First part not in syllabus, but if you are curious, for y = 4 times x^0.5…

The graph will be same shape as quadratic graph, except that the roles of the x-axis and the y-axis are reversed.

Means, if you normally take a piece of paper and sketch a smiley face curve, you will rotate your graph 90 degrees clockwise, and the shape of the y = 4x^0.5 graph will be like that.

Part 2 is regular simul, or slightly more difficult.

i didnt manage do part 2, subbed 4x^1/2 into the 2nd eqn and squared the whole equation to remove the square root but i got the wrong answer

my working:
4(4x^1/2)=7x+4
16 (sqrt x) = 7x +4
256x =49x^2 + 16
49x^2-256x+16
x = 5.16 x=0.06326

but the answer key stated x=4/49 and x=4

Because (7x2 + 4)^2 is not 49x2 + 16

(a + b)^2 is different from a^2 + b^2 remember?

256x = 49x2 + 56x + 16

ohh, we cant square the numbers individually? like (16x^1/2)^2= (7x)^2 + 4^2 as i actually intended to do that

Squaring has a different effect though.

Try drawing a square of sides (a + b) by (a + b) and then cut it accordingly. You will have a square of side a by a, a square of side b by b and two more rectangles of side a by b.

thx :) by the way do you have any tips to improve for proving questions? i always get stucked at every single proving questions i see...

There are lots of techniques to prove things, even in Trigo proving

- Convert expressions into sines and cosines only
- Pay attention to the structure of the signs and the fractions (is it a single fraction? Does it contain minus signs?)
- Rationalise if necessary
- Use basic identities if necessary
- Use substitutions if necessary, especially if double angle for A and 0.5A is involved
- Other techniques I have not mentioned yet might also work

trigo functions can be rationalised? for the double angles there is 3 different ways for cosine but it is difficult to tell which one to use tho...

btw can you help me with the new question i've posted? its already answered by someone but i still dont understand what 9(ii) is asking... (i've understood qn12)

Remind me again, I might forget but I am quite tired now, I have actually already forgotten about this

ok

trigo functions can be rationalised? for the double angles there is 3 different ways for cosine but it is difficult to tell which one to use tho...

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Sometimes when I see 1 + cos x in the denominator, I multiply it by 1 - cos x. This is useful when encountering fractions like 1 / (1 + cos x) because you cannot divide a numerator 1 by a denominator containing two terms, whereas the resulting denominator after rationalisation can be simplified into a single term leading to easy breakage of fractions.

For cosine, I look out for the number "1" accompanying it. If I see things like 1 + cos 2A, then my version for cosine would be the one that contains -1 (so as to cancel out the 1 during addition), and if I see things like 1 - cos 2A, I would pick the one that contains 1 (to cancel out the 1 during subtraction). If I see things like (a + b) (a - b) happening (as is the case for the other format I have not mentioned), then I will take that form.

btw can you help me with the new question i've posted? its already answered by someone but i still dont understand what 9(ii) is asking... (i've understood qn12)

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"Distance OX" simply means the straight-line distance from O to X, which is basically the displacement of X from the reference position O, though our value will be quoted as positive values in the event the displacement value comes out negative.