Undergraduate

Preparation Period Course Listings & Syllabus

  1. Geometry

    Section 1 – Euclidean Geometry

    1. Congruent triangles
    2. Equilateral triangle and the kite
    3. Inequalities in the triangle
    4. Existence of parallel lines
    5. Parallelogram
    6. Rhombus, rectangle and square
    7. Trapezoid
    8. Mid-segment of a triangle and a trapezoid
    9. Special points in the triangle
    10. Squares and inscribed and circumscribed polygons
    11. Circle – angles in the circle (inscribed, internal and external), chords and arcs
    12. Tangents to a circle
    13. Mutual status of two circles
    14. Pythagoras, area calculations
    15. Thales’ theorem
    16. Angle-bisectors, harmonic relationships
    17. Similar triangles and their uses
    18. Review on the relationships within a right triangle and relationships in a circle

    Section 2 – Trigonometry (Introduction)

    1. The trigonometric circle: the definitions of the trigonometric functions, basic identities
    2. The change in the function from 0 to 2
    3. Even and periodic functions
    4. Graphs of trigonometric functions and inverse trigonometric functions, Transformations
    5. Sum and difference of functions
    6. Multiple and half-angle functions
    7. Transformation of sum to multiplication and vice-versa
    8. Integrated problem solving
    9. Trigonometric equations and inequalities
    10. Geometric solutions: laws of sines and cosines and their integration, identifying triangles according to their characteristics
    11. Areas

    Sample Problem #1 ; Sample Problem #2 ; Sample Problem #3 ; Sample Problem #4 ; Sample Problem #5

    Geometry
  2. Physics

    1. Introduction

    • Graphs
    • Vectors
    • Basic trigonometry
    • Units

    2. Mechanics

    • Motion – one- and two-dimensional (projectile motion, circular motion and relative motion) Forces (Newton’s laws)
    • Work and energy
    • Impulse and momentum
    • Simple harmonic motion
    • Gravitation

    Physics
  3. Algebra

    Section 1:

    1. Number systems: natural ( ), integer ( ), rational ( ), real ( ). Basic multiplication formulas. Simplification of algebraic expressions. Linear and parabolic equations. Viete’s formulas.
    2. Two simultaneous equations. Absolute value. The interval method. Irrational equations and inequalities.
    3. Exponential and logarithmic equations and inequalities.
    4. Vectors: addition, subtraction, multiplication by a number. Coordinates. Division of a segment into a given ratio. Scalar product. Vector and mixed products.
    5. The line in the plane and in space.
    6. The plane, circle and ellipse.
    7. Hyperbola, parabola.
    8. Review

    Section 2:

    1. Arithmetic and geometric sequences.
    2. The concept of the functions and the limit of a function.
    3. Derivative. Tangent and normal.
    4. Angle between graphs.
    5. Analysis of functions.
    6. Maximum and minimum problems.
    7. Integral Review

    Algebra

For a detailed syllabus of the BSc in Civil Engineering program click here.