Cambridge IAL Mathematics case studies
Cambridge IAL Mathematics · Put your knowledge to work in context.
Cambridge International AS & A Level Mathematics (9709) is a Cambridge Advanced qualification assessed by written examination. It is designed for learners in the final years of secondary schooling who want a mathematically rigorous subject that supports progression to higher education or directly into employment. The Cambridge IAL Mathematics case studies are 5 cases and about 2,095 words.
1Cubic with a Parameter: Exactly Two Real Roots
A curve C has equation y = x^3 - 6x^2 + 9x + k, where k is a real constant. A student is asked to determine the values of k for which C has exactly two distinct intersections with the x-axis.
445 words, about 2 min2Logarithmic Equation and Domain Restrictions
An equation is given as log 2(x + 3) + log 2(x - 1) = 3. A student combines the logarithms, solves the resulting quadratic, and obtains x = -1 + 2 sqrt(3) and x = -1 - 2 sqrt(3).
429 words, about 2 min3Projectile Passing Two Walls
A ball is projected from point O on horizontal ground with speed 20 m/s at 35 degrees above the horizontal. A vertical wall of height 5 m stands 18 m from O.
371 words, about 2 min4Connected Particles with a Slack String
Block A of mass 3 kg rests on a rough horizontal table and is connected by a light inextensible string over a smooth pulley at the table edge to block B of mass 2 kg, which hangs vertically. The coefficient of friction between A and the table is 0.25.
363 words, about 2 min5One-Tailed Binomial Test and Sample Size
A company claims that 30% of customers prefer a new design. A researcher suspects the true proportion is lower and surveys 40 customers, of whom 8 prefer the new design.
487 words, about 2 min