Interactive Voting - 1995 mathematics paper a

1995 MATHSPAPER A

1995 Mathematics Paper A1995 Mathematics Paper AInput your name and press send.Input your name and press send.

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1995 Mathematics Paper A Q1

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This is a number triangle with some numbers missing.The numbers along each edge must add up to 90.Put all the numbers 20, 30, 50 and 60 in the circles to make the totals correct.

10

40

2 Marks


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Which symbol would go in the circle to make the calculation correct?

8 x 5 10 = 4

A. +

B. -

C. X

D. ÷

1995 Mathematics Paper A Q3 a

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This is a list of the highest temperatures each day for one week.

Day Tem perature

S unday

M onday

Tuesday

W ednesday

Thursday

Friday

S aturday

6ºC

5ºC

8ºC

12ºC

13ºC

11ºC

7ºC

How many degrees warmer was it on the hottest day than on the coldest day?

°C

1995 Mathematics Paper A Q3 b

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This is a list of the highest temperatures each day for one week.

Day Tem perature

S unday

M onday

Tuesday

W ednesday

Thursday

Friday

S aturday

6ºC

5ºC

8ºC

12ºC

13ºC

11ºC

7ºC

Here is a chart of the temperatures. Saturday is missing.

Draw in the bar for Saturday.

Day

Sunday

M onday

Tuesday

W ednesday

Thursday

Friday

Saturday0 4 8 12

Tem perature °C

(b) Bar to 7º C 1Give the mark for any bar which is more than 6º and less than 8º.

Answer Key:

1995 Mathematics Paper A Q4a

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Here is a row of numbers.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Find three numbers next to each other which add up to 39.

What would the first number be?

1995 Mathematics Paper A Q4b

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18


What would the second number be?

1995 Mathematics Paper A Q4c

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18


What would the third number be?


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? ÷ 5 = 22

What is the missing number?


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Here are 4 shapes

Each shape has two parallel sides.Write TWO other things which are the same about ALL the 4 shapes.

Answer key:

(a)(b) Award ONE mark for each appropriate mathematical characteristic to amaximum of TWO marks, eg. up to 2

· “They all have a right angle.”· “Each has straight edges (or sides).”· “They are all irregular.”· “They are all polygons.”· “They all have corners.”· “They all have 4 or more sides.”

If 2 correct reasons are given as one statement, marks for both (a) and (b) should be awarded, eg.· They all have at least 4 sides and a right angle.


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Here are three badges.

A B C

A You may use a mirror and tracing paper in the actual test.

Which badges have reflective symmetry? B Draw ONE line of symmetry on this

badge.

Show answers - click


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This is what it costs to visit a castle.

Allington CastleCost per person

Children(under 11)

£2.45£1.30

95p

AdultsChildren(11 and over)

Helen is 10 years 9 months old.How much will it cost Helen to visit?

(Answer in pence).

1995 Mathematics Paper A Q8 b (i)

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On one day the number of visitors was:

C hildren (under 11)

A dults

C hild ren (11 and over)

4

16

12

Here is a graph to show the number of visitors.Complete the scale for the axis called “Number of Visitors”.

C h ildren (under 11)

Adults C hildren (11 and over)

0

5

Num berof

Visitors

What number should go here?

1995 Mathematics Paper A Q8 b (ii)

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A dults


4

16

12




0

5

Num berof

Visitors


1995 Mathematics Paper A Q8 b (iii)

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A dults


4

16

12




0

5

Num berof

Visitors


1995 Mathematics Paper A Q8 c

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This is what it costs to visit a castle.

Allington CastleCost per person

Children(under 11)

£2.45£1.30

95p

AdultsChildren(11 and over)

How much will it cost for 18 children (under 11) to visit the castle?

(Answer like so: £ 2.50)


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In your book draw a grid of 12 by 12 squares.

On the grid draw a quadrilateral.It must have only one pair of parallel sides.

Award ONE mark for a 4-sided shape with one pair of parallel sides.1No mark is awarded unless the shape has four sides.No mark is awarded for a shape which has more than one pair of parallel sides.

Answer key:


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This calculation has the same number missing from each box.What is the missing number?

X – = 42

Link to XL file


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Write in the missing number.

Link to XL file

5

X 8

456


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Look at the shape on the grid.Turn it through one right angle around the point A.

Draw its new position.You may use tracing paper.

A

Link to Word file


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A

A

A

Award TWO marks for either of the shaded positions.

up to 2

Award ONE mark for the correct rotation, but incorrect positiondrawn anywhere on the grid, eg:

OR incorrect rotation (orientation wrong) but point A used correctly, eg:

One of the marks is awarded for correct rotation, ie 90º of rotation and shape in the correct orientation.The second mark is for the rotation beingaround the point A.[2]


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13

2

3 32

61

2

5 34

4

45

5

6

6

spinner A spinner B spinner C

Sam has 3 different spinners.

He chooses ONE of his spinners.He spins it 100 times and writes down how it lands each time.The results of the 100 spins are numbers only from 1 to 3.

Which spinner do you think he is using?

Give ONE reason why you chose this one.

Spinner?


(a) Both A and B have the numbers 1 to 3. The reason given for choosing A or B

should make reference to this, eg:· “Because A has only the numbers 1 to 3 on it.”

· “Only the numbers 1, 2 or 3 might turn up on B.”· “Because A has the most 3s, 2s and 1s.” 1

No mark is awarded for choice of spinner.Do not award marks for reasons which are vague or inappropriate,

eg:· “Because it’s got the right numbers.”

A reason is inappropriate if it refers to non-mathematical criteria or irrelevant mathematical criteria, eg:

· “Because it’s his favourite.”

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Answer key

13

2

3 32

61

2

5 34

4

45

5

6

6

spinner A spinner B spinner C

1. Sam has 3 different spinners.

Sam spins A 100 times and B 100 times.The arrows on the line show how many times each spinner lands on an odd number.

He spins C 100 times.Put an arrow on the line to show your estimate of how many times spinner C will land on

an odd number.

0 20 40 60 80 100

B A

Explain why you put the arrow there.


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(b)

The arrow should be within the shaded range of 25 to 40, inclusive.

0 20 40 60 80 100

B A

(c) Explanation which refers to the fact that 1/3 or 2/6 of the numberson C are odd OR which makes a comparison with the number ofodd numbers on A or B, eg: 1· “There are less odds on C.”· “Because it has only two odd numbers on.”The answer for (c) should be considered independently of the answer for (b).Accept(c) may be correct even if (b) is wrong.

1. Here are some picture frame sizes. For each frame, the length is twice the height, subtract 4.

What is the length (in cm) of a frame which has a height of 36cm?


Two marks for correct answer, 1 for correct working.

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1. Here are some picture frame sizes.

For each frame, the length is twice the height, subtract 4.


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Answer Key

For each frame, the length (L) is twice the height (H), subtract 4.Write this in symbols.

• (b) Award TWO marks for expressions such as:

L = 2H – 4L = 2(H – 2)L = H + H – 4.

• If incorrect award ONE mark for evidence of multiplication of H by 2,eg: 2H H2 H × 2 2 × H 2.H H.2or ONE mark for evidence of subtraction of 4,eg: L = H – 4

– Do not accept L = × 2 – 4 = H– Do not award marks for a repeat of the formula in

words as given in the question.


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Two marks for correct answer, 1 for correct working. Next Page

Answer key

A new frame has its length twice its height.It is made with 126cm of wood.

What is the length (in cm) of this frame?



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A new frame has its length twice its height.It is made with 126cm of wood.

What is the length (in cm) of this frame?

(c) Award TWO marks for 42cm, even if there are errors in the working.up to 2If answer is incorrect, award ONE mark for evidence that the

relationship “length is twice the height” has been used, eg:2H + 4H = 126H + 2H + H + 2H = 12620 + 40 + 20 + 40 = 120

The answers may be implicit, eg:· 21 + 42 + 21 + 42 = 126(Two marks)· 126 ÷ 6 = 21 × 2 = 42(Two marks)· 126 ÷ 3 (answer incompleteOne mark)


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Answer Key

1. Boxes measure 2.5cm by 4.5cm by 6.2cm.

2.5 cm

4.5 cm6.2 cm

The shopkeeper puts them in a tray.

31 cm9 cm

2.5 cm

Work out the largest number of boxes which can lie flat in the tray.



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1. Boxes measure 2.5cm by 4.5cm by 6.2cm.

2.5 cm

4.5 cm6.2 cm

The shopkeeper puts them in a tray.

31 cm9 cm

2.5 cm

Work out the largest number of boxes which can lie flat in the tray.

Award TWO marks for the correct answer of 10, even if there are errors up to 2in the working.

If the answer is incorrect, award ONE mark for evidence of any attempt at solution, by any method, eg:· 31 ÷ 6.2 and 9 ÷4.5 are attempted calculations;· 31 ÷ 6.2 and 9 ÷4.5 are estimated;· “You can get two boxes widthways and 5 lengthways”.


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Answer Key

1. The Year 6 children in a school were asked to choose a musical instrument. This is a pie chart of their choices.

G uitar

Vio linRecorder

Trum petD rum

Keyboard

Estimate what fraction of the children chose a drum.


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G uitar

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Keyboard

Estimate what fraction of the children chose a drum.

(a) The answer is approximately 1/7. Accept any fraction, percentage or decimalin the range:

· 1/9 to 1/5, inclusive· 11% to 20%, inclusive· 0.11 to 0.2, inclusive

Pie Chart

Demo’

1995 Mathematics Paper A Q16 b

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Answer Key


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Keyboard

There are 80 children in Year 6.Estimate the number of children who chose a

violin.


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G uitar

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Keyboard

There are 80 children in Year 6.

Estimate the number of children who chose a violin.

(b) The correct answer is 10. Accept any number in the range 8 to 12, inclusive.

Pie Chart

Demo’


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Answer Key


G uitar

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Keyboard

There are 80 children in Year 6.Estimate the number of children who chose a

violin. Explain how you decided.


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G uitar

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There are 80 children in Year 6.

Estimate the number of children who chose a violin. Explain how you decided.

(c) The explanation should make reference, in some form, to appropriate fractional estimates, eg:

·“Because it looks like a quarter of a half and that’s 10.”“I thought the violin looked like half the trumpet and that was about a quarter.”“I decided this because 1/4 was 20 children, so I halved 20 and made it 10.”

Explanations which lack specific reference to appropriate fractions should not be awarded the mark, eg:

“Because it’s a bit less than the trumpet.”“Because there are 6 parts to the pie chart.”

Pie Chart

Demo’

1995 Mathematics Paper A Q16d

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Answer Key


G uitar

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Trum petD rum

Keyboard

15% of the 80 children chose a guitar.How many children is this?



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G uitar

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Keyboard

15% of the 80 children chose a guitar.

How many children is this?

(d) Award TWO marks for the correct answer of 12, even if there are errors in the working.

Award ONE mark if the answer is incorrect, but there is evidence of an attempt to calculate 15% of 80 by any method, eg:

· 15/100 × 80 = (incorrect answer given)· 10% of 80 = 8, 5% is 4, so 15% of 80 = (incorrect answer given)· 1% of 80 = 80/100 = 4/5, so 15% = 4/5 × 15 = (incorrect answer given)

The writing of “15/100 × 80” (or equivalent) alone is not sufficient evidence of an attempt to calculate.

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Demo’


Write in the missing digit.

92 ÷ 14 = 28

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Answer Key


Write in the missing digit.

92 ÷ 14 = 28

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Simple version: ? ÷ 2 = 3

What is ?

? = 6 so what did you do with 3 and 2 to make 6?

3 * 2 = 6

So replace with the actual numbers 28 * 14 =

392

Keep It Simple Stupid!


Kim wants to estimate the probability that her friend Tony will answer the phone when she rings the house.

Here are two ways she could do it.A There are four people in the house, so there is a probability of 1 out of 4 it will be Tony.B The last time Kim rang, Tony answered, so it won’t be Tony this time.

Kim says A is not a good way to estimate the probability.

Explain why not.

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Answer Key

She also says B is not a good way to estimate the probability.

Explain why not.




Kim says A is not a good way to estimate the probability.Explain why not.

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Answer Key

(a) Explanation which suggests that the people in the house are not equallylikely to answer the phone, eg:

· “Some of them might be babies.”· “Some of them might never answer the phone.”· “He doesn’t know what’s happening in the house.”· “They don’t all answer the phone the same amount.”

Do not accept answers that make specific assumptions that are unjustified, eg:

· “Because normally children are asked to answer the phone.”· “They might all be out.”




Kim says A is not a good way to estimate the probability.

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(b) Explanation which suggests that what happened on just one occasion is aninadequate guide to estimating probability, eg: 1

“Just because Tony answered last time doesn’tmean it won’t be him next time.”“Anyone could answer the phone next time. It could be Tony again.”

Do not accept answers that offer an arbitrary or unjustified reason, eg:

· “Because it’s just a guess.”· “Tony usually answers.”

She also says B is not a good way to estimate the probability.

Explain why not.


Write in the missing digits.

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=323 x 7 1518

The first one is?


Write in the missing digits.

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=323 x 7 1518

The second one is?

XL File


Mr Green sells apples Mrs Ball sells applesat 40p per kilogram. at 24p per pound.

Work out who sells the cheaper apples.Show how you worked it out.

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Answer Key


Mr Green sells apples Mrs Ball sells applesat 40p per kilogram. at 24p per pound.

Work out who sells the cheaper apples.Show how you worked it out.

End of paper

Evidence of conversion from lbs to kg OR kg to lbs, such as multiplication ordivision by 2 or 2.2, eg:· 24 × 2.2· “There’s more than 2 pounds in a kilogram so it will be about 50p for a kg of apples.So, Mr Green.”· “40p per kg is about 20p a pound.”

No mark is awarded or forfeited for the name, Mr Green or Mrs Ball.

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