Welcome to the Maths Feast! - Further Mathematicsfurthermaths.org.uk/docs/2015 teachers booklet v2.pdf · · 2016-12-14Welcome to the Maths Feast! Teachers Booklet In this pack

Welcome to the

Maths Feast!

Teacher’s Booklet

In this pack you will find copies of all of the materials and questions

used today, along with answers to help you mark the rounds.

Please take these materials with you and use them in your school, but

when using the booklet today, please make sure that no student can

see the answers!

Enjoy the Feast!

We hope that you enjoy our Maths Feast. Please feel free to run these rounds in your own school –

you could even ask your Maths Feast team to run their favourite round with their classmates.

There are six rounds in total:

Amuse-Bouche (15 minutes): We split this round into three, but you don’t need to do this. Teams

should be given card sets A, E, W, T and the blank cards, together with the Answer Sheet.

Hors d’oeuvres (15 minutes): Teams should be given the 10 questions Hors d'oeuvres -

Comparison Round to answer. You or supervisors may tell any team unsure of the ‘<’ or ‘>’ sign

what they mean.

Entrée (20 minutes): Teams should be given just the poster ‘Set Theory and Venn Diagrams’ for 3

minutes and asked to study the contents. They may write on the poster is they wish. Teams should

then be given the ‘Three Set Venn Diagrams’ sheet and the questions Entrée: Comprehension

Round on Set Theory. Teams should not be given any help with any questions in this round.

Mains (20 minutes): It would be worth explaining, before the questions are given out, that teams

are not expected to answer all of the problems in this round, although they may attempt all

problems if they wish. Only four solutions will be marked and it should be made clear that this will

be the first 4 solutions that the supervisor sees, so if they do attempt more than 4 questions, they

should only submit their best 4. Full solutions must be shown to score maximum marks. Teams

should be given the questions: Mains: Problems, Problems, ......

Dessert (20 minutes): Teams should be given the instructions sheet Dessert - Folding a Columbus

Cube and the pack of origami paper. There is also a short video which can be shown while teams

are attempting to make the cubes to support them.

Petits-Fours (15 minutes): For this round, the team should be sat in two pairs opposite each other.

The pairs are allowed (and should be encouraged) to discuss answers between themselves, but are

not allowed to communicate with the other pair. Once the pair has an answer, they pass the

answer sheet to the supervisor who marks it. If it is correct, the team scores 2 marks, if there is an

error the supervisor corrects the error immediately and passes the answer sheet, with the correct

answer written on it, to the other pair so they can complete their question. It is possible for a pair

to begin working on some of their other questions while they are waiting for the answer from the

other pair. If a team achieves four correct answers in a row then they get an extra 2 points and the

count of four is started again. Each pair should be given their questions Petits Fours: Four in a Row

and pair A should be given the answer sheet Petits Fours: Four in a Row Team Answer Sheet at

the start of the round.

Amuse-Bouche: Algebra Cards Instructions

Your task is to create groups of cards that you think go together. There are eight groups.

Enter the card number in the appropriate box as you match the cards.

You will score two marks for each correct group.

There are some blank cards; for extra marks you can create cards! Each card code (B1, B2, etc.) must also be written on your answer sheet in the correct group (row) and column.

Each additional card, marked in the correct position will score 1 mark, up to a maximum of 6 marks.

This round will be marked after you have received and complete all three sections of the answer sheet.

Amuse-Bouche: Algebra Cards Set A

Amuse-Bouche: Algebra Cards Set E

E1

n 6

2

E2

3n2

E3

2n + 12

E4

2n + 6

E5

2(n + 3)

E6

n 6

2

E7

(3n)2

E8

(n + 6)2

E9

n2

+ 12n + 36

E10

n 3

2

E11

n2 + 6

E12

n2

+ 62

Amuse-Bouche: Algebra Cards Set W

W1

Multiply n by two, then

add six.

W2

Multiply n by three, then

square the answer.

W3

Add six to n, then

multiply by two.

W4

Add six to n, then

divide by two.

W5

Add three to n, then

multiply by two.

W6

Add six to n, then

square the answer.

W7

Multiply n by two, then

add twelve.

W8

Divide n by two, then

add six.

W9

Square n, then

add six.

W10

Square n, then

multiply by nine.

Amuse-Bouche: Algebra Cards Set T

n

n

n

n

n

n

n

n

Amuse-Bouche: Algebra Cards Blank Set

Use these to add to your groups for extra marks!

B1

B2

B3

B4

B5

B6

B7

B8

B9

B10

FMSP Year 10 Maths Feast 2015

Hors d'oeuvres - Comparison Round (30 marks)

Compare the answer to A with the answer to B, then ring the correct

statement.

1.

A: 6 0.05 0.9

B: 0.9 6 20

A B

2.

A: 8th Triangle number

B: 6th Square number

A B

3.

Aslam and Simba took part in an 800m running race.

Aslam ran the first 400m at an average speed of 9 ms-1 and the second 400m at an average

speed of 7 ms-1.

Simba ran for 50 seconds at an average speed of 9 ms-1 and ran for 50 seconds more at an

average speed of 7 ms-1.

A: Aslam's average speed for the 800 metres

B: Simba's average speed for the 800 metres

A B

4.

A: The interior angle of a regular hexagon

B: The exterior angle of an equilateral triangle

A B

5.

A red die has numbers 0, 1, 2, 3, 4, 5.

A blue die has numbers 1, 2, 3, 4, 5, 5.

Both dice are rolled.

A: The probability that the number on each dice are the same

B: The probability of the total score is 7

A B

6.

A: The area of a circle of radius 2 cm

B: The area of a square with sides of length 2 3 cm

A B

7.

Line P passes through the points (0,4) and (4,7).

Line Q is perpendicular to the line 6x y and passes through the point (4,8)

A: Gradient of line P

B: Gradient of line Q

A B

8.

Joanne invests £480, compounded at a rate of 5% per annum for 3 years.

Greg invests £400, compounded at a rate of 4.5% per annum for 4 years.

A: The total interest paid to Joanne

B: The total interest paid to Greg

A B

9. 34Volume of a sphere =

3r

A: The volume of a cube with a surface area of 150 cm2

B: The volume of a sphere with a radius of 3 cm

A B

10.

Below is the list of ingredients to make 12 carrot cup cakes.

150g self raising flour 1 teaspoon baking powder 1/4 teaspoon cinnamon 1/4 teaspoon nutmeg 125g softened butter 125g brown sugar 75g grated carrot 2 eggs 100g full fat or low fat cream cheese 2 tbsp icing sugar a few drops lemon flavouring or lemon rind

There is a large supply of the required ingredients in the pantry.

A: The number of cup cakes that can be made with 2 dozen eggs

B: The number of cup cakes that can be made with 1.8 kg of carrots

A B


Hors d'oeuvres: Comparison Round (30 marks)

1. A: 6 0.05 0.9 120.9 B: 0.9 6 20 120.9 A = B (3 marks)

2. A: 8th Triangle number=36 B: 6th Square number=36 A = B (3 marks)

3. A: Aslam's average speed = 7.9 ms-1

B: Simba's average speed = 8 ms-1 A < B (3 marks)

4. A: The interior angle of a regular hexagon = 120o

B: The exterior angle of an equilateral triangle = 120o A = B (3 marks)

5. A: The probability that the number on each dice are the same = 6

36

B: The probability of the total score is 7 =5

36 A > B (3 marks)

6. A: The area of a circle = 4 cm2

B: The area of a square = 12 cm2 A > B (3 marks)

7. A: Gradient of line P = 3

4 B: Gradient of line Q = 1 A B (3 marks)

10. A: The number of cup cakes that can be made with 2 dozen eggs = 144

B: The number of cup cakes that can be made with 1.8 kg of carrots = 288

A < B (3 marks)

TOTAL - 30 marks

Entrée: Comprehension Round poster

Entrée: blank Venn Diagrams

Year 10 Maths Feast 2015

Entrée: Comprehension Round on Set Theory (30 marks)

1. Given A = {1, 2, 4, 8, 16}, B = {2, 4, 6, 8, 10, 12} and = {1, 2, 3, 4, .... 20}

Write down:

n( A ) = A B =

n(A BC) = A B =

AC B =

2. The shaded region on the Venn diagram shows A B. For each diagram below, write down the description for each shaded area.

__________ __________ __________

__________ __________

{ }

{ }

{ }

A B

A B A B A B

A B A B

3. Shade each diagram to show the region described by the statement underneath the diagram:

X Y X (Y Z)

XC (Y Z) X Y ZC

(X YC) (Y XC) (ZC X Y)

X Y

Z

X Y

Z

X Y

Z

X Y

Z

X Y

Z


Entrée: Comprehension Round on Set Theory (30 marks)

1. Given A = {1, 2, 4, 8, 16}, B = {2, 4, 6, 8, 10, 12} and = {1, 2, 3, 4, .... 20}

n( A ) = (2 marks) A B = (2 marks, 1 mark if only one error)

n(A BC) = (2 marks) A B = (2 marks, 1 mark if only one error)

AC B = (2 marks, 1 mark if only one error)

2. The shaded region on the Venn diagram shows A B. For each diagram below, write down the description for each shaded area.

AC B (2 marks) A B (2 marks) (A B)’ C (A B )

or (AC B) (A BC) (2 marks)

(A B) C AC B

or AC BC (2 marks) or (A BC) C (2 marks)

{ 2, 4, 8 }

5

{ 1, 2, 4, 6, 8, 10, 12, 16}

17

{ 6, 10, 12 }

A B

A B A B A B

A B A B

3. Shade each diagram to show the region described by the statement underneath the diagram:

X Y (2 marks) X (Y Z) (2 marks)

XC (Y Z) (2 marks) X Y ZC (2 marks)

(X YC) (Y XC) (ZC X Y) (2 marks)

X Y

Z

X Y

Z

X Y

Z

X Y

Z

X Y

Z


Mains: Problems, Problems, ...... (20 marks)

There are six problems below – as a team you will score

maximum marks for correct solutions to FOUR of them.

You can attempt all six if you wish, but only hand in a maximum

of FOUR.

You can answer each question as a group or as individuals – it’s

up to you!

There is space on each sheet for rough working.

Write the solution to a problem in the answer box below the

question. Draw a diagram if that helps to explain your answer.

Set out your answers clearly so that the working can easily be

followed to score maximum marks.

Each question will score up to maximum of 5 marks.

The answer on its own will only score 1 mark.

Problem A:

Sam wants to paper the wall in her bedroom with vertically striped paper. The wall is 2 metres high

and 6 metres wide and has no windows or doors.

Each roll of paper is 56cm wide and 10m long and costs £4.99.

How much will it cost to paper the wall?

Problem A: Answer (explain your solution fully)

Rough working space (will not be marked)

Problem B:

The loading bay of a van is approximately a cuboid of internal dimensions 1.5m wide, 1.5m high

and 3m long.

What is the maximum number of boxes of dimensions 40cm by 50cm by 30cm that can be fitted in

the loading bay?

Problem B: Answer (explain your solution fully)


Problem C:

The doctor has told Graham that he needs to take 5ml of medicine every 6 hours and has given

him a bottle containing 25cl.

If Graham takes his first dose at noon on 9th September, when will he take his last dose?

Problem C: Answer (explain your solution fully)


Problem D:

Hayley wants to store her photos on a 1GB SD memory card.

Each image is between 2MB and 5MB in size.

How many images can Hayley store?

Problem D: Answer (explain your solution fully)


Problem E:

In a field there is a shed on a rectangular base, 10 metres long and 6 metres wide. A goat is

tethered to a rope 12 metres long, attached to a corner of the shed.

The goat cannot get into the shed, there is grass growing in every part of the field outside the shed

and the goat cannot reach the edge of the field.

Find the area of grass the goat can graze, in terms of π.

Problem E: Answer (explain your solution fully)


Problem F:

The school Sports Day has separate 100m races, 200m races and 400m races for girls and boys,

and for each year group from 7 to 10 inclusive.

Each 100m race takes about 30 seconds, each 200m race takes about 1 minute and each 400m

race takes about 2 minutes.

If it takes 5 minutes to set up each race, how long will Sports Day last?

Problem F: Answer (explain your solution fully)



Mains: Problems, Problems, .... (20 marks)

Only accept answers to four problems from the team.

Answer only is 1 mark only.

Problem A:

Wall is 6m wide and the paper is 0.56m wide. So 6 0.5 10.7 , means we require 11 strips. [2 marks]

A roll is 10m long and each strip is 2m long. So a roll contains 5 strips. [1 mark]

11 5 2 rem 1 . We require 3 rolls. [1 mark]

Cost is £4.99 x 3 = £14.97 [1 mark]

Problem B:

Van 300cm x 150cm x 150cm Box 50cm x 30cm x 40cm

Number of boxes 10 x 3 x 3 = 90 boxes or Number of boxes 6 x 5 x 3 = 90 boxes [ 2marks]

Better solution: Van 300cm x 150cm x 150cm

Box 40cm x 50cm x 30cm

Number of boxes 7 x 3 x 5 = 105 boxes [3 marks]

Best solution: From either 90 box solution there is a space of dimensions 300cm x 150 cm x 30 cm.

So an additional 1 x 3 x 6 = 18 more boxes will fit. This gives a total of 108. [4 marks]

Or 1 x 3 x 7 = 21 more boxes will fit. This give a total of 111. [5 Marks]

Problem C:

25cl = 250 ml [1 mark]

250 5 50 doses [1 mark]

1st dose is at midday on the 9th. 49 doses at 6 hour intervals is 12 days and 6 hours [1 mark]

Final dose is at 6.00pm on 21st September [1 mark correct time, 1 mark for the correct day]

Problem D:

1 GB = 1000 MB or 1024 MB [1 mark]

Maximum number of small images = 1000 2 500 images [1 mark]

Maximum number of large images = 1000 5 200 images [1 mark]

Number of images on the card is between 200 and 500 images [2 marks]

Allow correct calculations with 1024.

Problem E:

Diagram [1 mark]

2 2312 108 m

4 [1 mark]

2 216 9 m

4 [1 mark]

2 212 m

4 [1 mark]

Total area of grass to be eaten

2118 m [1 mark]

Problem F:

There are 2 x 4 = 8 races of each distance. [1 mark]

Total number of races = 8 x 3 = 24 races. [1 mark]

Set up time = 24 x 5 = 120 minutes. [1 mark]

Running time = 8 x 1/2 + 8 x 1 + 8 x 2 = 28 minutes. [1 mark]

Total time for the sports day = 120 + 28 = 148 minutes or 2 hours 28 minutes. [1 mark]

Dessert - Folding a Columbus Cube (25 marks)

In this round you are going to make some Columbus Cubes.

Each cube is made from six paper squares.

You have enough squares to make up to 4 cubes.

You will be scored for

Each correctly folded side

Each complete cube

The highest tower you can make with your cubes

1. Fold the paper to find a point half way along each side. Make a small crease to mark it but try not to crease the centre of the paper.

2. Do the same to find the half-way points for the other two sides.

3. Fold in the opposite edges so they meet along the centre line of the paper. Make strong creases along your folds.

4. It should now look like this:

5. Fold the other two edges in so they meet along the centre line. Make strong creases along your folds.

6. Open out the last two folds you made.

7. Make six of these “modules”.

8. Take three of your “modules”. You are going to adapt these.

9. Fold down the two flaps on each of these three “modules” to make a square.

10. Fold the top left-hand

corner in to make a 45° crease. Crease it firmly.

11. It should now look like this:

12. Open your last fold back out, turn your module over and then fold it the other way along crease you’ve just made.

13. Open the fold back out. The “module” should look like this:

14. Push the corner in as shown:

15. You need three of these. They must be identical.

16. Interlock two of the modules. They need to be held together by hand at this stage.

17. Lock it all together with the third one of these “modules”.

18. It should look like this:

19. Complete the cube by interlocking the remaining three simple “modules” to the outside of the object you made in 18.

20. The finished cube should look like this: If all of the faces are interlocked correctly then no glue or tape is needed to hold it together.

21. Once you have made more than 1 cube, you can stack them, like this:

There are bonus marks for making a tower of cubes.


Dessert: Columbus Cube (25 marks)

1 mark for each face correctly folded, up to a maximum of 3 marks.

1 mark for each face correctly folded with the corner folded in, up to a maximum of 3 marks.

For a cube with all the faces locked together correctly - 4 marks.

A partial construct scores 2 marks.

Hence a total of 10 marks for the first correctly constructed cube.

The second correctly constructed cube [4 marks] stacked upon [1 mark] the first cube, scores 5

marks. A partially constructed second cube scores 2 marks.

Each subsequent cube scores either 2, 4 or 5 marks, up to a maximum of 25 marks for the round.


Petits Fours: Four in a Row (40 marks)

PAIR A

1.

Given the equation 2( 3) 6 4a a , find the value of a .

3.

The number you are given is b .

A second hand car is priced at £b.

Jane buys the car after being offered a discount of 15%.

£c is the amount she paid. What is the value of c?

5.

The number you are given is d .

e is the angle marked on the diagram.

Calculate the value of e in degrees.

7.

The number you are given is f .

Given that 2 ( 1)

( 1)

10

1.2 10

f

f

fg

,calculate the value of g .

d

e

0.84d

PAIR A

9.

The number you are given is h .

A hundred Hobbits, who live in Matamata, were interviewed. They all liked either kiwis or pukakos

(or both). h like kiwis, whilst 2h like pukakos.

i is the number of hobbits who like both. Calculate the value of i .

11.

The number you are given is j .

j can be written in the form 22 5k k .

Find the value of k .

13.

The number you are given is l .

The train that Imran catches in the morning takes

l minutes to travel from Bath to Swindon.

m is Imran's total journey time from Bristol to

London in minutes.

Find the value of m .

15.

The number you are given is n .

The diagram shows part of a regular polygon with n sides.

op is the size of angle ACE.

Calculate the value of p .

Train Timetable

Bristol 07.10 07.25 07.40 07.55

Bath 07.30 07.45 08.01 08.15

Swindon 07.40 08.02 08.14 08.29

Didcot 08.00 08.24 08.35 08.49

Reading 08.10 08.35 08.45 08.58

London 08.35 09.00 09.10 09.33

A

B C

D

E


Petit Four: Four in a Row (40 marks)

PAIR B

2. The number you are given is a .

A printing firm uses this formula to work out the cost of printing a postcard: 10000

c ab

,

where c is the cost in pence of printing a card and b is the number of postcards.

Calculate b , if the cost of printing a postcard is 6p.

4. The number you are given is c .

A train is climbing a hill on a track with a gradient of 1 in 17.

The horizontal distance travelled by the train is c metres. The height climbed is d metres.

Calculate the value of d .

6. The number you are given is e .

The graph shows the number of goals scored

by Joanne during a water polo season.

f is the number of matches in which

she scored just one goal.

The mean number of goals per match is 2.5 .

Calculate the value of f .

8. The number you are given is g .

The diagram shows a trapezium with an area of g cm2 .

h cm is the perpendicular height of the trapezium.

Calculate the value of h .

h

50 cm

100

3

5e

e

1

10e

f

Number of

goals

Number of

matches

1 2 543

PAIR B

10. The number you are given is i .

The bearing of B from A is 5oi .

The bearing of A from C is 040o .

Distance AC = AB.

oj is the bearing of C from B. Calculate the value of j .

12. The number you are given is k .

A right angled triangle has sides of length 2k and 4k

as shown in the diagram. l is the length of the hypotenuse.

Calculate the value of l .

14. The number you are given is m .

n is the number of factors in m . Find the value of n .

16. The number you are given is p .

The length of a pendulum is directly proportional to the square of the period T of the pendulum.

A pendulum of length 76.8 cm has a period of 4 seconds.

q is the period of a pendulum of length p cm.

Calculate the value of q .

C

A

B

N

N

N

k+2

4k

l



Team Answer Sheet

Question Number Answer Correction

Marks (2 for a correct answer)

Bonus (2 marks for 4

correct answers in a row)

1 a =

2 b =

3 c =

4 d =

5 e =

6 f =

7 g =

8 h =

9 i =

10 j =

11 k =

12 l =

13 m =

14 n =

15 p =

16 q =

TOTAL SCORE (40)



Answer Sheet

Question Number Answer

1 a = 2

2 b = 2500

3 c = 2125

4 d = 125

5 e = 20

6 f = 6

7 g = 3000

8 h = 40

9 i = 20

10 j = 250

11 k = 3

12 l = 13

13 m = 90

14 n = 12

15 p = 120

16 q = 5

The Further Mathematics

Support Programme

Our aim is to increase the uptake of AS and A level Further

Mathematics to ensure that more students reach their

potential in mathematics.

The FMSP works closely with

school/college maths

departments to provide

professional development

opportunities for teachers and

maths promotion events for

students.

To find out more please visit

www.furthermaths.org.uk

http://www.furthermaths.org.uk/

Documents

Welcome to the Maths Feast! - Further Mathematicsfurthermaths.org.uk/docs/2015 teachers booklet v2.pdf · · 2016-12-14Welcome to the Maths Feast! Teachers Booklet In this pack