If L = 100 and M = 0.1, which of these is largest ?

You want to combine each of the shapes (A) to (E) shown below separately with the shaded shape on the right to make a rectangle

You are only allowed to turn and slide the shapes, not flip them over. The finished pieces will not overlap and will form a rectangle with no holes

For which of the shapes is this NOT possible ?

A plumber has 12 lengths of drain pipe to load on his ute. He knowa that the pipes won’t come loose if he bundles them so that the rope around them is as short as possible. How does he bundle them ?

The numbers 1 to 6 are placed in the circles so that wach side of the triangle has a sum of 10. If 1 is placed in the circle shown, which number is in the shaded circle ?

Follow the instructions in this fow chart

A square piece of paper is folded along the dashed lines shown and then the top is cut off

The paper is then unfolded. Which shape shows the unfolded piece ?

Say, Li and Raheelah have birthdays on different days in the week beginning Sunday 2 August. No two birthdays are on following days and the gap between the first and second birthday is less than the gap between the second and third. Which day is definitely not one of their birthdays ?

A square of side length 3 cm is placed along side a square of side 5 cm

What is the area, in square centimetres, of the shaded part ?

A cube has a letters A, C, M, T, H and S on its six faces. Here are two views of this cube

Which one of the following could be a third view of the same cube ?

A 3 x 2 flag is divided into six squares, as shown. Each square is to be coloured green or blue, so that every square shares at least one edge with another square of the same colour.

In how many different ways can this be done ?

There are many ways that you can add three different positive whole numbers to get a total of 12. For instance, 1 + 5 + 6 = 12 is one way but 2 + 2 + 8 = 12 is not, since 2, 2 and 8 are not all different.

If you multiply these three numbers, you get a number called the product.

Of all the ways to do this, what is the largest possible product ?

Alex is designing a square patio, paved by putting bricks on edge using the basketweave pattern shown

She has 999 bricks she can use, and designs her patio to be as large a square as possible. How many brick does she use ?

A newspaper open on the table had page 42 opposite page 55 because someone had removed pages from the centre. What is the number of the last page of the news-paper ?

Jill has three large piles of coins: 10c, 20c and 50c. In how many different ways ca she make one dollar ?

Tom borrowed some items from the stationery cupboard. He found that 5 glue sticks weigh the same as 2 staplers, and that 3 staplers weigh the same as 20 erasers

How many glue sticks balance with how many erasers ?

Molly is thinking of a number. Twice her number take away seven is the same as her number plus five. What is her number ?

This shape is made from two overlapping rectangles. What is its area in square centimetres ?

The numbers 40, 19, 37, 33, 12, 25, 46, 18, 39, 21 are matched in pairs so that the sum of each pair is the same. Which number is paired with 39 ?

Grandpa had 400 dollars in his wallet. He gave half the money to his wife. From what was left, he then gave one-quarter to his son. Half of the remainder went to his grandson. How much money did his grandson receive ?

The numbers 1 to 6 are placed in the circles so that each side of the triangle has a sum of 10. If 1 is placed in the circle shown, which number is in the shaded circle ?

Simon has some 24 cm log strips. Each strip is made from a different number of equal-sized tiles

Simon took 1 tile from each strip to make a new strip. How long is the new strip ?

Rod had fewer than 100 blocks. When he made five equal rows, he had one block left over. With four equal rows, he had one block left over. With nine equal rows, there were no blocks left over. How many blocks did he have ?

A square piece of paper is folded alog the dashed lines shown and then the top is cut off.

The paper is then unfolded. Which shape shows the unfolded piece ?

Follow the instructions in this flow chart.

John wrote his name on his book. Martha said he wrote with a black pen. Aaron said it was a brown pencil. Frankie said it was a black crayon. If each of john’s friends were half right, what did he really use to write his name ?