Physics Quiz on Fundamental Concepts

Syllabus Selection Exam - Mathematics & Physics

• Introduction: The exam covers fundamental topics in mathematics, physics, and selected first-year material, based on Dutch VWO curriculum.

Mathematics

• Functions and Graphs: Candidates must recognize and construct compositions of standard functions, including polynomials, n-root functions, power functions, logarithms, exponentials, and trigonometric functions (sin(x), cos(x)). Analysis, sketching, and transformations of these functions, along with determining limits, domain, range, asymptotes, and symmetry, are required. Understanding and finding inverses of functions (and their compositions) is also essential.

• Algebraic Solving: Manipulating expressions to isolate variables, substituting expressions into functions, simplifying expressions, and recognizing special products are key skills. Solving equations and inequalities involving standard functions, finding roots of functions (using factorization and the quadratic formula), and solving systems of linear equations are assessed.

Differential Calculus

• Derivatives of standard functions: Candidates must know the derivatives of standard functions.

• First and Second Derivatives: Calculating first and second derivatives, using the product, quotient, and chain rules. Evaluating locally increasing/decreasing behavior, extreme values, concavity/convexity, and inflection points through the use of derivatives is crucial.

• Tangent and Normal Lines: Applying differentiation to determine slopes, tangent lines and normal lines. Problem-solving related to distance, velocity, and acceleration.

Integral Calculus

• Integration Concepts: Understanding integration concepts like limits of integration, definite/indefinite integrals, and constants of integration.

• Antiderivatives: Calculating antiderivatives (indefinite integrals) for standard functions and expressions of the form cf(ax + b) + d.

• Definite Integrals: Applying definite integrals to calculate areas and volumes of solids of revolution.

Trigonometry

• Trigonometric Functions: Understanding the trigonometric functions sin(x), cos(x), and tan(x), and their relationship to the unit circle.

• Angles and Radians:Converting between degrees and radians, finding exact values of sin(θ), cos(θ), and tan(θ) for specific angles. Knowing periodicity and symmetry properties are important.

• Solving Equations: Solving trigonometric equations of the form sin(x)=c, cos(x)=c, and tan(x)=c. Solving equations involving compositions of trigonometric functions with linear arguments. Applying Pythagorean identities, sum/difference identities, and double angle formulas.

Geometry

• Two-Dimensional Shapes: Calculating perimeter and area of triangles, rectangles, circles (and other common shapes).

• Three-Dimensional Shapes: Determining volume and surface area of cubes, pyramids, cylinders, cones.

Vectors

• Vector Concepts: Understanding vectors, their lengths and direction, vector decomposition, scalar multiplication, addition, subtraction, and dot products.

• Applications of Vectors: Applying vectors to calculate angles and distances, determining velocity and acceleration of moving points, calculating vector equations of lines, deriving local tangents of parametric curves . Determining the center of gravity of two-dimensional shapes.

Physics

• Fundamentals: Understanding SI base units (meter, kilogram, second, ampere, kelvin, mole), dimensional analysis, and the concept of vector quantities (direction and magnitude). Using metric prefixes (micro, milli, kilo, Mega, etc.). Familiarity with mathematical expressions such as logarithms, exponentials, and trigonometric functions.

• Mechanics: Understanding relationships between distance, velocity, and acceleration. Newton's laws, and applications to various force types (gravity, friction, drag, tension, spring force). Calculations of work, energy, power, and efficiency, conservation of energy related to potential and kinetic energy, and circular motion.

• Electricity & Magnetic Fields: Understanding concepts like conductors, insulators, charge, current, voltage, resistance, circuit diagrams, and applying Kirchhoff's laws. Calculating forces between electrically charged particles using Coulomb's Law . Understanding magnetism, including concepts like flux, homogenous/inhomogeneous magnetic fields, and Lorentz force.

• Vibrations & Waves: Knowing terms related to vibrations and waves (period, frequency, amplitude, phase, resonance, damping, longitudinal/transverse waves and the associated quantities (wavelength, speed of sound/light)) and their analysis . Understanding simple harmonic motion and wave phenomena.