Further maths core pure

Question 1

Roots of polynomials - sum of squares for quadratic

Answer 1

(α + β)^2 - 2αβ

Question 2

Roots of polynomials - sum of squares for cubic

Answer 2

(α + β + γ)^2 - 2(αβ + αγ + βγ)

Question 3

Roots of polynomials - sum of squares for quartic

Answer 3

(α + β + γ + δ)^2 - 2(𝜶𝜷 + 𝜶𝜸 + 𝜶𝜹 + 𝜷𝜸 + 𝜷𝜹 + 𝜸𝜹)

Question 4

Roots of polynomials - sum of cubes for quadratic

Answer 4

(𝜶 + 𝜷)^𝟑 − 𝟑𝜶𝜷(𝜶 + 𝜷)

Question 5

Roots of polynomials - sum of cubes for cubic

Answer 5

(𝜶 + 𝜷 + 𝜸)^𝟑 − 𝟑(𝜶 + 𝜷 + 𝜸)(𝜶𝜷 + 𝜷𝜸 + 𝜸𝜶) + 𝟑𝜶𝜷𝜸

Question 6

Volumes of revolution - limitations

Answer 6

The equation of the curve may not be a suitable model
The sides of the ornament will not be perfectly smooth
There may be flaws/bubbles within the glass
The corner (ABC) may not be a perfect right angle

Question 7

Maclaurin, why -1 <= x <= 1 for ln(1+x)

Answer 7

Series does not converge for values beyond this range

Question 8

3x3 Matrix transformation for reflection in x=0, y=0, z=0

Answer 8

[ 1, 0, 0]
[ 0, -1, 0]
[ 0, 0, -1]

[-1, 0, 0]
[ 0, 1, 0]
[ 0, 0, -1]

[ -1, 0, 0]
[ 0, -1, 0]
[ 0, 0, 1]