A square of paper has its corners folded in as shown to make a smaller square with an internal square, as shown on the right. What is the area of this internal squares ?

Ancient Egyptian matheaticians used fractions but only with a numerator of 1, such as $\frac{1}{2}$ or $\frac{1}{7}$ or $\frac{1}{14}$ . They made other fractions by adding these fractions together. For example, $\frac{3}{4}$  was written as $\frac{1}{2}+\frac{1}{4}$ . Which of the following is an Ancient Egyptian way of writing $\frac{11}{16}$  ?

This symmetrical star is made up of two overlapping equilateral triangles of the same size. The area of the star is 60 square centimetres. What is the area of the shaded region in square centimetres ?

In this correctly worked addition, P, Q, R and S represent different digits, and all seven digits are different. What is the sum of P, Q, R and S ?

In a competition between four people, Sally scored twice as many points as Brian and 30 points more than Corrie. Donna scored 50 points more than Brian. Which of the following statements is definitely true ?

A plane was travelling at an altitude of 4500 metres for 20 minutes. It then climed at a rate of 500 metres per minute for 5 minutes before descending at 350 metres per minute for 8 minutes. Which of the following graphs best describes the altitude of the plane over this time ?

Mrs Graham wants to fill her swimming pool for the summer. She knows that if she uses the backyard hose it will take 12 hours, or if she uses the frontyard hose it will take 4 hours. How long will it take if she uses both hoses together ?

Four soccer teams played each other four times in a season of competition. Each winning team was awarded 3 points. Teams that had a draw were awarded 1 point each, and losing teams were awarded no points. The season ended with Kangaroos on 21 points, Kookaburras on 17 points, Koalas on  16 points and Crocodiles on 12 points. How many games ended in a draw ?

Five different whole numbers, chosen from the numbers from 1 to 30, add up to 30. What is the greatest possible value of the largest of these numbers ?

A 3 by 5 grid of dots is set out as shown. How many straight line segments can be drawn that join two of these dots and pass through exactly one other dot ?

A cube is made up of 1 cm x 1 cm x 1 cm blocks and measures 12 cm x 12 cm x 12 cm. Sharyn is using the same set of blocks to make a set of stairs

The picture shows how she started, making a set of stairs 4 blocks high, 4 blocks from front to back and 5 blocks wide

Her finished set of stairs will use all the blocks and be 8 clocks high and 8 blocks from front to back. How many clocks wide will they be ?

How many three-digit numbers are there in which one of the digits is the sum of the other two ?

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