interactive voting - 1996 mathematics paper a

1996 MATHS PAPER B

1996 Mathematics Paper A1996 Mathematics Paper AInput your name and press send.Input your name and press send.

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1996 Mathematics Paper A

Q1a What is the missing number?

4 * 20 =

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Q1b What is the missing number?

+ 79 = 91

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Q1c What is the missing number?

60 - = 26

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Q2a Kim has a shape sorter toy.

How many different ways does each piece fit into its hole?

This piece?

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Q2b Kim has a shape sorter toy.


This piece?

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Q2c Kim has a shape sorter toy.


This piece?

Award TWO marks for the correct answer of

up to 2 If the answer is incorrect award ONE mark for two numbers in correct positions,provided the two numbers are drawn only from 3, 4, 1 OR only from 6, 8, 2.

3 4 1 o r 6 8 2


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Q3a. John and Paula go to a fair.

G a l a x y

p e r r i d e£ 1 . 5 0

L a s e r

p e r r i d e9 0 p

B i g W h e e l

p e r r i d e£ 1 . 2 0

S p a c e s h i p

p e r r i d e7 5 p

John has £2.He goes on one ride and has exactly 80p left.

Which ride does he go on?A. Galaxy

B. Laser

C. Big Wheel

D. Spaceship


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Q3b. John and Paula go to a fair.

G a l a x y

p e r r i d e£ 1 . 5 0

L a s e r

p e r r i d e9 0 p

B i g W h e e l

p e r r i d e£ 1 . 2 0

S p a c e s h i p

p e r r i d e7 5 p

Paula has a 50p coin and three 20p coins.She pays for a ride on the Laser.

How many pennies are left?

Two marks for correct answer, 1 for correct working.


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Answer Key

Q4. Here are four number cards.

2 7 96

Use all the number cards to make an addition.The answer must be MORE than 100.


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Q4. Here are four number cards. 2 7 96

Use all the number cards to make an addition.The answer must be MORE than 100.

9 26 7

7 26 9

2 67 9

2 69 7

9 67 2

7 69 2

2 79 6

9 76 2

7 96 2

2 97 6

o r o r

o r o r o r

o r o r o r

o r

OR any inversion of these pairs.No mark is awarded or lost for calculating the sum of the two numbers.

Only the numbers given must be used, without repeats.The only unacceptable combinations of the given numbers are those with 2 and 6 in the tens place, ie:

OR

2

26

6


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Complete the table.

s h a p e p r o p e r t y o f s h a p e

o n e o r m o r er i g h t a n g l e s

4 s i d e s o n l y

t w o p a i r s o fp a r a l l e l s i d e s

Does this shape Have 4 sides only?


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Complete the table.



4 s i d e s o n l y


Does this shape Have one or more right angles?


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Q5c. John and Paula go to a fair.

Complete the table.



4 s i d e s o n l y


Does this shape Have two pairs of parallel sides?


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Q5d. John and Paula go to a fair.

Complete the table.



4 s i d e s o n l y




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Q5e. John and Paula go to a fair.

Complete the table.



4 s i d e s o n l y




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Answers

Q5f. John and Paula go to a fair.

Complete the table.



4 s i d e s o n l y




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Complete the table.



4 s i d e s o n l y



1

2

3

4


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Q5c. John and Paula go to a fair.

Complete the table.



4 s i d e s o n l y



1

2


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Q5d. John and Paula go to a fair.

Complete the table.



4 s i d e s o n l y



1

2

34

5


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Q5e. John and Paula go to a fair.

Complete the table.



4 s i d e s o n l y



1

2


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Q5f. John and Paula go to a fair.

Complete the table.



4 s i d e s o n l y



1


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Q6a Here is the cost of some pizzas.

P I Z Z A S

S m a l l M e d i u m

H a m

S a l a m i

M u s h r o o m

C h e e s e

T u n a

£ 4 . 2 0

£ 4 . 4 0

£ 4 . 5 0

£ 3 . 8 0

£ 4 . 2 5

£ 5 . 5 0

£ 5 . 7 5

£ 6 . 0 0

£ 4 . 9 5

£ 5 . 4 0

E x t r a t o m a t o

E x t r a c h e e s e

5 0 p

6 0 p

Jill orders one small cheese pizza with extra tomato.What is the total cost in pence?


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Q6b Here is the cost of some pizzas.

P I Z Z A S

S m a l l M e d i u m

H a m

S a l a m i

M u s h r o o m

C h e e s e

T u n a

£ 4 . 2 0

£ 4 . 4 0

£ 4 . 5 0

£ 3 . 8 0

£ 4 . 2 5

£ 5 . 5 0

£ 5 . 7 5

£ 6 . 0 0

£ 4 . 9 5

£ 5 . 4 0

E x t r a t o m a t o

E x t r a c h e e s e

5 0 p

6 0 p

Ben buys one small pizza and one medium pizza.They cost him £10.

Which two could they be?one small ........................................................................................... pizzaand one medium ............................................................................... pizza


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Q7a Children run a 100 metres race on Sports Day.

Here are their times.

N a m e T i m e t a k e n

S u e 1 5 . 9 7 s e c s

J a n 1 6 . 3 9 s e c s

S a m 1 4 . 8 3 s e c s

T o m 1 7 . 0 0 s e c s

R a j 1 5 . 8 9 s e c s

What is the winner’s time in seconds? (Answer to two decimal places)


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Q7b Children run a 100 metres race on Sports Day.

Here are their times.

N a m e T i m e t a k e n

S u e 1 5 . 9 7 s e c s

J a n 1 6 . 3 9 s e c s

S a m 1 4 . 8 3 s e c s

T o m 1 7 . 0 0 s e c s

R a j 1 5 . 8 9 s e c s

Who has the time nearest to 16 seconds? (Answer to two decimal places)

XL File


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Q7c Here are their long jump results.

Q7d Use the graph to estimate how much further Sam jumped than Jan.

Sue jumped 212 cm.Draw Sue’s long jump result on the graph.

0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 1 7 5 2 0 0 2 2 5 2 5 0

R a j

T o m

S a m

J a n

S u e

c e n t i m e t r e s

l o n g j u m p r e s u l t s


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Q7c Here are their long jump results.

Q7d Use the graph to estimate how much further Sam jumped than Jan.

Sue jumped 212 cm.Draw Sue’s long jump result on

the graph.

0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 1 7 5 2 0 0 2 2 5 2 5 0

R a j

T o m

S a m

J a n

S u e

c e n t i m e t r e s

l o n g j u m p r e s u l t s

(c) Bar line drawn to anywhere between 200 and 225, EXCLUSIVE(ie bar must not end on 200 or 225 lines).

(d) Answer in the range 55 to 65 INCLUSIVE.



Q8 A line starts at A and goes along the dotted lines to B.It divides the area of the grid into halves.

A

B

Draw a 4 by 6 grid into your book like so:

Mark in A and B as shown then divide the area of the grid into halves. Start at A and go along the dotted lines to B.

A

B


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A

B

Any line that partitions the grid into two blocks of 12 squares, eg:

A

B

Line must run from A to B. Line must be on dotted grid lines only.

Do not accept. lines along the edge of the grid.


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Q9aTwo of these numbers divide by 5 with no remainder.

67 33 25 57 13 60

Working from left to right.

Which is the first number?

C. 67

D. 33

E. 25

F. 57

G. 13

H. 60


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Q9bTwo of these numbers divide by 5 with no remainder.

67 33 25 57 13 60

Working from left to right.

Which is the second number?

C. 67

D. 33

E. 25

F. 57

G. 13

H. 60


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Q10a Here are two spinners. .

543

216

87

6 543

21

J i l l ' s s p i n n e r P e t e r ' s s p i n n e r

Jill says,“I am more likely than Peter to spin a 3.”

Give a reason why she is correct.



Q10b Here are two spinners. .

543

216

87

6 543

21


Peter says,“We are both equally likely to spin an even number.”

Give a reason why he is correct.Peter is correct because…


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Q10a Here are two spinners. .

543

216

87

6 543

21


Jill says,“I am more likely than Peter to spin a 3.”

Give a reason why she is correct.(a) Reference to the fact that on Jill’s spinner, 3 is one number out of 6, but on Peter’s it is one number out of 8.,ORthe area/angle occupied by a section on Jill’s spinner is greaterthan it is on Peter’s spinner, eg:

· “She has less numbers than Peter.”· “She has only got 6 numbers and he has got 8.”· “3 is bigger on hers.”· “He has got more triangles.”

Do not accept vague or arbitrary reasons, eg:

· “He has a bigger square.”· “She is luckier than he is.”· “Her numbers are lower.”


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Q10b Here are two spinners. .

543

216

87

6 543

21


Peter says,“We are both equally likely to spin an even number.”

Give a reason why he is correct.Peter is correct because…

(a) Reference to the fact that the spinners have equal proportionsof even numbers, eg:

· “They both have the same number of odds and evens.”

· “It’s 50-50 for both.”Do not accept vague or arbitrary

reasons, eg:

· “He has got even numbers, so has she.”

· “Because they are mostly even numbers.”

· “It’s just luck.”


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Q11Karl puts 6 pegs in a pegboard.

He turns the board through 1 right angle.Draw below how the board would look.

Word File


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Q12 n stands for a number.

n + 7 = 13

What is the value of n + 10 ?

.

XL File


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Q13a Here is a shaded rectangle.

y

x

A ( 2 , 7 ) B

C ( 8 , 3 )D ( 2 , 3 ) M

00

What are the co-ordinates of B?

( , )


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y

x

A ( 2 , 7 ) B

C ( 8 , 3 )D ( 2 , 3 ) M

00

( , )

M is half way between D and C.What are the co-ordinates of M?




y

x

A ( 2 , 7 ) B

C ( 8 , 3 )D ( 2 , 3 ) M

00

( , )

M is half way between D and C.What are the co-ordinates of M?


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Q13a & b Here is a shaded rectangle.

y

x

A ( 2 , 7 ) B

C ( 8 , 3 )D ( 2 , 3 ) M

00

(a) (8, 7) Do not accept (7, 8). 1Accept co-ordinates written on diagram with or without commas and brackets, eg:

· (8 7)· 8 7· 8,7

(b) (5, 3) Do not accept (3, 5). 1Accept co-ordinates written on diagram with or without commas and brackets, eg:

· (5 3)· 5 3· 5,3

7

1 2 3 4 5 6 7 8

y

x

A ( 2 , 7 ) B

C ( 8 , 3 )D ( 2 , 3 ) M

00

(b) 2 to 8 = 6 steps half of 6 = 3 2 plus 3 = 5


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Q14 This diagram shows the proportions of waste by weight a family throws away in one year,

G l a s s a n d M e t a l

P l a s t i c

O t h e r m a t e r i a l

O r g a n i c

P a p e r a n d C a r d

a. Estimate what fraction of the waste is organic.

b. The family throws away about 35 kilograms of plastic in a year.

Use the diagram to estimate the weight of glass and metal they throw away.


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P l a s t i c


O r g a n i c


C The family throws away 130 kg of paper and card.

70% of this is newspapers.What is the weight of newspapers in kg?






P l a s t i c


O r g a n i c


a. Estimate what fraction of the waste is organic.

b. The family throws away about 35 kilograms of plastic in a year.

Use the diagram to estimate the weight of glass and metal they throw away.

(a) An answer in the range 1/5 to 3/10 OR 20% to 30%OR 0.2 to 0.3 INCLUSIVE.1

Numbers in range 20 to 30 must have % sign, eg:· Do not accept ‘25’

0%

20%

40%

60%

80%

100%

(b) An answer in the range 15 to 25 kg INCLUSIVE.





P l a s t i c


O r g a n i c




1% of 130 kg = 1.3kg

10% of 130 kg = ? kg





P l a s t i c


O r g a n i c




1% of 130 kg = 1.3kg

10% of 130 kg = 13kg

70% = 100% - 30% so

30% of 130kg = ?kg


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P l a s t i c


O r g a n i c




1% of 130 kg = 1.3kg

10% of 130 kg = 13kg

70% = 100% - 30% so

30% of 130kg = 39kg

70% = 100% - 30% so

70% = ?kg

(You could get the same answer by finding 10% and multiplying it by 7 to get 70%)


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Q15 Write in the missing digit.

7 x 9 = 3 3 3

XL File


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Q16a Vicki puts 10 books on a shelf.The 10 books take up 28 centimetres.

What is the mean (average) thickness of her books in cm?

XL File




Q16b The shelf is 120 centimetres long.Vicki fills the shelf with a mixture of books like the first ten books.

Estimate how many books she can get on the 120 cm



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(b) Award TWO marks for WHOLE NUMBER ANSWER in therange 40 to 50 inclusive, eg:

· 42.8If answer is outside range, award ONE mark for

anappropriate calculation , eg:

· 120 ÷ 28 × 10 = wrong whole number answer.· 120 ÷ 30 × 10 = wrong whole number answer.· 30cm is 10 books.60cm is 20 books.120cm is ... wrong answer.

If answer is outside range, a calculation MUST be performed for award of one mark. If calculation is based upon incorrect answer to 16a, award TWO marks for correct calculation using an appropriate strategy AND rounding of answer to whole number, even if outside range 40–50, eg:

· 120 ÷ answer to 16a = rounded whole number.ORONE mark if there is either an error in calculation or failure to round to whole number.


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Q17a A drink and a box of popcorn together cost 90p.

2 drinks and a box of popcorn together costs £1.45.

What does a box of popcorn cost in pence?



Q17b A drink and a box of popcorn together cost 90p.


What does a box of popcorn cost in pence?

Explain how you got your answer.


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Q17b A drink and a box of popcorn together cost 90p.


What does a box of popcorn cost in pence? (a) 35p Answer to 17a may be

embedded in answer to 17b. In this case, award one mark for correct answer.(b) Explanation which includes reference to any appropriate method even if theanswer is incorrect, eg:

· I took 90 from 145 and took my answer from 90.· If a drink and popcorn costs 90p you add to it however much it takes to make 145, which is 55p so you times 55 by 2 which is 110 and take away 145 and you get 45 (incorrect answer).ORa trial and improvement approach, eg:· I thought they might both cost 45p. I guessed the drink and doubled it to make 90p, then added another 45 but I got 10 less than £1.45. So I tried 55 and it worked so the popcorn is 35.

Accept appropriate numerical working elsewhere on page as adequate explanation. If there is no working and no explanation, there is no mark for 17b, even if 17a is correct.If answer to 17a is correct, accept appropriate non-numerical answer to 17b, (ie no reference to actual amounts of money).


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Q18 For information

Here is the start of a spiral sequence of right-angled triangles.Draw accurately the next right-angled triangle on the diagram.

You may use an angle measurer.

A

3 c m

3 c m

3 c m

3 c m

3 c m

3 c m

Use a the angle measurer and ruler tool to find the size of angle A.



Q19 This three-digit number has 2 and 7 as factors.

2 9 4

Write another three-digit number which has 2 and 7 as factors.


End of test

Q19 This three-digit number has 2 and 7 as factors. 2 9 4Write another three-digit number which has 2 and 7 as factors.

Any 3-digit number that is a multiple of 14, eg: 308

Any acceptable answers will be even numbers which divide by 7Do not accept ‘0’ in the hundreds box.Only three digit numbers are acceptable.

interactive voting - 1996 mathematics paper a

Documents

mathematics paper anext

number cards

missing number

pairs of parallel sides

piece fit

given numbers

correct answer ofup

right angles