IB SL – Assn 2 - Juniors
Date ________
Name ___________________
1) Begin by drawing one point, next to it draw two points. Since you started with one point only, there
is not another point to connect it with. But with two points, you can connect the points with a line
segment. Now draw three points that are non-collinear. Connect each point with another one of the
points until every point is connected to any other point. Continue this process with four non-collinear
points. Complete the table with two rows, one labeled number of points and the other labeled number
of connections. Draw five and then six non-collinear points. Complete the chart. What pattern do you
see and predict the number of connections with n points.
# of points
1
2
3
4
5
6
n
# of connections
2) Construct and shade in an equilateral triangle with each side measuring 2 inches. Determine the area
of the triangle writing it in exact form. Construct the same size triangle again and find the midpoint of
each side. Construct and shade in the equilateral triangle from these points. Find the area of this
triangle. Construct this triangle again with the shaded triangle inside. There are three triangles that are
not shaded. Inside each of these non-shaded triangles, construct another triangle in each section using
the same method. Determine the area of each one of the triangles. Complete the chart below.
Length of side
2
n
Area of Triangle
Inspect each of the following sequences of numbers and list the next three values in the list:
3)
1 1 1 1
, , ,…
2, 4 8 16
4)
1 1 1 1
, , , ,…
2 4 6 8
−2 4
, 9,
3
−8
,…
27
5) 2, 7, 12, 17, …
6) 1,
7) 0, 2, 6, 12, …
8)
9) 1, 2, 4, 8, 16, …
10)
2 3 4 5
, , , ,…
1 2 3 4
12)
1
1
1
1
,
,
,
,…
(1)(3) (2)(4) (3)(5) (4)(6)
11)
2 3 4 5
, , , ,…
1 4 9 16
1 1 1 1
1
, , , ,
,
1 2, 6 24 120
…