My teacher goes thru the content quite fast in class, and I feel I need more practice as I am struggling. I did the qs in the textbook, but I found it hard and would like more practice.
What are some free resources that I can utilise?
Thnx
I need some help on a couple questions http://m.imgur.com/a/rEeRc
For Q5b) what's wrong with my equation/method to working this out? I'm lost on how to solve this problem even though it's almost exactly the same to the others.
For 8b) the answer says 72 minutes, but I got 90. x=50 is correct as well.
For 8a and 10, I did these with a scientific calculator because the square root looked pretty messy. Are these questions intended to be solved by hand?
Thanks
Hey Adequace, they were just minor errors:Thanks man, appreciate it a lot!
For 5b, it was 600/x = 600/(x-5.5) - 220, instead of 600/x = 600/(x-5.5) + 220: remember that the plane's speed is faster, thus we substract the 220 from the plane.
For 8b, instead of 75/x (which is the usual time), they are looking for 75/(x+12.5), as this is the actual time taken for that particular journey. The question was probably a bit vague anyway though.
Questions like 10 and 8a are definitely doable by hand (although they ARE a bit tedious!). Sometimes, to speed up the process (such as in question 10) you can use km/min or another unit to avoid fractions during working out, then convert it back to km/h at the end.
Another question.16. You're working is good, you're reading of the question not so much haha. p has to be a positive integer. 2sqrt(21) is roughly 9.16 therefore p must =10 since that is the closest integer that is both positive and larger than 9.16
http://imgur.com/a/vZeP5
For Q16) the answer just has p=10 but I can't get to answer. I've attached my working as well.
For Q12) I struggle greatly with worded problems. I don't think the denominators in my pipe equations are correct. Is there anything I did wrong? Haven't really tried solving this question due to my lack of confidence..
Thanks
16. You're working is good, you're reading of the question not so much haha. p has to be a positive integer. 2sqrt(21) is roughly 9.16 therefore p must =10 since that is the closest integer that is both positive and larger than 9.16Thanks regardless, but yeah the worded one is a pain.
12..can't be bothered sorry
I have a solution for Q12, but it is by no means elegant, and I think there's probably a better way to do it that I've missed:Thanks a lot man! Also, when you factorised 5t^2 -87t +180 =0. Is this expected to be done by hand?SpoilerLet C = the capacity of the tank. Let r1 and r2 be the initial flow rates through the first and second pipes respectively. Let r1_new and r2_new be the new flow rates. Let t1 and t2 be the initial time it takes to fill the tank using the initial flow rates of the first and second pipes respectively.
Using the formula Capacity = Rate * Time (and its rearrangements), we can form the following six equations:
Equation 1: r1 + r2 = 3C/20
Equations 2 and 3: r1 = C/t1 ; r2 = C/t2
Equations 4 and 5: r1_new = C/(t1 - 1) ; r2_new = C/(t2 + 2)
Equation 6: r1_new + r2_new = C/7.
I now substitute Eqs. 2 and 3 into 1, and Eqs. 4 and 5 into 6, to get the following:
Now I factor out C from both equations (C > 0, or else the question makes no sense). We arrive at:
Our goal is therefore to work out the value of t1 and t2, so we can work out (t1-1) and (t2+2), which is the ultimate aim.
Algebraically manipulating the fractions, we get the following:;. I now treat this as a system of (non-standard) simultaneous equations, and try to solve. We get:
. But notice that we previously had Therefore, we may subtract these two equations to get We can substitute this back into 5t1-4t2=27 to get This quadratic can be factorised to give . If you substitute these values back into 5t1-4t2=27, you will get the corresponding solutions Of course, we can't have a negative time value, so it follows that . Those are the initial times to fill the tank for each pipe. To get the new times, we simply evaluate t1-1 and t2+2, to get new times of 14 minutes for both pipes! Therefore, under the new flow rates, each pipe will take 14 minutes to fill the tank!
In summary: Initially, the first pipe took 15 minutes to fill the tank, and the second pipe took 12 minutes. Hence the first pipe fills 1/15 of the tank per minute, and the second pipe fills 1/12 of the tank per minute. If you combine the two pipes, they fill 1/15 + 1/12 = 3/20 of the tank per minute, and hence it takes 20/3 minutes to fill the tank. After the flow rates were adjusted, the two pipes both take 14 minutes to fill the tank individually, and hence both fill 1/14 of the tank per minute. So when you combine the two pipes, they fill 1/14 + 1/14 = 1/7 of the tank per minute, and hence it takes 7 minutes to fill the tank.
There has seriously got to be a better way to do this :-\.
Thanks a lot man! Also, when you factorised 5t^2 -87t +180 =0. Is this expected to be done by hand?
Yes - you are expected to be able to solve all quadratics by hand. Don't forget about techniques like completing the square and the quadratic equation!Ah, thanks!
Ah, thanks!For part f, x^2 -x isn't an irreducible quadratic factor because it can be written as x(x-1) so you would write A/x + B/x-1
I have another question http://m.imgur.com/a/iVNip
For parts f and h
For f: why can't you solve it using (Ax+B)/x^2 -x)
For h, I can't tell what I'm doing wrong but the answer has x/(x^2 +3) for the 2nd part of the partial fraction.
Don't worry about j, I just realised what I did wrong.
Sorry about all the questions :'( hopefully in 2 years time I can look back on this and be happy with what I've achieved :)
Ah, thanks!
I have another question http://m.imgur.com/a/iVNip
For parts f and h
For f: why can't you solve it using (Ax+B)/x^2 -x)
For h, I can't tell what I'm doing wrong but the answer has x/(x^2 +3) for the 2nd part of the partial fraction.
Don't worry about j, I just realised what I did wrong.
Sorry about all the questions :'( hopefully in 2 years time I can look back on this and be happy with what I've achieved :)
For h, they've probably mucked up, because neither of the denominators should have x^2+3 there.Whoops I meant x^2 +4 for the denominator
Hi everyone!
Doing an exercice on Arithmetic Series and I'm struggling a lot so I would appreciate any help :)
1) For the sequence 4,8,12,…4,8,12,…, find {n:Sn=180}. (My answer: 10, textbook's answer: 9)
2) There are 110 logs to be put in a pile, with 15 logs in the bottom layer, 14 in the next, 13 in the next, and so on. How many layers will there be? (Textbook's answer: 11)
3) Dora’s walking club plans 15 walks for the summer. The first walk is a distance of 6 km, the last walk is a distance of 27 km, and the distances of the walks form an arithmetic sequence.
How far is the 8th walk? (Textbook's answer: 16.5km)
Hi everyone!
Doing an exercice on Arithmetic Series and I'm struggling a lot so I would appreciate any help :)
1) For the sequence 4,8,12,…4,8,12,…, find {n:Sn=180}. (My answer: 10, textbook's answer: 9)
2) There are 110 logs to be put in a pile, with 15 logs in the bottom layer, 14 in the next, 13 in the next, and so on. How many layers will there be? (Textbook's answer: 11)
3) Dora’s walking club plans 15 walks for the summer. The first walk is a distance of 6 km, the last walk is a distance of 27 km, and the distances of the walks form an arithmetic sequence.
How far is the 8th walk? (Textbook's answer: 16.5km)
assistance needed please, got an outcome tomorrowHi there,
Have no idea how to start this. I will probably work this out eventually, but I'll just leave this here in case I don't :P Thanks!If you have real coefficients then you can utilise the conjugate-root theorem to solve this problem :)
Solve for x:
|x-4| - |x+2| = 6
http://imgur.com/a/hN7pz
I need some help for part a. My working was a random method but I'm not sure why this doesn't work?
Another way which seems more likely is finding AB then using the cosine rule to find the magnitude of the angle, my problem is how do I find the length AB?
Thanks
How do you simplify the cosine rule in terms of sine? Teacher said it a trig identity , but someone explain to me what is and how you do it. Thnx
Two questions, see the attached pictures.
http://imgur.com/a/eYMxC quick question. I had to copy the 2nd line from the book to solve this but on the RHS, why don't they have a y^2 in the square root as well since (y-0)^2.Only had a quick look but for the line x=-1, it has the coordinates (-1,y), and what you've said is that it is a single point (-1,0) instead of a vertical line that can have infinitely many y values. So effectively you get (y-y)^2 which is why the term is absent. :)
Ty
Hello
I was wondering if I could get advice in what to put on the notes that we are given for
the specialist exam. I know that the calc free section you can't use notes or calc and that
for calc assumed you can. But I am confused on what I should know how to do without notes and
what I should put on the notes. We've covered vector proof, component form ,dot product, scalar projection, permutation, combination, Pascal's triangle/ proofs, converse, contrapositive and inverse as well as circle proofs. Help is greatly appreciated for my study ;D
Hi everyone,
I have the following question and I'm just wondering if my answer and working is all correct.
"Find the locus of the point P(x ,y) such that AP=6, given point A(3 ,2)"
This is circle with a centre of (3, 2) and a radius of 6.
Looks good to me
Hi i was wondering if i fould recieve help on solving these proofs. I am still relatively new to proving trig identities so i didnt know what i can and should do
10)
11)
Thank you so much for your help :D
I wanted to ask some questions if that's okay
For Q10
How did It go from
to
Further explanation would be greatly appreciated :D
I am still greatly lacking in understanding how to apply the trig identities and manipulating them
I also wanted to ask about Q11. How did you prove it from this step onwards?
I am still relatively new to trig identities proofs
I am still a bit confused
-1 was taken out
what happened here? why is it 2x?
I have a question on changing Cartesian equations to their polar form and I'm a bit stuck on how to do this one.Are you sure that this was the question
The Cartesian equation is , so far I've converted it to .
I have a feeling I'm way off with this question, could someone please provide some advice with it? If I have somehow done it correctly so far, can I simpilify the equation any further than this?
Are you sure that this was the question
Because that's about as simplified as it can get.
Thanks for that! Yeah, that was the question I was given. I just wasn't 100% sure on the answer because it seemed a bit 'messy' compared to the other questions we've done so far.
Hi, I need help with this question, http://m.imgur.com/a/WlmIG
For part c) I'm not sure how to do it but the answer went AB - [ans of part c]. However, I don't get how that gets us the shortest distance?
Thanks
Hi, I need help with this question, http://m.imgur.com/a/WlmIG
For part c) I'm not sure how to do it but the answer went AB - [ans of part c]. However, I don't get how that gets us the shortest distance?
Thanks
Could I have some help with these 2 questions for vector proofs http://m.imgur.com/a/KPQDEQ9) Since, AC and BD have the same midpoint, the diagonals of the parallelogram bisect (divide into two equal pieces) each other
For Q9) How does the linked solution prove that they bisect with their working? They proved that BM = MD, are we supposed to then assume that the other diagonal is just going to bisect it with logic..?
For Q10) I'm completely lost with their working. How did they form those 2 simultaneous equations and what are they actually representing?
Thanks
Q9) Since, AC and BD have the same midpoint, the diagonals of the parallelogram bisect (divide into two equal pieces) each otherSorry for double post, but I'm still a bit unsure on why you can assume the dot product of A to BC and B to AC are equal even though they are perpendicular?
(http://amsi.org.au/teacher_modules/C3/C3g4.png)
Q10) An altitude is a line segment, which is perpendicular to the base.
(https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcQyNHY3Hvxel2Ai1sWG4WDgmZk9mhumbda3EaPI7K-S10JnlfhnVA)
Since, they all are perpendicular and meet at the point O (assume it's the point where all the lines intersect in the image), you can assume that the dot product of A to BC and B to AC are equal. So here, you basically have to prove that OC (c) is perpendicular to AB (-a+b), by equating the two dot products, and showing that they equal c . (b-a)
Sorry for double post, but I'm still a bit unsure on why you can assume the dot product of A to BC and B to AC are equal even though they are perpendicular?
Wouldn't vector a and b be different lengths?
Thanks
Could i get help with these questions?Are these proofs?
I've been trying to solve them the past 2 hours TTT ^ TTT
Are these proofs?
I was really confused on how to solve this questionThis is a fairly routine method, outlined in the Cambridge textbook (SM 1/2)
This is a fairly routine method, outlined in the Cambridge textbook (SM 1/2)Why do you set the domain for u between [0,pi]?
Then solve on CAS. You'll find this method works as long as sin and cos have the same argument.
Do they teach the tangent half-angle substitution or the auxiliary angle method in this course?Nope! (at least not in units 3/4 specialist)
Please help me ASAP! I have a test very soon on this. A tram decelerates uniformly from a speed of 60 km/h to rest in 60s. Find the time taken for it to travel half the total distance. Thank you so much in advance :)Use constant acceleration formulae
Are these proofs?
I am still a bit confused did you use the double angle formula for the 3rd line? Also where did the cos^2theta - sin^theta come from in line 4?
How would you prove q19?
I am still a bit confused did you use the double angle formula for the 3rd line? Also where did the cos^2theta - sin^theta come from in line 4?
How would you prove q19?
This is a fairly routine method, outlined in the Cambridge textbook (SM 1/2)
Then solve on CAS. You'll find this method works as long as sin and cos have the same argument.
Could i get further explanation please? I am still quite the novice in how to approach this question. Would you use the formula for sin (a+x)?
In a lift that is accelerating upwards at 2 m/s2, a spring balance shows the apparent
weight of an object to be 2.5 kg wt. What would be the reading if the lift were at rest?
2.5 = m(9.8+2)I'd personally leave your value of m as a fraction, this would allow for more accurate results without having to waste time writing out 300 decimal places.
m = 0.211864406 (try to get as many decimal places possible)
scale reading = m x (g+0)
= 2.1 kg wt.
2.5 = m(9.8+2)Why is it (9.8+2)? So lost
m = 0.211864406 (try to get as many decimal places possible)
scale reading = m x (g+0)
= 2.1 kg wt.
Why is it (9.8+2)? So lost
For this question http://m.imgur.com/3UDbKU3
So I found N = 8cos25, but the answer is resolving the normal force in to its components and then equating the vertical component to the weight. Isn't the reaction of the plane to the body, the entire normal force? They got 8/cos25
http://imgur.com/dhCbbsi
How do you do question 16b?
Ans for a is ]100/(9g)
Ans for b is ]2sqrt3
You can solve this question using the work-energy principle (I am not sure if it is part of the specialist curriculum).Don't what that is lol.
Could i please get help qith these 2 questions?
Have been really busy since the past week.. :-\ sorry about the late reply.
Q15)
Therefore it have been proven that x^5-x is divisible by 5, since x^5-x = 5n.
Q14 can be proved using a similar approach.
Thank you for the help.Start with the formulas
I was also windering how would yoj solve this question?
Start with the formulas
\begin{align}
A&=2\pi rh+2\pi r^2\\
V&=\pi r^2 h
\end{align}
Substitute the volume in to \(V\) and solve for \(h\) in terms of \(r\). Substitute this relationship into \(A\), and then you now should have \(A\) in terms of \(r\) only. Derive \(A\) with respect to \(r\) and set to 0 to find the minimum value of \(r\). The substitute this value of \(r\) into \(V\) with the volume to find \(h\).Spoiler\(h\) in terms of \(r\) is
\begin{align}
h=\frac{535}{\pi r^2}
\end{align}
Sub into \(A\) to get
\begin{align}
A&=2\pi r\frac{535}{\pi r^2}+2\pi r^2\\
&=\frac{1070}{r}+2\pi r^2
\end{align}
Derive with respect to \(r\)
\begin{align}
\frac{dA}{dr}&=-\frac{1070}{r^2}+4\pi r
\end{align}
Set to 0 to find where the minimum of \(A\) is (plotting \(A\) reveals that it is a local minimum and not a local maximum when \(\frac{dA}{dr}=0\)).
\begin{align}
0&=-\frac{1070}{r^2}+4\pi r\\
\implies r&=\left(\frac{535}{2\pi}\right)^\frac{1}{3}\\
&\approx 4.4
\end{align}
Sub into the volume equation to find \(h\):
\begin{align}
535 &= \pi \left(\frac{535}{2\pi}\right)^\frac{2}{3} \times h\\
\implies h&\approx 8.8
\end{align}
Does sin(pi/2+pi/3) give cos(pi/3) or -cos(pi/3)
(Tech free)Determine the locus of points such that if P=(x,y) ,A=(-2,0) and B=(2,0) the PA+PB=4
Help! My exam is in 3 days!
Disclaimer: No idea if this working out is VCE friendly. Just thought I'd lend a hand.Thanks!
Hey Gogo! We'll take the points and substitute them into expressions for the distances PA and PB to start:
Now let's play with that relationship a bit so we can bring in the expressions without the square roots:
Notice we got a whole heap of cancellation into that last line. That's what we wanted to see. We can continue:
So this locus lies on the x-axis; however, it isn't the whole x-axis. We need to check something else to find the missing restriction, remember that for our condition to make sense, PA must be less than or equal to 4, and so must PB. Let's check that condition:
These two regions overlap only for \(-2\le x\le2\), so that's where our locus lies. Putting it together, this locus is just the line segment joining A and B.
Note that you could do this last bit just with some clever thinking. Clearly we can't venture beyond A or B with our locus, because that just doesn't make sense. As soon as we do, one of our distances is immediately, clearly, too large. You could probably not do any algebra for this question if you are good at picturing loci, but I thought I'd show everything :) sorry if this isn't VCE friendly, but I thought I'd lend a hand anyway! :)
I have attached the question and its answer. What I do not understand is the 195 different sums possible. Isn't there 18 different possible sums from 1 to 18? Can some please explain this question I do not understand the answer given in the solutions manual.
Thanks a lot, any help is appreciated.
Dumb question alert!
I'm not too sure if I recall this question, but it's been baffling me:
If z=-4i what is the modulus-argument of Iz^3I
Wouldn't the modulus be 64 and the argument be 0?
However the teacher said that the argument was pi/2
Please help this poor soul
Edit: Just saw the bars around Iz^3I. Was that intended?
If yes then the argument is certainly 0 because the modulus is a real number
Edit: Just saw the bars around Iz^3I. Was that intended?
If yes then the argument is certainly 0 because the modulus is a real number
Dumb question alert!
I'm not too sure if I recall this question, but it's been baffling me:
If z=-4i what is the modulus-argument of Iz^3I
Wouldn't the modulus be 64 and the argument be 0?
However the teacher said that the argument was pi/2
Please help this poor soul
Hi can someone give me any good suggestions for a specialist tutor, I really wanna start nowderrick ha, usually he only does yearly intakes and only at a unit 3/4 level. However you need to get in pretty early to secure a place. Otherwise check out anyone found HERE
Does anyone know how to model the heartbeat ekg using trigonometry, using e^(-x^2), where you multiply a sine or cosine function by another trigonometric function to look like this: https://malouffsaandpblog.files.wordpress.com/2013/03/trevor-ekg.jpg
Does anyon have the worked solutions for the book
It's the specialist unit 1/2 book
It's the specialist unit 1/2 book
It's the Cambridge one like it is blue
Does anyon have the worked solutions for the bookSorry unfortunately we cannot post copyright material on the forums
Hi :D I've been able to do this vector question and get the correct answer, however, I've been doing under the assumption the angle between the two is 0 (going in same direction). Can someone explain why this happens? Or am I wrong in my working out?You don't need to substitute a dot b in this case (you can, but a there is a simpler method). The dot product works very much like multiplication, so we can use that property in this question.
http://i.imgur.com/Q0ce9bp.jpg
Hi :D I've been able to do this vector question and get the correct answer, however, I've been doing under the assumption the angle between the two is 0 (going in same direction). Can someone explain why this happens? Or am I wrong in my working out?Great answer by VanillaRice (beaten by 1 minute haha)
http://i.imgur.com/Q0ce9bp.jpg
Great answer by VanillaRice (beaten by 1 minute haha)I really hate to do this but it's the dot product not cross. Cross product is not studied in spec maths. :) :)
a.(a+b) = a.a +a.b
It's one of the properties of the cross product :)
So then you end up with (a.a +a.b -a.b) / |a| = a.a / |a| which results in the answer - you don't need to assume theta = 0
I really hate to do this but it's the dot product not cross. Cross product is not studied in spec maths. :) :)Nevertheless, distributivity is still a property of both cross and dot products ;D
I really hate to do this but it's the dot product not cross. Cross product is not studied in spec maths. :) :)Oops! Accidentally wrote cross instead of dot (been doing a lot of dot and cross product in maths lately). Applies to both but meant to say dot :)
You don't need to substitute a dot b in this case (you can, but a there is a simpler method). The dot product works very much like multiplication, so we can use that property in this question.
i.e.
With this in mind, have another go at the question. The most likely reason you are able to substitute theta = 0 is that when you do so, you are assuming the angle between a and b is 0, and also that the angle between a and (a+b) is 0 - note the two dot products are not the same.
Hope this helps :)
Hey guys, I'm a year 11 student wondering if it is ok to do spesh 3/4 without 1/2.Your chances are good :)
I have been recommended to do spesh 3/4 on MANY occasions by my methods and recently, physics teacher (both also teach spesh 3/4).
If i can arrange "catch-up lessons" with either of the above teachers as well as studying by myself, what are my chances of surviving Spesh 3/4? Thanks
These questions seem really straightforward but how do you figure out the different vectors and write them in correct format? :)Ok so unit vector i represents one unit in the positive x direction, whilst the unit vector j represents one unit in the positive y direction. Moving from C to D is going 6 units in the negative x direction, so it is -6i. Moving from C to A is going 7 units in the negative x direction and 3 units in the positive y direction, so it is -7i+3j. Going from C to B is moving one unit in the negative x direction and three units in the positive y directoin, so it is -i+3j.
Cheers Eric, I'm familiar with how to calculate the scalar product of vectors in two dimensions but I'm not completely sure on how to tackle questions with 3 dimensions. I assume its a similar process but I don't have answers to the questions ;DYes its a similar process, just add the products of the corresponding coefficients for each unit vector. So for part a, it would ge -2 x 4 + -5 x -1 + 1 x 3 = 0
Cheers Eric, I'm familiar with how to calculate the scalar product of vectors in two dimensions but I'm not completely sure on how to tackle questions with 3 dimensions. I assume its a similar process but I don't have answers to the questions ;DYep, Eric's right. Just a bit of background knowledge:
So (2i+3j).(2i+3j)=2i.2i+2*2i.3j+3j.3j = 4+0+9 = 13. (You don't have to do this in the exam or anything)
So just multiply the coefficients for each unit vector, as Eric said :)
I'm not exactly sure what you have done here ??? :-\ Don't u just multiply the coefficients in front of i and j so you get 2*2 + 3*3 = 14.Sorry :P it's not exactly necessary to show it just thought some background info would be nice
I know it is the same answer but where does the zero come from?
I'm not exactly sure what you have done here ??? :-\ Don't u just multiply the coefficients in front of i and j so you get 2*2 + 3*3 = 14.Adding up the products of the coefficients only works in unit vector notation because the vectors involved have magnitude 1 and each unit vector is perpendicular to the other two. Later you'll encounter questions that will involve the dot product of vectors which are not in unit vector notation (such as in vector geometry proof questions). Its important to know about the properties of the dot product.
I know it is the same answer but where does the zero come from?
What I did was expand it out, and just wanted to show that i.j =0 as they're perpendicular (same with i.k and j.k)
How do you calculate the magnitude of vector AB when you don't know the individual 'i' and 'j' values of a and b?
How do you calculate the magnitude of vector AB when you don't know the individual 'i' and 'j' values of a and b?a.b = 0 means that vector a and b are perpendicular
How do you approach a question like this. I have tried to split up A into its perpendicular and parallel components in relation to B but I don't know what to do from there :-[draw a large diagram to scale it may help you see things you haven't considered before
Any help would be great ???
I drew out a large diagram. Am I right in saying you want to calculate the component of (i +j) which is perpendicular to (3i + j); meaning you would find the dot product of these two position vectors divided by the magnitude of (3i +j)^2. When I do this I just get a fraction 2/5 instead of root17/5 (the answer to the question). What am I missing here?I agree with LifeisaConstantStruggle - I haven't actually been able to get the answer for this question either. However, I will show you my thought process:
Wouldn't be the first time I've been given work with incorrect answers :-XIf you think about it, the distance (or length) implies magnitude :)
What you said is exactly what I did and wouldn't the answer include 'i' and 'j' in it anyway since it doesn't ask for magnitude?
How do you answer a question like this? I know once I have values for cos u and sin u I just need to use one of the double angle formulas for cosine. But I have no idea how to find out what these values are
Yeah I know the 3 different cosine double angle formulas but I was asking about what values you set sin/cos equal to. For this example, if you used a double angle formula with cos in it, would the value for cos u or cos v (Depending) be 4/5 because of pythag theorem?You can absolutely use the Pythagorean theorem to find the value of cos, however be sure to consider the domain of alpha and beta (i.e. is it 4/5 or -4/5?).
Yeah I know the 3 different cosine double angle formulas but I was asking about what values you set sin/cos equal to. For this example, if you used a double angle formula with cos in it, would the value for cos u or cos v (Depending) be 4/5 because of pythag theorem?You can find cos(alpha) or cos(beta) using pythag but you wouldn't need to for this question.
Hi guys, first post here :o,Hey :)
Just a kinematics question that I want to make sure I've gotten right:
"Two particles, travelling in the same direction, pass a given point together at 8 m/s. Thereafter, one particle begins to slow down with a constant retardation of 2/7 m/s^2. The other continues for 6 seconds at 8 m/s and then slows down with a retardation of 1/9(t-6) m/s^2 where t is the time after the two particles were together. "
"Find how far each of the particles gave travelled when they come to rest."
The first particle was pretty simple; I got 112m. For the second one, I got an answer of 97m, which is the one I'm not quite sure about. Let me know! Cheers
Hi guys.It's the second one.
I can't seem to figure out how to prove this and was hoping somebody could run me through it?
I am pretty sure that the question was the first one but there is a slight possibility that it is the second one.
Thank you!
It's the second one.
Beginning from the RHS and using the identity 1 + tan2(x) = sec2(x)Spoiler
I'll let you finish it off :) Please post if you're having any issues.
Hope this helps :)
I had the exact same question in a recent test! I get to the stage cos^2(x/2) - sin^2(x/2) and I don't know what to do :P Which identity applies to this part??Has your teacher talked about the formula sheet which you receive in both exam 1 and 2?
I can't get the answer 3 root 2 :-[So OD = -i +2j
Can someone please tell me where im going wrong. To find vector ED I have been finding vector OE and OD. To find OE I subtracted vector OA from OE and to find vector OD i multiplied vector OB by 0.5. When I subtract vector OD from OE and and proceed to find the square root of the two coefficients of 'i' and 'j' squared; I always get an answer larger than 3 root 2!
Hi everyone !Have a sketch of the vectors a and b. You can see that the shortest distance from point A to the line OB can be represented by a line which is perpendicular to OB. In other words, this line between the line OB and point A is actually the component of a perpendicular to b! If you can find the magnitude of this 'line', you can find the shortest distance.
Can anyone explain question 8c to me please .
There isn't any examples for these type of questions :/
(https://uploads.tapatalk-cdn.com/20171112/193dc31a74588fd740ed6bdcd15901dd.jpg)
Thanks in advance !
Have a sketch of the vectors a and b. You can see that the shortest distance from point A to the line OB can be represented by a line which is perpendicular to OB. In other words, this line between the line OB and point A is actually the component of a perpendicular to b! If you can find the magnitude of this 'line', you can find the shortest distance.
Hope this helps :) Please post if you're still stuck.
Hi everyone !So shortest vector from A to the line OB is the vector component of a perpendicular to b.
Can anyone explain question 8c to me please .
There isn't any examples for these type of questions :/
(https://uploads.tapatalk-cdn.com/20171112/193dc31a74588fd740ed6bdcd15901dd.jpg)
Thanks in advance !
So shortest vector from A to the line OB is the vector component of a perpendicular to b.
To find the distance, you simply need to find the magnitude of this vector, the magnitude of the answer to b)
Can someone help me with this question?In this case, you can't take out t as it's inside the function (although they could have been clearer). If you could, however, you should know that cos(2π)=1 and sin(2π)=0
I took t out as a common factor then divided both sides by (2cos2pi + 2sin2pi) then I get stuck :(
Hey I just started Specialist today and i found it quite challenging... But the thing is that I actually got 95% as overall mark for my year 10 maths exams and i was in an accelerated maths class... Since im also doing two unit 3/4 subjects right now, should i give up specialist and switch into legal studies instead, or should i try to stick to specialist and see if things will work out?? THANKS A LOT!!Hey Elsa
Hey ElsaI see... I'm not sure yet but I think im going to stick with specialist xD Thank u xD
I don't think anyone can say anything regarding the 95%/accelereated maths since it would be different at every school and generally years 7-10 and units 1/2 can't say anything about how well you will do for 3/4. I would stick with spec at least for 1 year and just see how it goes then if you don't like it / unhappy with it switch into legal. Which subject would you prefer spec or legal?
In this case, you can't take out t as it's inside the function (although they could have been clearer). If you could, however, you should know that cos(2π)=1 and sin(2π)=0Just saw this... ew why don't they teach you guys the auxiliary angle transform?
I think this is a harder question than you'd normally expect.
Just saw this... ew why don't they teach you guys the auxiliary angle transform?
I don't recall ever being taught it, nor seeing a question like that :-\
It's part of the course but nobody pays that much attention to it
Just saw this... ew why don't they teach you guys the auxiliary angle transform?They should :P
It's part of the course but nobody pays that much attention to it
Mirroring Shadowxo, auxiliary angle is not in the course. :P But also, fuq dat. We don't do enough trig to warrant learning it.<Solves asin(x)+bcos(x)=c equations>
<Solves asin(x)+bcos(x)=c equations>
hi all how would you go by answering this question?
Hello everyone. :)none of the maths is meant to be hard it's all about where you fall amongst everyone in the state which will depend on how many careless errors you make.
I just started Specialist Maths last week (we're doing complex numbers) and it's... really easy. Lots of fun, but easier than Methods easy. (off topic but even though I got an A+ on the final maths test last year I forgot just about everything, RIP.) Does Specialist pick up later?
Also, the teacher ran through partial fractions for like 40 minutes then moved on and I don't think I 100% understand them. There's nothing in my textbook about them, so if anyone knows where to find practice questions I would really appreciate it.
Hi, can I get some help on this question? I have no idea on how to start this question.
Find the value of sec θ if tanθ = 0.4 and θ is not in the 1st quadrant.
IfJust use the double angle formula twice. You should actually get 2 answers within the principal value of -Pi , pi
Then what is the value of
Just use the double angle formula twice. You should actually get 2 answers within the principal value of -Pi , pi
What do you mean by use it twice? Can you please demonstrate?\begin{align*}\sin 4\theta &= 2\sin2\theta\cos2\theta\\ &= 4\sin\theta\cos\theta(\cos^2\theta-\sin^2\theta)\end{align*}
Can I please get some help on how to answer this?√3 cos(2x) − sin(2x) = r cos(2x + α).
√3 cos(2x) − sin(2x) in the form r cos(2x + α).
Hi could I get some help on this question?
Write in the form
My answer is
but the textbook answer has 5pi/4 instead of pi/4.
This gives \(d_2 = 3\) and \(d_1 = -6\), assuming I did not mess up basic arithmetic
Four teachers decide to swap desks at work. How many ways can this be done if no teacher is to sit at their previous desk?
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
How do you do this question?Firstly, a vector in the direction of \(\textbf{a}\) with magnitude 1 is the unit vector, \(\hat{\textbf{a}}\):
Let a =3i + 4j and b = i - j
Find the vector with the same magnitude of b with the same direction of a
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.
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
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’m 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.use vectors for the proofs (if you have learnt it) and it also would be helpful to revise all the circle thoerems.
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’m having trouble with are the ones that ask you to prove something.
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’m 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’m having trouble with are the ones that ask you to prove something.
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.
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!
Hi everyone,
I've come across something strange in my antidiff homework, I've attached the question for those who want to check.
I know it's the integral of the equation between x=4 and x=5 so I long divided it then used partial fractions etc and i checked this part on the CAS so i'm sure it's all fine, and one part of equation that I had to anti differentiate was 1/3(x-3) so i just took out the 1/3 and differentiated it as usual, so I got 1/3loge|x-3|. But I got an incorrect answer for the question as a whole.
Then I thought if i just expand those brackets in the denominator I get 1/3x-9 and that antidifferentiated is 1/3loge|3x-9|.... so two different answers from the same equation.... how do I know which one is right and what's the difference between these 2? Is there only one way to correctly antidifferentiate 1/3x-9 or are both acceptable?
I'm so confused!
plz help question 8B, dont really get this topic either...
For learning:Is there anywhere I can find any year 11 practise exams free though?
Khan Academy (and practice)
Paul's Online Math Notes
Better Explained
If you're running out of fresh questions to do, maybe try a methods textbook? Obviously not all the content will be the same but there's plenty of relevant stuff in there. You should ask your teacher too, they might have more resources. Personally, I learned the most during practice (and actual ::) ) SACs. This might also be helpful :)
Is there anywhere I can find any year 11 practise exams free though?As schools teach and assess different content it's quite difficult to get practice exams online that are indicative of what you will recieve from your teacher. Furthermore, commercial practice exams cannot be shared online due to copyright.
Because as it's the end of the year, I feel what I need to do most is exam style questions.
The thing is.
Our teacher doesn't really give us anything at all!
I've just got the textbook, and it doesn't have exam-like questions.
Even for Methods 1&2 though, I got like 5 practise exams off a friend.
So why isn't it possible to find any for 1&2 Specialist. I know that the content's slightly different but still.
Shouldn't there be like topic tests for like Geometry and Circle Geometry with like exam styled questions?
Thanks a load dude
The difference is that the Methods course is completely prescribed (ie. every school teaches exactly the same content). Specialist 1 & 2 is not; there is a lot of flexibility in what topics are chosen and how they are taught. So while there are commercial exams available for Specialist 1 & 2, schools may choose not to purchase them because the course they have run doesn't align with the questions on the commercial exams.
This also puts teachers in a difficult position because, typically, there is only one class and hence one teacher, so it's asking a lot for that one teacher to produce a whole lot of exam-like questions.
Don't worry, Units 3 & 4 is much better resourced.
(https://i.imgur.com/x7LXdmZ.png) Hey y'all can someone give us a hand with this one. Been trying for a while but I think I'm just missing 1 step repeatedly lol.For these types of questions (only MCQ so you always have your CAS and don't need to show working out) if you are struggling to convert the question into an answer a not so eloquent solution would be to assume x = some random number (you can go to heaps of decimal places) and then substitute that same number for all 6 expressions (The question + 5 answers) then you can select the one that matches.
I've checked all 5 answers on WolframAlpha and none of them are true.
A
B
C
D
E
It may be worth mentioning that I got it down to \( \frac12 \tan x \cos 2x \), which Wolfram does agree with.
For these types of questions (only MCQ so you always have your CAS and don't need to show working out) if you are struggling to convert the question into an answer a not so eloquent solution would be to assume x = some random number (you can go to heaps of decimal places) and then substitute that same number for all 6 expressions (The question + 5 answers) then you can select the one that matches.
EDIT: the above is more of an exam technique when you can't do the question rather than something you should always rely on :)
4. A woman has three children and two of them are teenagers, aged between 13 and 19.
The product of their three ages is 1050. How old is each child?
how do i even start this question
4. A woman has three children and two of them are teenagers, aged between 13 and 19.
The product of their three ages is 1050. How old is each child?
how do i even start this question
4. A woman has three children and two of them are teenagers, aged between 13 and 19.
The product of their three ages is 1050. How old is each child?
The methods suggested by other people will work, but they are not efficient.I think, in this case they are more efficient. The efficiency would break down if the range of numbers were greater, but here you only had to guess and check a total of 7 numbers. Here, the prime factorisation is perhaps moderate in difficulty to compute, however having to pair things off can also take time. You could've started by doing, say, 2*3 instead of going to 3*5. (When I looked at those, I seemed to be drawn to the last 3 numbers first, making numbers exceeding 20 before I considered the whole bundle in the one go.)
The best method is to use prime factorisation. The prime factorisation of 1050 is 2*3*5*5*7. Now just use these prime factors to find the ages of three children, two of which are between 13 and 19.
Perhaps... I think the prime factorisation is pretty immediate, since 2*5 is clearly a factor, and there are very few ways to use the prime factors to get a product between 13 and 19...
Then again, once you find that 1050 is divisible by 14, the other two ages are pretty obvious.
sorry if this is obvious/assumed knowledge but what does this mean from the worked solutions?
7 × 2 = 14
5 × 3 = 15
does it mean that any of the factors multiplied together also equals another factor of the original number?
When do you use tildes (~) and 'hats' (^) with regards to vectors, mechanics, etc? Also, with mechanics, do you write 'direction of motion', 'DOM', or 'positive direction', etc?
Thanks :)
Consider the quadratic equation:Your answer is correct. I can see that you solved \(a^2 - 4(4)(3) > 0\) because Wolfram gives the same answer.
Find all values of a such that the equation will have two distinct real solutions.
Is the following answer that I found correct? Also, how would you write the answer (first or second one, or do they mean the same thing)?
Thanks :)
Consider the quadratic equation:Both are fine in terms of vce
Find all values of a such that the equation will have two distinct real solutions.
Is the following answer that I found correct? Also, how would you write the answer (first or second one, or do they mean the same thing)?
Thanks :)
I don't know where to start with this question.
If the roots of are complex numbers and z is one of them, find:
i) Re(z) in terms of a
ii) The values of a such that Re(z) < 0.5
Thanks :)
HELP: 1. The number of ‘type A’ apple bugs present in an orchard is estimated to be 40 960, and the number is reducing by 50% each week. At the same time it is estimated that there are 40 ‘type B’ apple bugs, whose number is doubling each week. After how many weeks will there be the same number of each type of bug?
2.Consider the geometric sequence 1,a,a2,a3,.... Suppose that the sum of two consecutive terms in the sequence gives the next term in the sequence. Find a.
The numbers of Type A and Type B bugs each follows a geometric sequence. For Type A bugs, the initial value is 40960 and the ratio between consecutive terms is 0.5. Hence, the number of Type A bugs at week n is 40960*(0.5)^(n-1). Similarly, for Type B bugs, the initial value is 40 and the ratio between consecutive terms is 2. Hence the number of Type B bugs at week n is 40*(2)^(n-1). The number of each type of bug is the same when 40960*(0.5)^(n-1) = 40*(2)^(n-1).
If the sum of two consecutive terms gives the next term, then the sum of the first and second terms is equal to the third term. So 1 + a = a^2. (We could also use a + a^2 = a^3, and so on, but these all reduce to the first case).
having trouble with this question. Any thoughts?
“If tanƟ=4/3 and 180˚<Ɵ<270˚, evaluate (sinƟ-2cos(-Ɵ))/(cotƟ-sinƟ)”
*no calculator
-thanks
For number systems and sets, 2D question 11. Image attached.
How do you do this question? Obviously provide working out, thanks.
Hello guys.To share the kindness DBA shared through helping me, in part a of this question you determined BD.
I was wondering if anyone knew how to do question b?
To share the kindness DBA shared through helping me, in part a of this question you determined BD.
As it suggests to do, use the sine rule to work out CD.
Determine the angle opposite CD by determining the other unknown angle since this is possible using the known information. Once two angles are known, obviously the remaining angle can be found.
Refer to the attachment for the actual worked solution, I was merely explaining the process / what was done and why.
Ahahaha it would have been more kind if I gave you a fully worked solution but im too lazy to learn latex. Next time I might write it and attach a photo if time allows.The ambigiuous case? Hasn't done trigonometry for a while but wouldn't that break the triangle - sum of internal angles = 180° and if we considered the ambigiuous case, this angle plus the other known angle would already exceed 180°. Hence the ambiguous case isn't in this scenario as the angle has to be below 180 less the known angle (rough inequality)
However, for this question, why disnt you consider the ambiguous case? Just something to ponder over. Not trying to sound smart or whatever, but this might help you with your understanding. :)
When all eight factors of 30 are multiplied together, the product is 30k. What is the value of k?\begin{align*}30k&=(1\times 30)\times(2\times 15)\times (3\times 10)\times (5\times 6)\\
someone help me ......................... :-[
\begin{align*}30k&=(1\times 30)\times(2\times 15)\times (3\times 10)\times (5\times 6)\\
\implies 30k&=30^4\\
\implies \quad k&=30^3=27\,000\end{align*}
Yeah I got the same answer, the user who posted the question said that it is 30^4,in spec 3/4 question thread. imo its an error on the question's/textbook's part- can you confirm?
For the sequence 12, 6, 3, ..., S8 is equal to what?
Thnx in advance
im legit dying cause I got a methods SAT and a specialist SAT tomorrow ...and I had a 3/4 Psych SAC yesterday ... :-[
Hi.
I was wondering how to find x when y=1/8
hey is it me or is spec way more easier and interesting than methods
honestly methods is actually feeling more difficult than spec in year 11
I really want to drop a math but I know I can't drop methods...so rip spec :-[
Hi guys, first time posting on a forum! I feel like an old man with new technology, so if I've formatted anything wrong...oops.
Anyway, I just wanted to know if anybody could help me with this question? I don't know what I'm doing wrong, but I can't seem to come up with an answer (I sort of get it, but I need to show working/formal proof):
Prove that the recurrence relation xn+1 = (xn)2 + 2 does not converge to a single value.
If anyone could take a look at it it'd be so helpful for me! Thanks.
A stronger argument is to prove not only that the sequence does not converge, but that it is unbounded (ie. the terms approach infinity). This can be shown by noting that (xn)^2 > xn when n ≥ 1. Hence x(n+1) > xn + 2. So for any number L, we can find always find a term in the sequence that is larger than L.Tiny subtlety. \((x_n)^2 > x_n\) only if we can assume that \( |x_n| > 1 \). Just need to add in that if \(|x_n| \leq 1\), then \( x_{n+1} = (x_n)^2 + 2 > 0+ 2 > 1 \geq x_n\).
Tiny subtlety. \((x_n)^2 > x_n\) only if we can assume that \( |x_n| > 1 \). Just need to add in that if \(|x_n| \leq 1\), then \( x_{n+1} = (x_n)^2 + 2 > 0+ 2 > 1 \geq x_n\).
Otherwise makes sense. Is this stuff actually in the spesh 1/2 course?
I'm confused with a few questions regarding sequences and series
1) I need to find the next 3 terms of,
2,-1,4,3,6,-6
2) I'm so confused about the conversion from explicit to recursive relations, for example,
how do you change u(n)=n^2-4n=7 into a recursive relation
3) find the value of a for which (3,a+2,a^2) defines an arithmetic sequence
Hi guys!
I was wondering how to do question 3 c (attached below)?
I'm pretty sure they're asking for the vector resolute. So, why are they giving us the magnitude of b and how can I use it to get the vector resolute? Wouldn't they have to give us the vector b?
Thank you for your help. I understand now!
I was also wondering how to do question 8 b (attached below)? I'm not sure how to approach it.
If v is the component of a in the direction of b, then a – v is the component perpendicular to b.Yeah but how do you know that and how did you get there?
Yeah but how do you know that and how did you get there?
Hey there, I am usually never stuck with questions like this (sorry for the low difficulty I know it is kind of dumb :P)
...
I managed to do question a through part variation formula, but I don't understand the difference between question a and b. I checked the answer key and there were different answers for a and b
...
Hi guys!
I was wondering how to do the question attached below?
I'm not sure how to go about working it out as the question just gave us the weights. Is this enough info to work this out?
Hi guys!
I was wondering how to do the question attached below?
I'm not sure how to go about working it out as the question just gave us the weights. Is this enough info to work this out?
Hi guys!
I was wondering how to do the question attached below?
I'm not sure how to go about working it out as the question just gave us the weights. Is this enough info to work this out?
Hi guys!
I was wondering how to do the question attached below?
I'm not sure how to go about working it out as the question just gave us the weights. Is this enough info to work this out?
Never be afraid to ask questions regardless of the difficulty.
"During the sixth second" actually refers to the time between \(t=5\) and \(t=6\).
Think about it this way. The first second is between \(t=0\) and \(t=1\), the second second is between \(t=1\) and \(t=2\), and so on.
Hi guys!
I was wondering how to do the question attached below?
I'm not sure how to go about working it out as the question just gave us the weights. Is this enough info to work this out?
Hi guys!
I was wondering how to do the question attached below?
I'm not sure how to go about working it out as the question just gave us the weights. Is this enough info to work this out?
Never be afraid to ask questions regardless of the difficulty.
"During the sixth second" actually refers to the time between \(t=5\) and \(t=6\).
Think about it this way. The first second is between \(t=0\) and \(t=1\), the second second is between \(t=1\) and \(t=2\), and so on.
Hey there, I am usually never stuck with questions like this (sorry for the low difficulty I know it is kind of dumb :P)
Here it is:
The distance travelled (s) by a particle varies partly with time and partly with the square of time. If it travels 142.5 m in 3 seconds and travels 262.5 m in 5 seconds, find:
a) how far it would travel in 6 seconds
b) how far it would travel during the sixth second.
I managed to do question a through part variation formula, but I don't understand the difference between question a and b. I checked the answer key and there were different answers for a and b
Thank you much appreciated ;D
If v is the component of a in the direction of b, then a – v is the component perpendicular to b.
Hi guys!I am currently in year 10 doing 1 and 2 business management. next year I am hoping to do eng 1&2 methodes1&2 chem1&2 business management 3&4 and specialist 1&2. I also want to do physics so I thought after I complete Business management, in year 12 I'll do physics 3&4 without 1&2. But teachers said that really hard, so now I am confused in doing physics 1&2 in year 11 and not do spec at all. Is it worth it or not. In my career I want to do medicine or astrophysicist, I really need help guys.
I was wondering how to do question 3 c (attached below)?
I'm pretty sure they're asking for the vector resolute. So, why are they giving us the magnitude of b and how can I use it to get the vector resolute? Wouldn't they have to give us the vector b?
Hey, guys, I am currently in year 10 doing 1 and 2 business management. next year I am hoping to do eng 1&2 methodes1&2 chem1&2 business management 3&4 and specialist 1&2. I also want to do physics so I thought after I complete Business management, in year 12 I'll do physics 3&4 without 1&2. But teachers said that really hard, so now I am confused in doing physics 1&2 in year 11 and not do spec at all. Is it worth it or not. In my career I want to do medicine or astrophysicist, I really need help guys.There are many factors that need to be taken into account. For example:
There are many factors that need to be taken into account. For example:
- Do you feel like Spec is right for you? I mean, are you capable of handling methods and spesh? If you feel like you enjoy maths in general and you are willing to put in enough hard work (I had to anyway) then from what I know you should be fine.
- You said you wanted to do medicine right, then have you ever thought of doing bio?
- Are specialist and/or prerequisites for your aspiring university course?
As for Physics units 3/4 without 1/2, I can't say much, but from what I know if you have enough determination it is possible to do it. But let me just warn you that you will be at a disadvantage (depends on your school as well tho), as some concepts of physics units 3/4 (like for example my textbook relies on prior knowledge to study the concepts like magnetic flux and stuff), but DW, the disadvantage is not relatively large.
Hey, guys, I am currently in year 10 doing 1 and 2 business management. next year I am hoping to do eng 1&2 methodes1&2 chem1&2 business management 3&4 and specialist 1&2. I also want to do physics so I thought after I complete Business management, in year 12 I'll do physics 3&4 without 1&2. But teachers said that really hard, so now I am confused in doing physics 1&2 in year 11 and not do spec at all. Is it worth it or not. In my career I want to do medicine or astrophysicist, I really need help guys.above 90, but also do I require Bio knowledge to pass the UCAT
I am not interested in bio, and my physics teacher has given me chapters to do from 1&2 physics which require the prior knowledge for 3&4, I am also in an advance maths class and currently receiving above 90, but also do I require Bio knowledge to pass the UCATWell if your physics teacher is giving you those chapters then I guess you should be fine. From what I can see, you should be able to easily survive a spesh class as well. As for UCAT, most likely not since UCAT should just be an aptitude test, but I would recommend bio bcos u said your career could be surrounding medicine as well. That's up to you anyway, since you also have chemistry as a VCE subject and given that you pursue it to units 3/4.
Well if your physics teacher is giving you those chapters then I guess you should be fine. From what I can see, you should be able to easily survive a spesh class as well. As for UCAT, most likely not since UCAT should just be an aptitude test, but I would recommend bio bcos u said your career could be surrounding medicine as well. That's up to you anyway, since you also have chemistry as a VCE subject and given that you pursue it to units 3/4.man for building up my willpower and helping me decide my subjects, I'll try my best to achieve the highest atar possible, Thanks again
Thanks man for building up my willpower and helping me decide my subjects, I'll try my best to achieve the highest atar possible, Thanks again
Hey! Am doing further trigonmetry from the Cambridge textbook and am really stuck on proofs (I'm horrible at them!)
Can anyone possibly help me prove this identity?
sec (x) + cosec (x) cot (x) = sec (x) cosec^2 (x)
Also, when doing proofs llike this, do we tackle them as a show that question? Whats the best place to start?
I'd really appreciate any help.
Thanks!!! :)
Yes, a "show that" question is essentially asking you to give a proof.
For trig-identity questions like this, you generally have three methods. (1) Start with the LHS, and show, using legitimate steps, that it is equal to the RHS; (2) Start with the RHS and show, using legitimate steps, that it is equal to the LHS; (3) Work with both sides independently and show that they are each equal to some other expression. There is no foolproof method for knowing which is best in any given case. Improvement requires experience and practice; with that comes good judgement and intuition for how to get started.
For the question you've given, my first instinct is to multiply the LHS by cos(x), because that gives 1 + cot^2(x). That's useful, because I also know (from Pythgoras) that 1 + cot^2(x) = cosec^2(x). So, working backwards, now I consider what happens when I start with 1 + cot^2(x) = cosec^2(x), and divide both sides by cos(x)...
Let a be the magnitude of acceleration of each mass; let T be the tension in the string. Writing an equation of motion (ie. using F = ma) for each mass we have:Thank you so much, S_R_K!
1: 50a = T
2: 20a = 20g – T.
Adding equations gives 70a = 20g, so the acceleration of each mass is 2g/7. Hence the speed of each mass is 2gt/7, where t is in seconds.
Hello,
Can I please have some help with question (b)
I attempted the question by making 3 cases:
1) x is less than or equal to 5/2
I got x = -9
2) x is greater than or equal to 4
I got x=11
3) x is between 5/2 and 4.
For this case, I got x=19/3 but the answers only say x=-9 and x=11
Why is this the case?
Hello everyone I am in year 9, and I have a question if you could help me answer it please thnx
The mathematician George enjoyed telling his friends he was x years old in the year x2. Find the year of Georges birth given he died in 1871 (rip George)
Can someone please help me with this question, I don't really understand how to do it even after looking at the worked solutions. If a, 4a - 4 and 8a - 13 are successive terms of an arithmetic sequence, find a. Thankyou in advanceIn an arithmetic terms, successive terms must have the same common difference.
If sin (x)=0.3, cos (a) =0.5, tan (b) =2.4, and x, a and b are in the first quadrant. Find the values of the following:(a) = cos-1(0.5)
sin (pi-a)
I got 1/2 but the answers say root 3/2
i just wanted some assistance on how to get to that answer.
thanks in advance!
Evaluate (sin a + cos a)^2 + (sin a - cos a)^2Using the formulas (x+y)^2=x2+2xy+y2 and (x-y)^2=x2-2xy+y2,
I also wasn't really sure about this one, thanks again!
hi! i was wondering how to do these questions:
|x-4|-|x-2|=6
|2x-5|-|4-x|=10
thank you! but how would i know what cases to break it into?
https://imgur.com/etBnp6h . Find angle COD where O is the center and abcd lie on the circumference. context: my school is closing tomorrow and i had a sac today, got stumped on this question.
If it helps this topic was on congruence (of triangles), similarity (of triangles) and circle theorems.
∠BCA = 40° (half the angle at the centre subtended by the same arc).
∠APC = 128°
Hence, ∠CAD = 12°.
Hence ∠COD = 24° (using the same theorem as above).
Hi
I really need help with this question:
You just need to find the value of x
Thanks
Hey there!
Here's a diagram of the situation we have in part (d):
(https://i.imgur.com/1sJbZk2.png)
Basically, the max height we have is if the truck passes right through the middle. We have that the tunnel is 17m wide, which is where all the numbers come from. Thus we can also deduce the radius - which I haven't labelled, then use Pythagoras' theorem to find the max height h as labelled on the diagram.
Hope this helps :)
Hey
I needed help with another question:
A tunnel 300 m long has a semicircular cross-section. It requires temporary supports, AB and BC, as shown.
Point B is vertically above D. If AB = 15 m and BC = 8 m, find:
(a) the diameter of the tunnel
(b) the height of B above the floor of the tunnel
(c) the distance D is from the wall at C
(d) the maximum height a 3-metre-wide truck could be and still pass under the supports.
I just needed help with question d
Thanks :)
For (d), without assuming that the truck drives down the middle, here's a method to find the maximum height:
Let X and Y be points on AB and BC, respectively, such that XY is 3 m. Then BXY is similar to BAC. From this you can deduce the distance from X to AC (or from Y to AC).
Hi all,Not an official response from ATAR Notes but it could possibly be because of the content for Specialist Maths 1/2 differs quite a lot between schools in Victoria. Teachers take a lot of control of this subject and sometimes skip heaps of parts of the study design and add new topics. The reason they do this is because the study design of Spec 1/2 is not a great precursor for preparing for specialist maths 3/4.
I was wondering why there isn't a specialist math 1/2 ATARNOTES complete course notes book?
It would be very helpful if there were to be one, as I am taking specialist maths units 1 & 2 next year.
Kind Regards,
Shirin.
1) the first 3 terms in geometric sequence are 1,p,q. If the first 3 terms of an arithmetic sequence are 1,q,p.1) On the one hand, we have \(q - 1 = p - q\). On the other hand, we have \(\displaystyle \frac{p}{1} = \frac{q}{p}\). So \(p^2 = q\). Then substituting that into our first equation, we get
Show that 2p^2 - p - 1 = 0
2) given that geometric series 1+p+q+... converges, find
i) p
i) 1+ p+ q +...
Thanks in advance
I have an upcoming SAC for Unit 1 for Spesh and its my first Spesh SAC. I was just wondering if someone could give me a heads up or pointers to what to look out for or study to do well on it?What topics have you learnt so far this year and what will be tested on the sac?
What topics have you learnt so far this year and what will be tested on the sac?I'm not too sure what will be tested, mainly because we've been at home and all? We've done Sequences and series, Circle geometry, Further Trig, Complex and now we are doing Trigonometric ratios and applications. I think our teacher said when we return to school we may be doing Stats
I'm not too sure what will be tested, mainly because we've been at home and all? We've done Sequences and series, Circle geometry, Further Trig, Complex and now we are doing Trigonometric ratios and applications. I think our teacher said when we return to school we may be doing Stats
I struggle with geometric proofs. Any good websites with videos and questions that would help me with geometric proofs? Thanks
Hey All!
When doing the quotient & chain rule for example for this function
Then is this the proper working out? Like am I using the proper notation? Sorry I am new to Latex. Please tell me if there is a quicker accepted way. My teacher makes us write it out using composite functions (she marks whether we have included it), So idk if this is the right way?
Thank you!😀
Hey,
How would you do this question? (attached it below). I can do a and c once I have looked at a graph of it on desmos (attached below). But I would have not know how to do it otherwise.
What is the transformations that takes f(x) = arccos (x) to f(x) = arccos (6/x) (I was thinking maybe its a dilation by a factor of x^2/6 from the y-axis - but idk how this works?)
Thank you!
F=Arccos(1/x)
G=arcsec(x)
X = sec(G)=1/cos(G)
1/X = cos(F)
X = 1/cos(F) hence cos(F)=cos(G) ==~== F =~= G.
Hello,
Do Trig Sum/Difference formulae work for sin^2,cos^2 and tan^2?
Like does this work?
\(sin^2\left(x\right)cos^2\left(a\right)-cos^2\left(x\right)sin^2\left(a\right)\) = sin^2(x-a)
Thank you!
Hi,
Encountered this question, but don't know how to go about proving it. If anyone could help, that would be much appreciated!
Which means that:
<RPQ=<RPN=180-<RNP-<NRP=180-(a+b)/2-(90-(a+b)/2)=90
Just the very last point (I was so close...), how does <NRP = (90-(a+b)/2). Maybe I'm just not seeing it tonight...
Can someone please show me step by step how I'd solve this? Thanks
What are you struggling with? What have you tried yourself?
I tried multiplying it repeatedly, utilising the fact that i^2 is a real number. Can't get more minute than that, need help
Yeah, so as you've seen, that'll quickly become an issue because it only works for when n is an integer - which it might not be. Have you learned about using De Moivre's theorem? Because that'll be integral to solving this question
I haven't learn that, no. I'll learn out the theorem then try the problem again, if that doesn't work then I'll come back here. Thanks for telling me about De Moivre's theorem!
All good - information on the internet can be confusing, but there should be information in your textbook - and here's a quick summary:
Once you've converted your complex number, z, to polar form, then it has a modulus (r) and an argument (theta), and has the form:
Then, the form of z^n is:
Hi, I tried using DM's theorem. I converted the given problem to polar form, and expanded n. My approach has been that basically sin((-pi*n)/3 cannot equal i, as if it did then i times i means a real number. However, I tried to use the CAS to solve for n, but it's simply returning "false". Where to now?
Hi,
I need help with the following question:
Find the values of p and q such that is parallel to the x-axis.
I have worked out that:
I don't know how to get specific values for p and q so is parallel to the x-axis.
Any assistance will be much appreciated.
Hey,
A little guidance on the attached question would be much appreciated! I'm definitely missing something here.
Absolutely - before I help, I'm curious. What do you notice in this picture? Is there anything that jumps out at you? The 'trick' with circle theorem questions is to not focus on what you need to find, and to instead think what you notice about everything else in the question, then slowly build through smaller links until you eventually find one which tells you an unknown. So, what smaller things (maybe related to the pronumerals - maybe not) have you noticed about this particular circle?
Uh all I notice is that it's not stated that BC is a straight line. Oh and triangle DOC is isosceles. So is triangle BOD. (due to radius) If, however, BC is diameter, then <BDC is 90, but I don't know if that helps.
That's awesome! So, I think you can assume BC is a straight line - and if it is, that also means that ABCD is a cyclic quadrilateral. So, this should tell you what the value of a is - and hopefully using the facts you've already noticed, you should be able to get the rest.
So if ABCD is a cyclic quadrilateral (opposites sum to 180), then a=180-65=115. But that would mean b = 180 -2a = -50...? If triangle DOC is isosceles.
Or have I managed to stuff up the angles of a triangle?
Yeah - the fact that this shape CANNOT exist makes me think it's just a dud question. Notice how a looks acute, but the angle BAD looks obtuse? That's not just because it looks that way, it's because the angles HAVE to be that way for this specific shape to exist. I'm curious if you have answers for this question? If not, why don't you assume that a=65 degrees. In the spoiler, I'll tell you what b and c are, so that you can work it out yourself and have something to check against:Unfortunately I don't have answers; it's an old school 1/2 Specialist exam, but the answers are just missing for this section A.
Unfortunately I don't have answers; it's an old school 1/2 Specialist exam, but the answers are just missing for this section A.
If we let a=65, I got the same answers as you.
Side note, how does your 'alternatively' section work? As in how can we say a+c+90=180? Is it still to do with the opposite angles of cyclic quadrilateral sum to 180?
That's using the theorem that an angle subtended on a circle from the diameter is always 90 degrees
this one was one my year 11 exam
if i have the values of sin(x) and cos(x) then what is sin(x/2).
im guesing i need to expand it but i dont know how to... on my exam i guessed sin(x/2) = sin(x)cos(x)
Hello I am in year 11 and I am doing Spesh in the holidays , to get a head start.
I was stuck at this series question in the text book Ex 4E Q12
Find 1−x^2 +x^4 −x^6 +x^8 −···+x^2m ,where m is even.
Also please explain the answer.
Thanks :'(
Hey, I haven't done spec so I'm not 100% on how they would expect you to find it but here are some thoughts that may help:
This is an alternating series (it's a series where we see it alternating b/w + and -)
This then leads to thinking, well how do they get that alternation? We can do this by having (-1)^n and then when n is an odd number it will be (-1)^n = -1 but if n is an even number (-1)^2 = 1. (When you apply this double check if you start at positive or negative, sometimes you might do n + 1 rather than n as the power.)
Let's move on from the signs for a moment, we can easily see that we are incrementing the power of x by 2 each time. Since we start at a_0 = 1, we know that the power is starting at 0. We can represent this information using x^2n
Let's put this together:
a_n is the sum of (-1)^n x^2n
we are told that m is even (so that gives us a plus for our last term)
Hope this helps!
Hello I am in year 11 and I am doing Spesh in the holidays , to get a head start.
I was stuck at this series question in the text book Ex 4E Q12
Find 1−x^2 +x^4 −x^6 +x^8 −···+x^2m ,where m is even.
Also please explain the answer.
Thanks :'(
Yes I have but this question is particular is baffling me, and I can’t see why there are supposed to be m+1 terms
Have you covered the geometric series at all? If not, I reckon you just need to read up on that, and you'll probably be fine
Yes I have but this question is particular is baffling me, and I can’t see why there are supposed to be m+1 terms
Okay, well try breaking the series up and see if that makes things easier. Eg,
When m=1, you go up to x^(2m)=x^2: 1 - x^2
When m=4, you go up to x^(2m)=x^8: 1 - x^2 + x^4 - x^6 + x^8
Try a few more, fill out the series, count up the terms, and see what you notice
Hey there!Open for a diagram(https://i.imgur.com/L0ckaKE.png)
If you open the above spoiler, I've drawn a diagram on paint. Hopefully it's clear enough, the green triangle corresponds to the buoy with bearing 337 and the red triangle corresponds to the buoy with bearing 308.
Try using different colours and angle your North-South axis a bit so you leave space for the vertical axis for 3D diagrams like this, and feel free to exaggerate the angles a bit as diagrams don't really need to be accurate as they only serve as an interpretive tool.
Further help in the spoiler below if you need it, just in case of followups:SpoilerFind the distance from the cliff to each of the buoys using trig ratios, then use the cosine rule to find the distance between the buoys.
Hope this helps :)
Can someone please explain CHAPTER 4A Q1E.
You should use the recurrence relation found in part b).
Given that \(t_0 = 94.3s\), you need to be finding \(t_8\) using the relation as this indicates 8 weekly 4% reductions from her time.
pls explain 4C Q12
Hey guys need help with this question
I got part a, but I am stuck with part b.
Let A and B be the points defined by the position vectors a=i+3j and b=i+j
respectively. Find:
a the vector resolute of a in the direction of b
b a unit vector through A perpendicular to OB