Variety of questions...

**Danielisew** · June 2nd 2007, 04:04 PM

Hey, i really need help with some kinds of questions and appreciate greatly any help I can get! I got a real GCSE test coming up on Monday! (I live in the UK...) Thanks

Q1: Below is a rough graph that shows a circle of radius 5cm, centre the origin.

Draw a suitable straight line on the diagram to find the estimates of the solutions of the pair of equations

x² + y² = 25
y = 2x + 1

x = _________ y = _________
x = _________ y = _________

Q2: Show that x² - 4x + 15 can be written as (x+p)² + q for all values of x. State the values of p and q.

p = __________
q = __________

Q3: The line y = 4 - 4x intersects the curve y = 3(x²-x) at the points A and B.

Use an algaebraic method to find the coordinates of A and B.

(___,___)
(___,___)

Q4: Prove algerbraically taht the sum of the squares of any two odd numbers leaves a remainder of 2 when divided by 4.

Q5: The table shows the number of students in each year group at a school.

Jenny is carrying out a survey for her GCSE Mathematics project.
She uses a stratified sample of 60 students according to the year group.

Calculate the number of year 11 students that should be in her sample.

That's all for now folks

Thanks very much if you can help me out with my exams coming up

Please can you keep an eye on my topic? I may post a couple more questions i come accross..

Thank you very much!

Dan

**Jhevon** · June 2nd 2007, 04:23 PM

Since it is to help you prepare for your exam, i will try not to give you any solutions, but to direct you on how to find the solutions on your own.

Originally Posted by Danielisew

Hey, i really need help with some kinds of questions and appreciate greatly any help I can get! I got a real GCSE test coming up on Monday! (I live in the UK...) Thanks

wow, a real GCSE test?! amazing. what are the fake ones like?

Q1: Below is a rough graph that shows a circle of radius 5cm, centre the origin.

Draw a suitable straight line on the diagram to find the estimates of the solutions of the pair of equations

x² + y² = 25
y = 2x + 1

x = _________ y = _________
x = _________ y = _________

umm...draw the line y = 2x + 1, and estimate the x and y values from the coordinates you see.

Q2: Show that x² - 4x + 15 can be written as (x+p)² + q for all values of x. State the values of p and q.

p = __________
q = __________

here you simply complete the square. don't know how to do that? just do a search. there are tons of posts where members (including myself) have instructed others on how to complete the square. find them and read them. you should get them. if not, get back to us.

Q3: The line y = 4 - 4x intersects the curve y = 3(x²-x) at the points A and B.

Use an algaebraic method to find the coordinates of A and B.

(___,___)
(___,___)

intersecting points occur when the two graphs are equal. that is, we must solve:

$4 - 4x = 3\left( x^2 - x \right)$
do that to find the x-values, then plug the answers into either of the original equations to find the y-values. get back to me with your solutions.

Q4: Prove algerbraically taht the sum of the squares of any two odd numbers leaves a remainder of 2 when divided by 4.

Hint: an odd number can be expressed as 2n + 1 for some integer n. a number that leaves a remainder of 2 when divided by 4 can be expressed as 4m + 2 for some integer m. show that when you add two numbers of the form 2n + 1 you get a number of the form 4m + 2

Q5: The table shows the number of students in each year group at a school.

Jenny is carrying out a survey for her GCSE Mathematics project.
She uses a stratified sample of 60 students according to the year group.

Calculate the number of year 11 students that should be in her sample.

this looks kind of like a statistics question or something. not good with that. but i think we can go off percentages here. you have the number of all the student in the table. find what percentage of students are 11 year students (put the number of 11 year students over the total number of students and multiply that by 100 to get the percentage). when done, find that same percentage of 60, it should give you the answer you seek

**Danielisew** · June 3rd 2007, 02:03 AM

yeah the 'fake' ones are called mocs!
Anyway, i did not understand ONE of those apart from the completing the square one

**Jhevon** · June 3rd 2007, 06:40 AM

Originally Posted by Danielisew

yeah the 'fake' ones are called mocs!
Anyway, i did not understand ONE of those apart from the completing the square one

you mean "mocks"

Originally Posted by Danielisew

Q1: Below is a rough graph that shows a circle of radius 5cm, centre the origin.

Draw a suitable straight line on the diagram to find the estimates of the solutions of the pair of equations

x² + y² = 25
y = 2x + 1

x = _________ y = _________
x = _________ y = _________

i have attached a diagram below. it should be a circle even though it doesn't look like it. on this diagram i re-graphed the circle and also graphed the line y = 2x + 1. the intersections are the points they want. can you estimate them from the graph? (i suppose in the exam they will give you the graphs on a grid so that it is easier to guess).

Q2: Show that x² - 4x + 15 can be written as (x+p)² + q for all values of x. State the values of p and q.

p = __________
q = __________

you said you got this, so i'll leave it

Q3: The line y = 4 - 4x intersects the curve y = 3(x²-x) at the points A and B.

Use an algaebraic method to find the coordinates of A and B.

(___,___)
(___,___)

i don't see why you didn't get this, i gave you the equation to solve.

$4 - 4x = 3(x^2 - x)$
$\Rightarrow 4 - 4x = 3x^2 - 3x$
$\Rightarrow 3x^2 + x - 4 = 0$

I trust you can solve this.

you will get two values for $x$ i will call them $x_1 \mbox { and } x_2$ . once you get them, plug them into the easier of the equations to find the corresponding $y$ -values. (You can plug them into either equation, but why make life hard?)

So, you will have: $y_1 = 4 - 4(x_1)$

and $y_2 = 4 - 4(x_2)$

the points you want are $(x_1 , y_1)$ and $(x_2 , y_2)$

Q4: Prove algerbraically taht the sum of the squares of any two odd numbers leaves a remainder of 2 when divided by 4.

An odd integer can be written as $2n + 1$ for $n \in \mathbb {Z}$

Let two odd integers be $2n + 1$ and $2m + 1$ for integers $m \mbox { and } n$ .

Then the sum of their squares are given by:

$(2n + 1)^2 + (2m + 1)^2$

expand this and try to get it in the form $4k + 2$ where $k$ is an integer. that will prove your claim.

Q5: The table shows the number of students in each year group at a school.

Jenny is carrying out a survey for her GCSE Mathematics project.
She uses a stratified sample of 60 students according to the year group.

Calculate the number of year 11 students that should be in her sample.

what is the percentage of 11 year students in the school? (or we can deal with fractions not percentage, you will get the same answer though).

$Percent \mbox { } of \mbox { } 11 \mbox { } year \mbox { } students = \frac {number \mbox { } of \mbox { } 11 \mbox { } year \mbox { } students}{total \mbox { } number \mbox { } of \mbox { } students} \times 100$

$= \frac {130}{190 + 145 + 145 + 140 + 130} \times 100$

$= \frac {130}{750} \times 100$

$= 17.33 \%$

Now, find $17.33 \%$ of 60 to find your answer

Please try something! I don't want to give you full solutions because that will not help you prepare for your exam. You have to try and do the material on your own so your brain gets used to thinking about things in the right way. Don't worry about making mistakes, if I see you make an honest attempt on a question, I will tell you where you went wrong and provide another hint, or even give you the full solution (which apparently is what you are after)

**Jhevon** · June 3rd 2007, 10:28 AM

Originally Posted by Danielisew

yeah the 'fake' ones are called mocs!
Anyway, i did not understand ONE of those apart from the completing the square one

remember, i'm looking forward to seeing your solutions. we want to have all these problems ironed out by tomorrow

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