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.

wow, arealGCSE test?! amazing. what are the fake ones like?

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

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 = _________

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.

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 = __________

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

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.

(___,___)

(___,___)

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.

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

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

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

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.