Specialist 1/2 Question Thread!

[RuiAce]

Help please

Let C and D be points with position vectors c and d respectively. If |c| = 5 and |d| = 7  and c dot d = 4, find the absolute value of vector CD

[PolySquared]

How do you do this question?

Let a =3i + 4j and b = i - j

Find the vector with the same magnitude of b with the same direction of a

[jazzycab]

How do you do this question?

Let a =3i + 4j and b = i - j

Find the vector with the same magnitude of b with the same direction of a

Firstly, a vector in the direction of \(\textbf{a}\) with magnitude 1 is the unit vector, \(\hat{\textbf{a}}\):

We need to adjust the length of this vector so that it is the same as \(\textbf{b}\). That is, the required vector, \(\textbf{v}=\left|\textbf{b}\right|\hat{\textbf{a}}\):

[randomnobody69420]

I feel like this question has already been asked a million times before but does anyone know where I can find worked solutions for Cambridge Specialist Maths 1&2 textbook?

[K888]

I feel like this question has already been asked a million times before but does anyone know where I can find worked solutions for Cambridge Specialist Maths 1&2 textbook?

Hey there, it's best to ask your teacher about this. No-one can provide them to you here as they are a commercial product and thus subject to copyright. Your teacher will likely have a copy that your school has purchased, or will know where to get one.

[PolySquared]

Hi could I get some help on this question please.

In triangle OAB, let a = vector OA and b = vector OB. The point P is on AB such that vector AP = 2 times vector PB. express vector PB in terms of a and b

[mzhao]

Hi could I get some help on this question please.

In triangle OAB, let a = vector OA and b = vector OB. The point P is on AB such that vector AP = 2 times vector PB. express vector PB in terms of a and b

Hey PolySquared,

From the question, we have:
$$ \overrightarrow{AP} = 2\overrightarrow{PB} $$
and since
\begin{align*}
\overrightarrow{AB} &= \overrightarrow{AP} + \overrightarrow{PB}\\
\\
\implies \overrightarrow{AB} &= 2\overrightarrow{PB} + \overrightarrow{PB}\\
&= 3\overrightarrow{PB}\\
\implies \overrightarrow{PB} &= \frac{1}{3}\overrightarrow{AB}\\
&= \frac{1}{3}(\overrightarrow{OB} - \overrightarrow{OA})\\
\therefore \overrightarrow{PB} &= \frac{1}{3}(b-a)
\end{align*}

[PolySquared]

Could I get soem help on this question please.

Points A and B are defined by the position vectors a=3i+4j and b = 5i+12j

find the unit vector which bisects angle AOB

[randomnobody69420]

Is circle geometry supposed to be insanely hard? I feel like half of the questions in the cambridge 1/2 are impossible for me to do. I consider myself a decent maths student but I知 really struggling with this topic. I had no trouble with doing circle geometry in year 10 but this year...idk this questions seem much harder.

Is there any resources out there that can help me improve my problem solving skills when it comes to this topic? Or anything else that can help me solve these difficult questions (I would post them here but honestly there are way too many).

edit: I should specify: the main type of problems I知 having trouble with are the ones that ask you to prove something.

[Sine]

Is circle geometry supposed to be insanely hard? I feel like half of the questions in the cambridge 1/2 are impossible for me to do. I consider myself a decent maths student but I知 really struggling with this topic. I had no trouble with doing circle geometry in year 10 but this year...idk this questions seem much harder.

Is there any resources out there that can help me improve my problem solving skills when it comes to this topic? Or anything else that can help me solve these difficult questions (I would post them here but honestly there are way too many).

edit: I should specify: the main type of problems I知 having trouble with are the ones that ask you to prove something.

use vectors for the proofs (if you have learnt it) and it also would be helpful to revise all the circle thoerems.

Also I found for circle gemotery proofs you sometimes had to be exposed to the solution in order to do the proof since the easiest proof counted in knowing really small details.

[jazzycab]

Is circle geometry supposed to be insanely hard? I feel like half of the questions in the cambridge 1/2 are impossible for me to do. I consider myself a decent maths student but I知 really struggling with this topic. I had no trouble with doing circle geometry in year 10 but this year...idk this questions seem much harder.

Is there any resources out there that can help me improve my problem solving skills when it comes to this topic? Or anything else that can help me solve these difficult questions (I would post them here but honestly there are way too many).

edit: I should specify: the main type of problems I知 having trouble with are the ones that ask you to prove something.

Don't be afraid to try a few different things. It can be very difficult to identify how to approach a lot of these proofs. If you feel that something isn't working, try a different approach.
For these particular types of proofs, try and identify the geometric representation of the starting point, but more importantly, the end point. Then work backwards in terms of identifying all necessary information that would be required for that end point, hence, try and identify how to show that information from the start point

[PolySquared]

How do you prove that the diagonals of a square are of equal length and bisect eact other using vectors?

[Sine]

How do you prove that the diagonals of a square are of equal length and bisect eact other using vectors?

First define two sides of different "direction" as vectors a and b, now you should be able to express everything with only those two vectors.
For equal length: First how do we express the diagnol in terms of a and b then think about how you find the length of a vector?
For bisect: What properties inherently show bisecting? Either finding the lengths of each half of the diagnol or to find that both midpoints of the diagnol occur at the same place.

[Sooomi]

Hey all!!
So i'm currently doing Circle Geometry in Spesh 1/2 and I struggle with proofs and was wondering if I could get sure tips or some advice on improving my proofs and what to look out for and etc.
Just anything that will help or personally that you found useful!
Much appreciated!!

[caffeine]

Hey guys,

Sorry if this was the wrong area to post this, but I was given the cambridge senior maths chapter 18 (matrices) because my methods tutor (i'm in year 11) said it would give us a bigger overall picture on matrices. I'm having a little bit of trouble with exercise 18C. I know how to do the basic multiplying, but don't understand a few of the trickier questions, and I'd be super grateful if you guys could assist me with the following!!

Question 2: http://puu.sh/A9Yqb/283fa45c3e.png
Question 4 and Question 5: http://puu.sh/A9YrO/0bea0789de.png
Question 12: http://puu.sh/A9Yts/f21438a27d.png

Even if you guys can help me with even one of the questions it'd help a lot!!

Cheers!