Lebanese University Faculty of Engineering Entrance Examination study plan

Rewrite the domain-1 formula sheet from memory: quadratic formula and discriminant, Vieta's relations, factor and remainder theorems, inequalities with sign charts, and absolute value equations and inequalities.

Factor and solve 30 polynomial, rational, and radical equations, logging each error by cause (sign, domain restriction, extraneous root) rather than just marking it wrong.

Sketch by hand 12 functions (polynomial, rational, exponential, logarithmic) identifying domain, range, asymptotes, intercepts, and monotonicity intervals without a graphing tool.

Solve 10 composite and inverse-function problems, verifying each inverse algebraically and by reflection symmetry.

Classify and solve 25 equation and inequality families: exponential, logarithmic, irrational, and systems mixing linear with quadratic.

Prove and apply the three logarithm laws and change-of-base in 15 computation problems without a calculator where exact values exist.

Solve 8 word problems that require building a function model (growth, mixture, rate) and interpreting the answer in context.

State domain restrictions before solving 15 problems, then check whether each candidate solution survives them.

Derive and apply the sine and cosine rules to 15 triangle problems, including the ambiguous SSA case where two triangles may exist.

Solve 20 trigonometric equations on a stated interval, expressing all solutions in general form and checking for lost or spurious roots.

Prove 8 trigonometric identities using sum, double-angle, and half-angle formulas, writing each step as a justified transformation.

Compute 15 coordinate-geometry results: distance, midpoint, line equations, circle equations, and intersections of lines with circles.

Compute limits of 25 functions, distinguishing removable discontinuities, vertical asymptotes, and limits at infinity, and stating the reason for each result.

Test continuity at a point and on an interval for 10 piecewise functions, and find the parameter value that makes a piecewise function continuous.

Differentiate 30 functions using product, quotient, chain, and implicit rules, and interpret 5 derivatives as instantaneous rates in applied settings.

Convert between degrees and radians fluently and compute arc length, sector area, and angular speed in 10 applied problems.

Analyze 10 functions fully: domain, asymptotes, first and second derivatives, sign tables, extrema, inflection points, and concavity, ending in an accurate hand sketch.

Solve 8 optimization problems by setting up the objective and constraint, differentiating, and justifying that the critical point is a maximum or minimum.

Apply the mean value theorem and Rolle's theorem to 6 stated functions, verifying hypotheses before drawing conclusions.

Compute 15 indefinite and definite integrals using substitution and integration by parts, and use the definite integral to find area between curves.

Solve 25 kinematics problems in one and two dimensions, explicitly separating horizontal and vertical motion and choosing a consistent sign convention each time.

Apply Newton's three laws to 15 free-body-diagram problems involving incline, tension, friction, and connected masses, drawing and labeling every force.

Solve 10 work, energy, and power problems using both the work-energy theorem and conservation of mechanical energy, and state why each method applies.

Solve 10 momentum and impulse problems, including elastic and perfectly inelastic collisions, and verify momentum conservation before and after.

Apply Ohm's law and Kirchhoff's laws to 15 DC circuits, including series, parallel, and mixed networks, computing equivalent resistance and branch currents.

Compute electric field and potential for 10 point-charge and uniform-field configurations, stating direction and sign explicitly.

Solve 10 problems on waves: frequency, wavelength, speed, superposition, standing waves, and resonance on strings and in pipes.

Solve 8 problems on reflection, refraction, Snell's law, total internal reflection, and thin lenses using the lens equation and sign conventions.

Write electron configurations and predict periodic trends (atomic radius, ionization energy, electronegativity) for 20 elements, justifying each prediction by shell and effective nuclear charge.

Balance 20 chemical equations including redox in acidic and basic media, and identify the oxidizing and reducing agents in each.

Compute moles, molarity, limiting reagent, percent yield, and empirical and molecular formulas for 15 stoichiometry problems.

Name and draw 20 organic structures, identify functional groups and isomers, and predict the major product of simple addition and substitution reactions.