Equations

Hong Kong

Stage 1 - Stage 3

Matches were used to make the pattern attached:

a

Complete the table:

Number of triangles ($t$t) |
$1$1 | $2$2 | $3$3 | $5$5 | $10$10 | $20$20 |
---|---|---|---|---|---|---|

Number of matches ($m$m) |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

Write a formula that describes the relationship between the number of matches ($m$`m`) and the number of triangles ($t$`t`).

$m$`m` = $\editable{}$ $t$`t`

c

How many matches are required to make $25$25 triangles using this pattern?

Easy

Approx 2 minutes

A diver starts at the surface of the water and starts to descend below the surface at a constant rate. The table shows the depth of the diver over $5$5 minutes.

When a number is added to both the numerator and denominator of $\frac{1}{5}$15, the result is $\frac{3}{7}$37.

The perimeter of the trapezoid below is $27$27 centimeters.

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