Algebra

New Zealand

Level 5

Sarah decides to put a bird feeder in her back garden. That day she sees $6$6 birds use the feeder. The next day she sees $12$12 birds, and on the third day she sees $18$18 birds.

a

If the number of birds continues to follow the pattern, how many birds will Sarah see on the fourth day?

b

If the pattern continues, write an expression for the number of birds Sarah will see after $y$`y` days.

Easy

Approx a minute

A tap has not been turned off properly, and water is dripping into the bucket underneath it. After one hour, the water level in the bucket is $6$6 cm. After two hours the water level is at $12$12 cm, and after three hours the water level reaches $18$18 cm.

Tom likes to go kayaking, and on Saturday he takes his boat down to the lake which is $350$350 m away from his house. After one minute of paddling he is $420$420 m away from his house. After two minutes he is $490$490 m away, and after three minutes he reaches $560$560 m away.

An isosceles triangle has two sides of length $6$6 cm.

If the third side has a length of $b$`b` cm, write an expression for the perimeter of the triangle.

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Generalise the properties of operations with fractional numbers and integers.