1. Sketch any rectangle
Now draw in the diagonals.
How many triangles have been formed by these six lines?
2. Using only current Australian coins, how many different ways can you make up 30 cents?
3. If you assembled these three rectangles together to make one larger rectangle;
4m X 4m, 4m X 1m, 3 m X 5m
(a) what dimensions, and
(b) what total area would it have?
4. What’s 3 to the power of 2 minus 2 to the power of 3?
5. A mother’s age in years and her daughter’s age have digits in reverse order. Last year, the mother was twice as old as the daughter. What are their ages?
6. Leo lies a lot.
He tells the truth only on one of the days of the week.
The days of the week in order are Sunday, Monday, Tuesday, Wednesday, Thursday,
Friday, Saturday, Sunday, Monday, Tuesday etc.
One day Leo said “I lie on both Mondays and Tuesdays”
The following day, he said “Today is either Thursday, Saturday or Sunday”.
The day after that, he said “I lie on both Wednesdays and Fridays”.
On which day of the week does Leo tell the truth?
7. In each vertical column the letters add up to 10.
What letter belongs in the empty box?
8. In the two designs below, combinations of cubes are stacked together.
All the rows are complete unless you can see their end. In other words, you can assume that there are some unseen cubes behind the visible ones.
Based on the visual evidence given, state how many cubes are in each design.
9. There was a race between four boys.
a. Place Adrian, Billy and Duncan in the correct finishing order,
1st to 3rd.
b. List all four children in order from youngest to oldest.
Keith was fourth.
Adrian is not the oldest, but is older than Duncan, who was not second.
The child who was next in age to the youngest, finished second.
The child who finished in third place is older than the child who finished first.
Billy is younger than the child who finished in third place.
10. A merchant can place 8 large boxes or 10 small boxes into a carton for shipping.
In one shipment, he sent a total of 96 boxes.
If there are more large boxes than small boxes, how many cartons did he ship?