I went to the lake with two containers, a four-litre container and a
nine-litre container. How can I return with exactly six litres of
water? The containers do not have any scale marked on them.
Problem 1.2 Chess Board
Determine the number of squares in the following diagrams:
By observing the pattern determine the number of squares on a chess board.
Problem 1.3 Dimensions of the Picture
A rectangular picture's length and width
dimensions are both equal to a whole number of centimetres, and its
rectangular frame is 2 centimetres wide. If the area of the picture and
the area of the frame are equal, find:
a. l in terms of w b. the dimensions of the picture.
This question has more than one answer. Explain.
Problem 1.4 Percentage Increase
A rectangle has a length of 40 metres and a width of 30 metres.
a. What is 20% of 30?
b. What is 20% of 40?
c. If each side of the rectangle is increased by 20%, by what
percentage will its area be increased?
Problem 1.5 Squares
Joining the midpoints of the sides of a square as shown in the
following diagram forms a smaller square. If the side-length of the larger
square is x metres, find a relationship between the areas of the
larger and smaller squares.
Repeating the above process gives the pattern shown below.
If the third square in the pattern
has a side-length of 12 cm, find the area of the eighth square without
measuring it.
Problem 1.6 Algebraic Expressions
a. Express the width of the shaded rectangle in terms of x and y.
b. Express the area of the shaded rectangle in terms of x and y.
c. If the area of the shaded rectangle is equal to 16 square metres,
show that
d. Find an expression for the area, A, of the square ABCD in terms of y.
e. If y = 16, find the area of the square ABCD.
