one. (-2\sqrt5)(-2\sqrt5) is not -4\sqrt5
    -20?

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    (Original post by RDKGames)
    First 3 terms are correct, but check that last one. (-2\sqrt5)(-2\sqrt5) is not -4\sqrt5


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    Correct number but wrong sign Notice that you are multiplying negative by a negative there so the answer must be a positive. Other than that, you have now expanded both brackets. Refer back to the Pythagorean theorem and see what you need to do with the two answers you just got.
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    (Original post by RDKGames)
    Correct number but wrong sign Notice that you are multiplying negative by a negative there so the answer must be a positive. Other than that, you have now expanded both brackets. Refer back to the Pythagorean theorem and see what you need to do with the two answers you just got.
    How's this?


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