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# Can anyone explain these maths questions?

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1. http://vle.woodhouse.ac.uk/topicdocs...s/smc1996Q.pdf
The questions 22, 23, 24 and 25 are really confusing me. Any help is great, thanks.
2. Not sure if it's because I'm on the phone but the link you provided only gives questions up to question 20
*Edit. Whoops, the last page is at the front, my mistake
3. Well 22 and 24 are the easiest to explain.

For 22, you need to know how the graphs work. Last number without an x simply moves it up or down on the graph so it doesn't matter.
Having the first number a minus starts with the graph going up so that's automatically out.
What's left is figuring out what kind of graphs they make. You should know that having all x numbers either positive or negative creates u shaped graph.
So we know the first number can't be a minus. Last number doesn't matter and that same type of numbers make u shaped graphs.
So you need graphs that begin with a plus, then have a minus and the single number sign does not matter.

24 is also simple. You just need to know that the area of equilateral is √3/4 x a^2 where a is the length of its side. The triangle is called that because all sides are equal and the task asks you to fit it into a square of side a. So you are literally given the a and just need to know the equilateral area formula and move it a bit to get the answer in correct format.
4. (Original post by Devify)
Well 22 and 24 are the easiest to explain.

For 22, you need to know how the graphs work. Last number without an x simply moves it up or down on the graph so it doesn't matter.
Having the first number a minus starts with the graph going up so that's automatically out.
What's left is figuring out what kind of graphs they make. You should know that having all x numbers either positive or negative creates u shaped graph.
So we know the first number can't be a minus. Last number doesn't matter and that same type of numbers make u shaped graphs.
So you need graphs that begin with a plus, then have a minus and the single number sign does not matter.

24 is also simple. You just need to know that the area of equilateral is √3/4 x a^2 where a is the length of its side. The triangle is called that because all sides are equal and the task asks you to fit it into a square of side a. So you are literally given the a and just need to know the equilateral area formula and move it a bit to get the answer in correct format.
Ohhhh okay thanks! I'll try answering them again
5. For 22, the graph has two roots, so the equation must have two real solutions and a complex conjugate pair of solutions to satisfy the graph equation.
6. For 25, we can consider BE to be "y" and DF to be "x".
From Pythagora's theorem, we know that (6+x)2+(6+y)2=202.
Triangles BCE and DFC are similar, meaning that sides DF and BC are proportional, and CF and EC are proportional.
Those proportionalities have the same constant, hence x/6=6/y.
Spoiler:
Show
(6+x)2+(6+y)2=202 develops into 36+12x+x2+36+12y+y2=400.
Rearanging the terms, we get x2+y2+12x+12y+72-400=0.

From there, we can complete the square with the x2+y2, which gives us x2+2xy+y2, then (x+y)2.

Knowing that x/6=6/y, xy=36, meaning that 2xy=72.
x2+2xy+y2+12x+12y+72-400=2xy
(x+y)2+12(x+y)-400=0

We're searching for the perimeter of the shape which corresponds to 20+6+6+x+y. We have a quadratic equation with (x+y), which we can solve to get: x+y=2*sqrt(109)-6

We get our final answer of 26+2*sqrt(109).
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