2023 Paper 1 (10/01/2025)

Question 1

cosx alternative form?

Answer 1

cosx = 1 - ( α ^2 / 2)

Question 2

Trapezium Rule?

Answer 2

{ 0.5 x h { yo + yn + 2(y1 + y2 ….)

Where “h” is the difference between each “x” term. “yo” is the first y term. “yn” is the last y term. “y1” This bracket contains the “y” values between yo and yn.

Question 3

Choosing constant in geometric sequence?

Answer 3

|r| < 1 . If this inequality is disproved when the constant is substituted into n2 / n1 = n3/ n2 then that constant can be ignored

Question 4

Differentiation First Principles Formula of sinx?

Answer 4

dy/dx = lim h->0 [ (sin(x+h) -sinx)/ ((x + h) -h) ]

Question 5

Maximum of any trig function?

Answer 5

1

Question 6

Summary of proof of odd and even numbers?

Answer 6

hence odd/even for all n ∈ ℝ