Level Curves and Contour Maps

The surface, seen from directly above.

12 problems · about 23 minutes · F-IF.B.4, F-IF.C.7

NameDate

Figures — use these to answer the problems

Raise a and the rings crowd together. Crowded contours mean a steep climb.

a, the x-steepness1

b, the y-steepness1

Figure 1

The same map for a saddle. The contours split into opposing pairs instead of closing into rings.

Figure 2

Straightforward practice. Get the method working first.

5 problems

The level curve of x² + y² at height 16. What is its radius?
Answer
2
What do closely spaced contour lines mean?
- The surface is steep there.
- The surface is flat there.
The level curve of x² + y² at height 36. What is its radius?
Answer
Can two contour lines of the same function cross? 1 yes, 0 no.
Answer
Contours are very close together. Is the slope steep? 1 yes, 0 no.
Answer

The same ideas with more to keep track of.

3 problems

Walking along a contour, how much does your height change?
Answer
f(x, y) = 2x + 3y. Its level curves are which shape? 1 lines, 2 circles, 3 parabolas.
Answer
Contours at 100, 110 and 120 metres over 40 horizontal metres each. What is the rise per metre, as a decimal?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each contour pattern by what it shows.
Write each item under the heading it belongs to: Nested closed rings · Contours splitting into opposing pairs · Rings shrinking toward one point · Two contours crossing at a pass
A peak or a pit
A saddle
A region of a map has no contours at all. Is it nearly flat? 1 yes, 0 no.
Answer
The Map
Contour lines are drawn every 10 metres. Between two adjacent lines, how much does the height change?
Answer
The Circle
The level curve of x² + y² at height 49 is a circle. What is its radius?
Answer