Advanced level 2025 BAEBOC Pure mathematics 2

Advanced level 2025 BAEBOC Pure mathematics 2

Advanced level 2025 BAEBOC Pure mathematics 2

This is for informational purposes only. For medical advice or diagnosis, consult a professional.

I’ve extracted the data from the image you shared:

1. Given that α and β are roots of the equation x2−3x+2=0.

(i) Show that α2+β2+12=2αβ. (ii) Hence without solving the equation above, state an equation whose roots are $\alpha \beta +2$ and $\alpha +\beta$. (iii) Solve for $x$ in the equation 42x−3(2x+1)−8=0. (iv) Find the set of values of $x$ for which $(x+1)(x+2)(x+3)\ge 0$.

2. Given that f(x)=x3+6x2+11x−12.

(i) Show that $x-1$ is a factor of $f(x)$. Hence or otherwise, solve the equation $f(x)=0$. (ii) Obtain the first three non-zero terms of the expansion (1−2x)1/4.

3. The sum to infinity of a geometric progression is 4. When the terms of the geometric progression are squared, the sum to infinity is 3.

(i) Find, for each progression, the first term and the common ratio. (ii) A quarter council consists of 6 men and 5 women. Find the number of ways in which: (a) this council can sit in a straight line given that the oldest man and oldest woman must be together; (b) a mixed gender executive team of 6 persons can be selected from the council given that it must contain at least 2 men and at least 2 women.