Applied Maths, One Strand at a Time
Leaving Certificate Applied Maths, strand by strand. The formulas that matter, the methods that save time, and the mistakes that quietly cost marks — Higher Level.
Applied Maths: Units and Vectors (Strand 1) — Higher Level Notes
Dimensional analysis, the i-j plane, dot products and polar form. The chapter that decides whether the rest of Applied Maths feels like algebra or like guesswork.
Applied Maths: Uniform Acceleration (Strand 2) — Higher Level Notes
The four equations of motion, time-velocity graphs, and the two-object problems that become simultaneous equations — plus the average-speed trap that catches nearly everyone once.
Applied Maths: Projectiles (Strand 3) — Higher Level Notes
Independent horizontal and vertical motion, range and time of flight, the two angles that give the same range, and why 45 degrees is optimal.
Applied Maths: Newton's Laws and Connected Particles (Strand 4) — Higher Level Notes
F = ma applied properly: tension, friction, the laws of friction, particles on slopes, and systems joined by a string over a pulley.
Applied Maths: Work, Power, Energy and Momentum (Strand 5) — Higher Level Notes
Work as force along the displacement, power as tractive effort times speed, conservation of energy, drag and terminal velocity, and conservation of momentum.
Applied Maths: Impacts and Collisions (Strand 6) — Higher Level Notes
Impulse, Newton's law of restitution, direct and oblique collisions, and projectiles that bounce. The chapter where momentum and energy stop behaving the same way.
Applied Maths: Motion in a Circle (Strand 7) — Higher Level Notes
Centripetal acceleration, horizontal and vertical circles, the conical pendulum, banked tracks and Hooke's law — plus why there is no such thing as centrifugal force.
Applied Maths: Difference Equations (Strand 8) — Higher Level Notes
First and second differences, recurrence relations, solving first- and second-order difference equations, and the interest and repayment problems built on them.
Applied Maths: Differentiation and Integration (Strand 9) — Higher Level Notes
Logarithms, standard integrals, integration by parts, the chain rule, differentiating vectors and the work done by a variable force.
Applied Maths: Differential Equations (Strand 10) — Higher Level Notes
Separation of variables, general versus particular solutions, motion against resistance, terminal velocity, and the population, cooling and finance models.