Secondary School Preparation
How to Best Prepare for Mathematics
Because of the highly quantitative nature of Carnegie Mellon’s curriculum, your four years of secondary school mathematics should include at least algebra, geometry, trigonometry, analytic geometry, and elementary functions. This level of preparation is strongly recommended for all three majors on the Qatar campus.
The following list of abilities reflects the basic skills important for success in Carnegie Mellon’s mathematics sequence. In addition, we look for students who can read carefully and interpret what has been read in the context of solving a problem.
You should be able to demonstrate these skills without a calculator:
- Be able to graph quadratic functions, ellipses, circles, and hyperbolas.
- Be able to manipulate algebraic expressions including using rules of exponents.
- Be able to complete the square of a quadratic expression and recognize when completion of the square is appropriate.
- Be able to determine the domain of a function.
- Understand the function concept including the composition of functions and be able to recognize the functions from which a given function is composed.
- Be able to determine the intersection of two lines or a line and a quadratic function.
- Be able to determine the equation of a line and understand when lines are parallel or perpendicular in terms of their slopes.
- Be able to solve linear inequalities and quadratic equations including equations that arise in novel circumstances.
- Be able to use properties of logarithmic functions to simplify expressions and solve equations.
- Be familiar with the graphs of logarithmic and exponential functions.
- Know the definitions of the trigonometric functions, be familiar with their graphs and periodicity, be able to evaluate trigonometric functions using standard triangles, and know basic trigonometric identities including the Law of Cosines.
- Know the Pythagorean Theorem and be able to apply it.
- Be able to recognize and use proportional relationships including those derived from similar triangles.
- Be able to use knowledge of basic plane and solid geometric figures to express relationships among them, e.g. when one is inscribed in another.
