LC Applied Maths case studies
LC Applied Maths · Put your knowledge to work in context.
Leaving Certificate Applied Mathematics is a senior-cycle subject in Ireland for students who want to model real physical situations with mathematics rather than memorise procedures. It suits candidates who are comfortable with algebra, trigonometry and calculus and who enjoy setting up a problem from a written description, choosing the right physical principle, and carrying the solution through to a numerical answer with correct units. The LC Applied Maths case studies are 5 cases and about 3,234 words.
1Block on a Rough Incline: Two Stages, Two Accelerations
A block of mass 2 kg is projected up a rough plane inclined at 30° to the horizontal with an initial speed of 8 m/s. The coefficient of friction between the block and the plane is 0.25 and g = 9.8 m/s².
695 words, about 3 min2Ladder Against a Smooth Wall: How Far Can the Painter Climb?
A uniform ladder of length 5 m and mass 20 kg rests with its foot on rough horizontal ground and its top against a smooth vertical wall. The ladder makes an angle of 60° with the ground and the coefficient of friction between the ladder foot and the ground is 0.3.
720 words, about 4 min3Conical Pendulum: Tension, Angle and the Minimum Speed
A small ball of mass 0.4 kg is attached to a light inextensible string of length 1.2 m whose other end is fixed. The ball is set moving in a horizontal circle so that the string traces a cone of semi-vertical angle θ with the vertical.
652 words, about 3 min4Filling a Conical Tank: A Rate That Will Not Stay Constant
An inverted conical tank has height 6 m and top radius 3 m. Water is pumped in at a constant 0.5 m³ per minute and the tank starts empty.
571 words, about 3 min5Batch Inspection: Binomial, Normal Approximation and a Conditional Check
A production line makes electronic components and, historically, 8% are defective. A batch of 150 components is inspected and rejected if more than 15 defectives are found.
596 words, about 3 min