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    Ok...

    1. How do you do questions such as the following:

    Without using a calculator, solve the equation: 4^2x-1 = 16^-1/2x
    Or: 3^(2x-1) = 9^-x.

    ________________________________ ________________________________


    2. How would you go about factorising the polynomial f(x)= x^3 - 5x^2 + 2x + 8?

    ________________________________ ________________________________


    3. Plot on the same axes the graphs of 'y = sin x' and 'y = 0.5 + cos x (for x 0-360).

    Use your graph to find the approx. solutions of:

    a) sin x = 0.5 + cos x
    b) 0.5 + cos x = 1.1
    c) cos x = 0.3

    Once I've drawn the graph, how would I go about getting the solutions?


    Thanks.

    Adam
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    (Original post by adk)
    Ok...

    1. How do you do questions such as the following:

    Without using a calculator, solve the equation: 4^2x-1 = 16^-1/2x
    Or: 3^(2x-1) = 9^-x.

    ________________________________ ________________________________


    2. How would you go about factorising the polynomial f(x)= x^3 - 5x^2 + 2x + 8?

    ________________________________ ________________________________


    3. Plot on the same axes the graphs of 'y = sin x' and 'y = 0.5 + cos x (for x 0-360).

    Use your graph to find the approx. solutions of:

    a) sin x = 0.5 + cos x
    b) 0.5 + cos x = 1.1
    c) cos x = 0.3

    Once I've drawn the graph, how would I go about getting the solutions?


    Thanks.

    Adam
    2. you have to guess factors to start off with and then use long division to find them. if u think x-a will be a factor then put a into the equation and if it is a factor then f(x)=0...so quickly u can see that if u put x=-1 into it f(x)=0, so (x+1) is a factor...divide this into it and u will get a qaudratic which will be easy to facotrise
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    (Original post by adk)
    Ok...

    3. Plot on the same axes the graphs of 'y = sin x' and 'y = 0.5 + cos x (for x 0-360).

    Use your graph to find the approx. solutions of:

    a) sin x = 0.5 + cos x
    b) 0.5 + cos x = 1.1
    c) cos x = 0.3


    Adam
    a. all u have to do is ifn the points where the lines cross as then y=sinx=y=0.5+cosx

    b. u have drawn 0.5cosx for all values of x...to find when 0.5+cosx=1.1, u simply have to draw a line across from 1.1 on the y-axis....i.ethe line y=1.1

    c. a similar idea....u want cosx=0.3 u already hace drawn y=cosx +0.5
    so bring 0.5 over to lhs and u have y-0.5=cosx..but u want 0.3=cosx so lhs has to be y-0.5=0.3 so u simply have to draw the line of y=0.8 and see where the lines cross.
    if u had drawn y=cosx, u would simply have draw y=0.3 and seen points of interesection...but u have drawn y=cosx+0.5 so y have to draw y=0.3+0.5 =0.8 beacause of this
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    (Original post by adk)
    Ok...

    1. How do you do questions such as the following:

    Without using a calculator, solve the equation: 4^2x-1 = 16^-1/2x
    Or: 3^(2x-1) = 9^-x.
    get teh bases the same
    16 = 4^2, so 16^-1/2x = 4^(2*-1/2x)

    then you have the bases the same so you can just look at the powers

    similar thing for the next
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    (Original post by adk)
    Ok...

    1. How do you do questions such as the following:

    Without using a calculator, solve the equation: 4^2x-1 = 16^-1/2x
    Or: 3^(2x-1) = 9^-x.


    Thanks.

    Adam
    1. You need to get the bases eqaul ...i.e have 3^z=3^y
    note that 16+4^2

    so u can rewrite as:
    4^(2x-1)=4^-1/x
    and so if the bases are equal and the terms are equal, the powers must also be equal...so
    2x-1=-1/x
    multiply across

    2x^2-x=-1
    so 2x^2-x+1=0

    however this does not appear to factorise so maybe no solutions????


    if u do a simliar thing to:
    3^(2x-1) = 9^-x.
    u get 3^(2x-1)=3^-2x
    so -2x=2x-1
    so 4x=1
    so x=1/4
    • Thread Starter
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    Thanks very much.

    However I don't understand what you meant in your explanation of the sin and cos graph.

    Once I've sketched the graphs, what would I do to find 'sin x = 0.5 + cos x'?!
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    (Original post by lgs98jonee)
    2. you have to guess factors to start off with and then use long division to find them. if u think x-a will be a factor then put a into the equation and if it is a factor then f(x)=0...so quickly u can see that if u put x=-1 into it f(x)=0, so (x+1) is a factor...divide this into it and u will get a qaudratic which will be easy to facotrise
    you mean actually GUESS?????????

    is there not a mathematical method, how do we start?
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    (Original post by KOH)
    you mean actually GUESS?????????

    is there not a mathematical method, how do we start?
    generally they're only going to give you ones in the range -3 to 3 as they know you dont have that much time in the exam. So start with 1 etc and work through methodically
    • Thread Starter
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    Ok...


    I understand how to do the previous questions now, but what about the following? How would you do them?

    1. Write down the values of the following leaving your answers in terms of surds:

    a) sin 120
    b) cos 300
    c) sin (-135)
    d) sin 405
    e) tan (-150)
    f) tan 150
    g) cos (-420)




    2. Write each of the following as trigonometric ratios of positive acute angles:

    a) sin 260
    b) tan 355
    c) sin (-194)
    d) cos (-336)
    e) cos 293



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    i think these are something to do with the special angles.

    eg: sin120=0.866...
    which is the same as sin60 due to the symmetry in the curve
    and according to the special angle triangles
    sin60=sqroot3/2

    edit: if this makes any sense whatsoever. please get me to clarify if not, sorry!
 
 
 
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