C2 Practice Paper (From the book)

Hey,

Just doing the practice paper at the back of the C2 Edexcel book (http://bit.ly/GQ7IzR).

The first question is:
1. The sector <AOB is removed from a circle of radius 5cm. The <AOB is 1.4 radians and OA=OB.
a) Find the perimeter of the sector AOB.
b) Find the area of sector AOB.

When I try part b), I get 1.4 rads = 80.214... And area = 1/2 x s1 x s2 x sin(theta) (Using the SAS rule). I therefore get 0.5 x 5 x 5 x sin(80.21...) which gives me 12.318... but the book says it's 17.5.

Any ideas on how to do this? Even better, anyone got a mark scheme for the paper *with* workings?

Thanks.

Reply 1

roar558

Original post by NotADuck

Why not just use the area of a sector equation

A=r^2(angle in radiens/2)

(edited 12 years ago)

Reply 2

NotADuck

Ok, that worked!

Thanks for your help, I really appreciate it (Can't believe I just spent 40 minutes using Heron's Theorem and the Cosine rule!)

Any ideas how to do part a)?

Thanks for your help.

Reply 3

roar558

Perimeter equation of a sector is
P=r(angle in radiens+2)

Reply 4

NotADuck

Ok, I managed to do a).

Pi x D = Circle perimeter.

10 x Pi = Circle perimeter (Diameter = 10).

.'. Each degree = (10Pi)/360.

1.4c = 80.214091318* (Angle given = 1.4c)

.'. Perimeter of sector = 5 + 5 + (10Pi)/360 x 80.21... (The two radii are 5).

.'. Perimeter of sector = 17cm.

Thanks again for your help!

Reply 5

NotADuck

This entire paper is hard.

Does anyone have the mark scheme with workings? (I have the answers, but no workings for it)

Thanks.

Reply 6

raheem94

Original post by NotADuck

This entire paper is hard.

Does anyone have the mark scheme with workings? (I have the answers, but no workings for it)

Thanks.

Tbh, this isn't a hard paper, these are fairly basic questions.

You can get the solutions of it from the solution bank, the solution bank is included in the cd that comes with the book.

If you don't have the cd, then reply so that i can tell you an alternative.

Reply 7

NotADuck

I need to show working to get full marks though, so the solution bank isn't much good :P

Any ideas as to where I can get working to the answers?

Thanks.

Reply 8

raheem94

Original post by NotADuck

I need to show working to get full marks though, so the solution bank isn't much good :P

Any ideas as to where I can get working to the answers?

Thanks.

The working in solution bank is good enough to score full marks.

Its just a 5 marks question so the below working is fine to score all.

Reply 9

NotADuck

In the solution bank there's just... uhh... The solutions xD There's no working whatsoever in my book.

Reply 10

raheem94

Original post by NotADuck

In the solution bank there's just... uhh... The solutions xD There's no working whatsoever in my book.

The solutions are in the cd that comes with the book. The book only contains the answers not solutions.

The image i posted in my previous post is from the solution bank given in that cd.

Do you have the cd?

Reply 11

NotADuck

I have the CD, but I'm on a Mac where I'm not admin so I can't run the .exe. Any ideas as to how I could get the solutions?

Reply 12

Implication

I know you've already had the answers to the questions you're stuck on, I just thought I'd give you a little hint for sector and circle questions.

The area of a sector is the area of the whole circle multiplied by how much of the circle you have, and the arc length of a sector is the perimeter of the whole circle multiplied by how much of the circle you have. "How much" of the circle you have is simply the angle in the sector over the total angle in a circle (i.e. 360 degrees or 2pi radians) :smile:

So,

A_{sector}=\pi r^{2} \times \frac{\theta}{2 \pi} = \frac{r^{2} \theta}{2}

, where theta is in radians.

A_{sector}=\pi r^{2} \times \frac{\theta}{360} = \frac{ \pi r^{2} \theta}{360}

, where theta is in degrees.

l_{arc}=2 \pi r \times \frac{\theta}{2 \pi} = r \theta

, where theta is in radians.

l_{arc}=2 \pi r \times \frac{\theta}{360} = \frac{2 \pi r \theta}{360}

, where theta is in degrees.

Reply 13

NotADuck

Original post by Implication

So,

A_{sector}=\pi r^{2} \times \frac{\theta}{2 \pi} = \frac{r^{2} \theta}{2}

, where theta is in radians.

A_{sector}=\pi r^{2} \times \frac{\theta}{360} = \frac{ \pi r^{2} \theta}{360}

, where theta is in degrees.

l_{arc}=2 \pi r \times \frac{\theta}{2 \pi} = r \theta

, where theta is in radians.

l_{arc}=2 \pi r \times \frac{\theta}{360} = \frac{2 \pi r \theta}{360}

, where theta is in degrees.

Wow that's extremely helpful for in the future. Thanks for that, must've taken you a long time!

Reply 14

raheem94

Original post by NotADuck

I have the CD, but I'm on a Mac where I'm not admin so I can't run the .exe. Any ideas as to how I could get the solutions?

The solution bank usually runs on internet explorer, it doesn't supports other browsers such as google chrome, so i don't know if it will work on mac.

Just try this,
Don't click on the .exe, click the contents folder.
From the 'contents' folder open the 'sb' folder.
From the 'sb' folder open the 'contents' folder.
Now click on .html or .xhtml files and run them.

Hope it works.

Reply 15

NotADuck

Thanks for that, but it requires IE.

I guess I'll have to hand this in late, it's due in in 25 minutes and I've done 1/9 questions.

Thanks to everyone for your help!

FTR: I don't willingly use a Mac, but it's all the school has.