Netherlands VWO 6 (eindexamenjaar) Mathematics C
Chapters: 2
1. Change
Change and sequences
- Rate of Change: How Fast Does It Change? – Rate of change tells you how much an output changes for each one-unit change in the input. A graph can rise (increasing), fall (decreasing), or turn at a highest or lowest point. To measure change between two inputs a and b, find the change in input, Δx = b − a, and the change in output, Δy = f(b) − f(a). The average rate of change is Δy ÷ Δx, which is the slope of the straight line (secant) through the two points. A table of differences shows if growth is steady (constant differences, linear) or speeding up (growing differences, for example exponential). If the two points come very close, the average rate becomes the slope of the graph at one point. Sequences are lists of values with a rule: a recursive formula builds each term from the one before, a direct formula gives any term at once.
2. Shape and space
Shape and space
- Perspective Drawing: Horizon, Vanishing Points and Shadows – Perspective drawing makes a flat page look deep. You draw a horizon line at eye level, then lines going away from you meet at vanishing points. Far objects are drawn smaller (size ∝ 1 ÷ distance). One-point perspective uses one vanishing point, two-point uses two. Shadows are found with two crossing lines.