2022 Paper 1 (13/01/2025)

Question 1

Exact Area of Rhombus using vectors?

Answer 1

Use magnitude of vectors to work out cross sections of the rhombus. Multiplying these by half will produce the height and base of a congruent triangle. Substituting this into the area of a triangle formula and multiplying by 4 will give the area of the rhombus

Question 2

|f(x)|?

Answer 2

This translation will turn the y-values positive

Question 3

lim Σ as an integral?

Answer 3

The top and bottom number on the sigma notation become the limits of the integral

Question 4

Contradiction statement for at least one odd?

Answer 4

Suppose both values are odd

Question 5

Maximum speed from modelled speed formula?

Answer 5

Differentiate and make the first derivative equal to zero

Question 6

e^-n x e^n?

Answer 6

1

Question 7

Arithmetic Series Proof?

Answer 7

Un = a + (n-1)d

Sn1 = (a) + (a+d) + (a+2d) + …. + (a + (n-2)d) + ( a + (n-1)d)
Sn2 = (a+ (n-1)d) + (a + (n-2)d) + …. + (a + 2d) + (a+d) + (a)

2Sn = Sn1 + Sn2
2Sn= (2a + (n-1)d) + (2a + (n-1)d) + (2a + (n-1)d)
2Sn = n(2a + (n-1)d)
Sn = 1/2n (2a + (n-1)d)