Further Pure 1

Question 1

What are the steps for proof by induction?

Answer 1

• Show that the statement is true for n=1
• Assume that the statement is true for n=k
• Prove that if the statement is true for n=k, it must also be true for n=k+1
• Write out the above steps coherently

Question 2

What does the determinant of a matrix transformation tell you about the shape it transforms?

Answer 2

The factor by which the area of the shape is enlarged

Question 3

What are the roots, (α, β, γ), of a polynomial ax³+bx²+cx+d?

Answer 3

• α + β + γ = -b/a (Sum of the roots Σα)
• αβ + βγ + αγ = c/a (Sum of the product of the roots Σαβ)
• αβγ = -d/a (Product of the roots Πα)