New Zealand
Level 7 - NCEA Level 2

# Problem Solving with Linear Equations

## Interactive practice questions

Matches were used to make the pattern attached:

a

Complete the table:

 Number of triangles ($t$t) Number of matches ($m$m) $1$1 $2$2 $3$3 $5$5 $10$10 $20$20 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
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.

### Outcomes

#### M7-7

Form and use linear, quadratic, and simple trigonometric equations

#### 91257

Apply graphical methods in solving problems

#### 91261

Apply algebraic methods in solving problems