Institute of Technology Carlow Curriculum

(i) rules of precedence (ii) D.A.L calculator (iii) rules of indices (iv) exponential format (v) units and prefixes (vi) LCM and the HCF of whole numbers (vii) unitary method problems (viii) percentages (ix) average of a set of numbers (x) Conversion between number systems.

(i) Addition, subtraction and multiplication of algebraic expressions (ii) Factorisation of algebraic expressions (iii) Solution of simple equations, simultaneous and quadratic equations (iv) Transposition of formulae (v) Transposition of formulae to solve mensuration problems (vi) Log laws and log equations.

(i) Interpretation of plotted graphs (ii) Properties of straight line and quadratic graphs (iii) Cubic graphs (iv) Plotting graphs of the form .

(i) Surd form for the trigonometric ratios sine, tangent and cosine for angles 60o, 30o and 45o. (iii) Right angled triangles, Pythagoras’ theorem, trigonometric ratios sine, tangent and cosine and the inverse trigonometric functions sin-1x, tan-1x and cos-1x (iv) Degree and radian measure (v) Sine and cosine rules in the solution of non-right angled triangles (vi) Trigonometric ratios secant, cosecant and cotangent (vii) Verification of trigonometric identities involving all six trigonometric ratios, compound angle formulae and sums and products of sines and cosines. (viii) Graphs of waves, wave theory and its applications to electrical principles (ix) Rewriting of addition of sine and cosine functions as cosine functions and applications of this in electrical principles and mechanics.

Supplementary, complementary, opposite, corresponding and alternate angles. Equilateral, equiangular, isosceles and scalene triangles; Basic geometry theorems related to angles of triangles, isosceles triangles, congruent triangles, quadrilaterals, parallelograms and angles with circles.

Exponential function. Application of the exponential function to engineering problems. Logarithmic function. Application of the logarithmic function to engineering problems. Application of logarithms to experimental data. Graphs of hyperbolic functions. Engineering applications of hyperbolic functions.

Derivative in terms of the limit of a function. Derivatives of common engineering functions and apply rules of differentiation. 2nd order derivatives and application to engineering problems. Second derivative test to find maxima, minima and points of inflexion and applications in engineering and kinematics.

Concept of indefinite integration and find indefinite integrals. Integration using substitution. Evaluation of definite integrals. Integration by parts formula. Integration using partial fractions. Use of integration to find areas under a graph, mean and root mean square values of functions. Use of integration to find the displacement and velocity of a particle. Apply integration to thermodynamics and structural mechanics problems.

General arithmetic operations on complex numbers. Graphical representation of complex numbers. Multiplication and division in polar form. Various representations of complex numbers such as rectangular and polar form. Finding and plotting roots of complex numbers. Powers of complex numbers. Complex number in exponential form. Applications of complex numbers in electrical principles.

General arithmetic operations on matrices. Solution of equations by using the matrix inverse method and application to engineering problems. Various types of solutions of linear equations such as no solution, unique solution and infinite number of solutions. Applications of matrices in electrical principles and mechanics.