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Why do I have to do 3cosx? Why can't I just graph cosx and then find the solutions from there?

How was 112 converted?

I need someone to explain the answer for me. I knew that there was a point of inflexion at -2 because it was a stationary point at f'(x), and I also knew that max at x = -1 and a min at x = 0 because the parabola cuts these points so these turning points turn into stationary points, even though...

Is the general form of a line y = mx+b or ax + by+ c = 0?

I need help for this unusual question. Sorry for the "HSC" word right in the middle lol.

I need help for this question even though it may seem easy. i), v = 0 when t = 3 ii) Basically I should be looking for the times when f''(x) = 0, or when it's a point of inflexion, right? But the answer says t = 1/2 and t = 2, and these are stationary points, but that's when f'(x)...

I need help for these two questions. They're two separate questions by the way.

How do I do this?

How do I draw |2x-3| By the way, those are absolutes.

I knew how to find the GA, but length of FA was confusing, in the answers, they say: In triangle AFB, sintheta = AF/15, but where's theta in triangle AFB?

I automatically thought the answer is B, but it turns out the answer is D. I'm 100% certain B is also right, but is it actually wrong?

Okay so I initially thought the answer was A, but the right answer was D. How is it? Direct Access uses mathematical algorithms to find the exact location of the data. So how is D right?

Does the HSC usually ask to draw system flow charts?

For this type of question, how do I graph velocity? Would also appreciate help on how to draw acceleration or displacement for the future.

I need help for this question, the answers were saying that "to the left of D tangent +ve", but how when it's clearly a negative gradient? Anyway I also wanna know what's the difference between vertical and horizontal pt of inflex. and how would I do this question.

The answer is D, but why?

How do I do these questions in the easiest way possible without using a graph?

I need someone to explain each of the answers, what does it mean if the particle is moving towards the origin? Doesn't it mean if it's moving towards (0,0)? But the particle in the graph isn't, so why can't that be an answer?

I just need some clarifying on what's in the red box, I know that if the velocity if negative it's travelling to the left (negative direction), but I know that acceleration, if negative, decreases in speed, but the answer says speeding up? Am I wrong? Can someone clarify for me?

I understand the answer to the first question, but the second and third question are weird. For the second question, I did (18/37)^6, but the answer says [(19/37)^5] x (18/37), why? Why is it even 19/37? For the third question I done 1- (18/37)^6 but the answer says otherwise.