Uni Admission Maths test help?

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Size:  10.5 KBHi, I've been trying to prepare for uni maths admission tests but half the content are topics that I haven't even covered or heard about in my A level syllabus. As a result I really need some urgent help, please post your method too, thank you.
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    For 8. Consider n+n+1+n+2+n+3=4n+6. This is not a strictly divisible by 6 in this form \forall n \in \mathbb{Z}. However let us assume n=3k, for k \in \mathbb{Z}, then our expression is 4(3k)+6=12k+6=6(2k+1) which is divisible by 6. Hope this helps. I am not willing to provide solutions to all the problems but if you need any hints message me.

    I assume you are familiar with the notation used. If not just say.
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    Jas1947 A hint for question 3. What does squaring do and what can result from it. i.e. (-4)^{2}=4^{2}
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    (Original post by Cryptokyo)
    For 8. Consider n+n+1+n+2+n+3=4n+6. This is not a strictly divisible by 6 in this form \forall n \in \mathbb{Z}. However let us assume n=3k, for k \in \mathbb{Z}, then our expression is 4(3k)+6=12k+6=6(2k+1) which is divisible by 6. Hope this helps. I am not willing to provide solutions to all the problems but if you need any hints message me.

    I assume you are familiar with the notation used. If not just say.
    I got to the part where 4n+6 but couldn't get any further, I understand that now. Thank you
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    (Original post by Jas1947)
    I got to the part where 4n+6 but couldn't get any further, I understand that now. Thank you
    For 5. Take the log of both sides i.e.\log_{3}(2^{5})\approx\log_{3}(3  ^{3})
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    (Original post by Cryptokyo)
    Jas1947 A hint for question 3. What does squaring do and what can result from it. i.e. (-4)^{2}=4^{2}
    Oh I see, x cannot equal -4 because you cannot square root a negative
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    (Original post by Cryptokyo)
    For 8. Consider n+n+1+n+2+n+3=4n+6. This is not a strictly divisible by 6 in this form \forall n \in \mathbb{Z}. However let us assume n=3k, for k \in \mathbb{Z}, then our expression is 4(3k)+6=12k+6=6(2k+1) which is divisible by 6. Hope this helps. I am not willing to provide solutions to all the problems but if you need any hints message me.

    I assume you are familiar with the notation used. If not just say.
    What is the symbol next to the n called?
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    (Original post by Jas1947)
    Oh I see, x cannot equal -4 because you cannot square root a negative
    You are half correct. You identified the incorrect solution but for the wrong reason. The reason is the square root function is only the positive answer as a function can only have a one-to-one or many-to-one mapping. i.e. y=|\sqrt{x}|
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    (Original post by Dynamic_Vicz)
    What is the symbol next to the n called?
    I am not sure of its name but it means "for all". In LaTeX you would write \forall.
 
 
 
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