M

C

S

E A

Rules for Team Competition• Answer all parts of a question THEN…• Hold up your 1st attempt so order recorders can see

your team number KEEP HELD UP until….• Runners take your sheet to markers• With remaining time work on your 2nd attempt…• Runners collect these at the end of each question..• 6 marks per question (marks will be awarded for

each correct part where a question has several parts)• Extra marks: +4 for 1st, +3 for 2nd, +2 for 3rd

Rules for Bonus Round

• Fill in the BONUS ROUND quiz in any spare time you have…it does not count towards the team competition

• Place upside down on your table during break

• Runners will collect in at the end• 1 mark per correct answer• Prizes for 1st , 2nd and 3rd…

You now have 30 seconds left 10987654321STOP

Trial Question

There are 2 painters.

David can paint a wall in 6 minutes, and Joanne can paint a wall in 3 minutes.

How long would it take to paint the wall if they worked together ?

Click when ready...

You now have 30 seconds left 10987654321STOP

1. The points in this circle are evenly spaced out.a) How many chords are there in this image?b) What is the smallest angle between any two chords?c) What if there were 200 points evenly spaced instead of

10?

You now have 30 seconds left 10987654321STOP

2) 2400 is a very large number.

a) What is the remainder when it is divided by 5?

b) What is the units digit if it is evaluated and written in base 10?

c) What is the remainder when 3400 is divided by 5?

You now have 30 seconds left 10987654321STOP

3. The number 324 as a product of prime factors is 2x2x3x3x3x3. The diagram below is the ‘factor frame’ for 324.

b) Draw a factor frame for 72.c) Find the smallest number with 18 factors.

x3x3 x3

x3x3

x3x3x3

x3

x3

x3

x3

x2

x2

x2

x2

x2

x2

x2

x2

x2

x2

324

162

81

108

54

27

36

18

9

12

6

3

4

2

1

You now have 30 seconds left 10987654321STOP

4. The image is made up of a unit square and circles as shown. a) What is the area of the shaded region? b) What would be the area of the equivalent region if the unit square was replaced by a unit equilateral triangle?

You now have 30 seconds left 10987654321STOP

5. The number m is a perfect square. What is the value of the next perfect

square above it?

You now have 30 seconds left 10987654321STOP

6. What fraction of this rectangle is blue ?

You now have 30 seconds left 10987654321STOP

7. A regular hexagon ABCDEF has sides of length 2cm. The midpoint of AB is M. Which line segment has length 13

M

F

E D

C

BA

You now have 30 seconds left 10987654321STOP

8. A cube has its vertices removed by slicing a tetrahedron off each corner in such a way that each square face is changed into a regular octagon of side 1.

a) What is the volume of the new solid?

b) What is the surface area of the new solid?

c) What is the total edge length of the new solid?

You now have 30 seconds left 10987654321STOP

9. Multiply out and simplify:

a) (x-1)(x4+1)(x2+1)(x+1)

b) (2x-1)(16x4+1)(4x2+1)(2x+1)

c) (3x-1)(81x4+1)(9x2+1)(3x+1)

You now have 30 seconds left 10987654321STOP

10. Circles with radii r and R (where r<R) touch each other and also touch two perpendicular lines as shown. What is the value of R/r?

Click when ready...

You now have 30 seconds left 10987654321STOP

11. In this flag of the area of the red is equal to the area of the white and the vertical and horizontal red stripes are of thickness x.

If the flag measures 40cm by 30cm what is the value of x?

You now have 30 seconds left 10987654321STOP

12. At what times do the hands of a clock make an angle of 180 degrees?

You now have 30 seconds left 10987654321STOP

13. What is the value of :

1+2(1+2(1+2(1+2(1+2(1+2(1+2(1+2(1+2(1+2(1+2)))))))))) ?

You now have 30 seconds left 10987654321STOP

14. Sarah the spider wants to walk to Fred the fly. She can only walk on the surfaces of the truncated square based pyramid shown. What is the shortest route?

16 16

2020

Perpendicular Height 12

You now have 30 seconds left 10987654321STOP

15. Find all four solutions of the equation:

(x2+5x-13)(x2-5x-24)

=1

You now have 30 seconds left 10987654321STOP

16. The ancient pyramid like tower shown below is called a Ziggurat.This one has 3 layers and is made from 35 cubes.

How many blocks would be needed for a Ziggurat of 23 layers?

You now have 30 seconds left 10987654321STOP

17. Which is the largest of these fractions?

7/15 3/7 11/23 4/9 6/11

You now have 30 seconds left 10987654321STOP

18. The diagram below has rotational symmetry of order 3. The regions I, II, III and IV all have the same area. The Circle is of unit radius.

What is the edge length of the equilateral triangle?

I

III

IV

II

You now have 30 seconds left 10987654321STOP

19. The two points (2, 3) and (8, 11) are corners of a square.

What are the possible coordinates of the other corners?

You now have 30 seconds left 10987654321STOP

20.The 3d match stick array below has edge length 3 and contains 144 matchsticks

How many matchsticks would there be for an edge length of 30?