New Zealand
Level 6 - NCEA Level 1

# Problem solving

## Interactive practice questions

A park has a walking track in the shape of an irregular quadrilateral. The four side lengths of the track are $8a$8a m, $6b$6b m, $2a$2a m, and $3b$3b m.

a

Write an expression for the length of one complete lap around the track.

b

What is the length of one lap around the track if $a=15$a=15 and $b=5$b=5?

Easy
Approx 2 minutes

A $23$23cm wire is cut into $2$2 pieces such that the length of the smaller piece is $4$4 cm. The longer piece is then bent to form a rectangle of width $3$3 cm.

A triangle has side lengths of $9x+3$9x+3 cm, $10x-3y$10x3y cm, and $12-4y$124y cm.

Each week, Aaron earns $\$m$$m more than Paul. Each week, Uther earns \u$$u more than Aaron.

If Paul earns $\$440440 per week, how much does Uther earn per week?

### Outcomes

#### NA6-6

Generalise the properties of operations with rational numbers, including the properties of exponents

#### 91027

Apply algebraic procedures in solving problems