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Has anyone ever heard of, or even better, used these things called a beauty spot summary? My teacher keeps asking my to use them, and praises their "transformational power" of summarising. I'm a little bit sceptical of them, and I was wondering if anyone here could offer me a second opinion with...

In how many ways can the host and hostess and 4 visitors be arranged around a round table if the host and hostess sit next to each other? My line of thinking: \\$Consider host and hostess as one group. There are 5 groups, and within the host and hostess, they can be arranged 2! ways.$\\5...

If someone could do a worked solution for this, I'd appreciate it. $If $|z|=r$ and $arg\: z=\theta$, show that $\frac{z}{z^2+r^2}$ is real and give its value.

Nine people are to be seated at a thin rectangular table with 4 people on one side and five on the other. How many different ways can these nine people be seated if: Mary and John must sit on the same side Mary and John must sit on opposing sides

I'm having trouble with a question from a past paper, please help. A rocket is fired vertically but begins to turn towards the tangent of Earth's surface. At a height of 260m the rocket runs out of fuel and is travelling at a 65 degree angle to the horizontal and follows a parabolic...

Question 14a from Cambridge 3 Unit Year 11 Exercise 11E $Sketch $y=x^2$ and mark the points A(a, $a^2$), B(-a, $a^2$), P(a, 0) and Q(-a,0).$\\$Show that $\int^a_0 x^2 \, dx = \frac{2}{3}$ (area of triangle OAP).$

I don't know how I would approach this question: All the letters of the word ENCUMBERANCE are arranged in a line. Find the total number of arrangements, which contain all the vowels in alphabetical order but separated by at least one consonant.

Question 5a and 5b from 2.1 in the Cambridge 4 Unit Maths textbook: $5a. $a\alpha^2+b\alpha+c=0$, where a,b,c are real and $\alpha$ is complex. Show that $a\bar{\alpha}^2+b\bar{\alpha}+c=0. I remember hearing that the roots to a quadratic are complex conjugates of each other, but I don't...

Cambridge 3 Unit HSC 10F, 16b. $Ten coloured marbles are placed in a row. What is the minimum number of colours needed to guarantee at least 10 000 different patterns? [HINT: This will need a guess-and-check approach.]$\\$My logic is: $3^{10}=59049$ but $2^{10}=1024$ therefore 3 colours are...

I struggle with this topic, though I'm trying to get better. I'd appreciate it if you could show me the working for this question: $Sophia, Gabriel and Elizabeth take their driving test. The chances they pass are $\frac{1}{2}$, $\frac{5}{8}$, and $\frac{3}{4}$ respectively. If only one of them...

I am 90% sure this question is wrong, but I wanted to post it here just in case I'm wrong. $Show that a polynomial with leading term $-x^3$ and a double root at $x=1$ has another root at point where $x>1. This is from Margaret Grove's Preliminary Maths in Focus 3 Unit textbook - 12.5 Q20. I...

Hey everyone, please explain how to do these... 1. Numbers are formed from the digits 1, 2, 3, 3, and 7 at random. In how many ways can they be arranged to form a number greater than 30 000? (Answer is 72). My thinking: In that question, I understand that the first number must be a 3, 3...

Ok, here's the deal. I've been trying to graph the function x^2+8x+y^2-8y+2xy+16=0, and on a graphing calculator such as this here, and I've noticed the graph is a circle, with centre (-4,4) and radius 4. x^2+8x+y^2-8y+2xy+16 seems to be equivalent to x^2+8x+y^2-8y+16, which is also a circle...

Hey everyone, I was just doing a past paper, and I found this question. I feel like x should be equal to 12, but I don't know how to show it. If I could see working out for this, that would, be great.

Does anyone have any good resources for circle geometry questions? I've done all of Maths in Focus, but the past papers I've been doing seem to have much harder questions (who knew?). The year 11 Cambridge textbook doesn't seem to cover it at all, and I can't find anywhere else.

$Express $\cos{x}+7\sin{x}=5$ in the form $A\cos{(x+\alpha)}$. Hence, solve $\cos{x}+7\sin{x}=5$, 0^{\circ}\leq x\leq360^{\circ} I can express it in as a sine, but how do I get it to a cosine?

Does anyone have any engineering studies preliminary yearly past papers? I can only seem to get my hands on a few.

\text{The point P(x, y) moves so that its distance AP from the point A(5, 1) is always twice its distance BP from the point B(-1,4).}\\\text{Show that the equation of the locus is: }x^2+y^2+6x-10y+14=0} I seem to be getting an answer different to the locus given.

Hi everyone, I have a school assignment which is due on the first day back to school (Tuesday 14th). I need to get in contact with my teacher before that in order to clarify something on the assignment. Is there some sort of directory of teacher email addresses for teachers who go to my...

I was just doing a past paper and my answer to a question didn't match the answer in the answers. Here's the question. A magician decides to use an electric field to levitate (float) a light plastic ball in the air. The ball has a mass of 15 grams and can be given a charge of +0.5 coulombs...