GSCE Maths

Question 1

even x even= even
even x odd= even
odd x odd= odd

Answer 1

even + even= even
even + odd= odd
odd + odd= even

Question 2

(2n+1)+(2n+3)

Answer 2

4n+4

4(n+1)

Question 3

proofs follow these formats

Answer 3

a number (n)
an even number 2(n)
an odd number 2(n)+1

Question 4

even number example

Answer 4

2n+4(n+1)+4 is always even
2n+4n+4+4
6n+8
2(3n+4)

Question 5

odd number example

Answer 5

4(2n-3)-3(2n-1) is always odd
8n-12-6n+3
2n-9
2(n-8)-1

Question 6

the sum of two consecutive odd numbers, is always a multiple of 4
example

Answer 6

(2n+1)+(2n+3)
4n+4
4(n+1)

Question 7

when x is even, (x-2)^2 is even

Answer 7

subtracting an even number keeps it even and any even number multiplied by any even number stays even
(x-2) is even, an even number squared is even
-2 and it stays even, x by itself and it stays even
even-even=even, even x even=even
even-even=even, and even x even/odd=even

Question 8

ax^2+axc+x+b=5x^2+11x+8

Answer 8

ax^2+axc+x+b=5x^2+11x+8

a=5, b=6, c=2

Question 9

prooving if a gradient is perpendicular

Answer 9

the two gradients multipled should equal -1

Question 10

Float and ping

Escalator

Answer 10

Float and ping the number (e.g -3 or 2)
x/4=12 take 4 up the escalator
4x=12 take 4 down the escalator