1997 mathematics paper b

1997 MATHS PAPER B

1997 Mathematics Paper B1997 Mathematics Paper BInput your name and press send.Input your name and press send.

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Calculator Allowed

1997 Mathematics Paper B

Q1a Write what the three missing numbers could be.

+ + = 75

Q1b Write what the two missing numbers could be:

– – = 2580

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Calculator check? What must these two boxes add up to?

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Q2 Here is a set of stamps.

David posts a parcel.It costs £1.90He uses two of these stamps.Which two stamps does he use?

A. 15pB. 50pC. 75pD. £1.50E. £1.75

Calculator check?

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Q3a Chris did a survey of the number of people who went into shops in one hour.

Number of people who went into a shopstands fo r 5 peop le

S hoe shop

N ew sagen t

P ost O ffice

B read shop

S uperm arke t

How many people went into the Supermarket in the hour?

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Q3b Chris did a survey of the number of people who went into shops in one hour.


S hoe shop

N ew sagen t

P ost O ffice

B read shop

S uperm arke t

How many more people went into the Post Office than the Shoe shop?

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Q3b Chris did a survey of the number of people who went into shops in one hour.


S hoe shop

N ew sagen t

P ost O ffice

B read shop

S uperm arke t

Here is part of a bar chart of the information.

Draw in the missing bar – use the pen function.

24

20

16

12

8

4

0

num berof

people

P eople w ho w ent into shops

S hoeshop

News-agent

PostO ffice

B readshop

Super-m arket

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Q4 Here is a pattern on a window.

Draw how the pattern would look from the other side of the window.

See this in a word file.

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Q5 Write what the missing numbers could be

is an num ber, and .odd is greater than 15

is a num ber and cangreater than 100be , w ith .divided by 4 no rem ainder

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1997 Mathematics Paper BQ5 Write what the missing numbers could be

is an num ber, and .odd is greater than 15

is a num ber and cangreater than 100be , w ith .divided by 4 no rem ainder

Keep It Simple Stupid!

(a) Any odd number greater than 15, eg: 17Do not accept 15.If more than one number is given, all must be correct, eg: 17, 19, 21.

(b) Any multiple of 4 greater than 100, eg: 104Do not accept 100.If more than one number is given, all must be correct, eg: 104, 108, 112.

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Q6a Some children do a sponsored walk.

Jason is sponsored for £3.45 for each lap.He does 23 laps.

How much money does he raise?{Answer using a decimal point e.g. 12.45}

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Q6b Some children do a sponsored walk.

Lynne wants to raise £100.She is sponsored for £6.50 for each lap.

What is the least number of whole laps she must do?

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Q7 Write what the three missing digits could be.

x 3 = 8

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Q7 Write what the three missing digits could be.

x 3 = 8

2

2

2

7

8

9

3 =

3 =

3 =

x

x

x

8

8

8

1

4

7

O R

OR

Strategies:


8? Must be a multiple of 3

81 => check with calculator Yes it is

Share 81 by 3 = 27

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Q8a This piece of cheese has a mass of 350 grams.

Mark an arrow ( ) on the scale to show the reading for 350 g.

0500g

1 kg1500 g

2 kg

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Q8b Here are some apples.

What is the total mass of these apples in grammes?

Reading Scales XL file

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Q9a Write what the two missing numbers could be.

= 8

Q9b Write what the two missing numbers could be.

x = 100(4 + )

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Q9a Write what the two missing numbers could be.

= 8Q9b Write what the two missing numbers could be.

x = 100(4 + )(a) Any two numbers such that the first is eight times the second, eg:

Numbers must be in the correct order.Accept 8 ÷ 1Accept other recognised formats for writing a division problem only if all the numbers are shown in the correct location, eg:16 082 = 8 OR 2)16

Accept correct fractions, decimals and negative numbers.(b) Any two numbers which make the equation correct, eg:

Accept (4 + 0) × 25 = 100.Accept blank boxes provided the answer is elsewhere on the page.Accept correct fractions, decimals and negative numbers.


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Q9c What is the missing number?

30 – 1 6 = 9 +


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Q10a The area of the small shaded square is 1 square centimetre.What is the area

of the larger shaded square in cm squared?

1 cm ²

Use the pen tool to mark off

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10b On the grid below, draw a square with an area of 2 cm².

Use the pen tool to mark off

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10b On the grid below, draw a square with an area of 2 cm².

(b) Square as shown, anywhere on the diagram, eg:

The square need not be shaded.Accept slight errors in drawing provided the intention is clear.

If the square is not drawn using the grid vertices, it must have sides in the

range 1.3 to 1.5cm, inclusive.

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Q12a Here is a graph.

0 x

y

A

(4 ,2)(6,3)

B

The dots (

What are the coordinates of the point A?The first coordinate is?

) on the line are equally spaced.

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Q12a Here is a graph.

0 x

y

A

(4 ,2)(6,3)

B

The dots ( ) on the line are equally spaced.

What are the coordinates of the point A?The second coordinate is?



Q12b Here is a graph.

0 x

y

A

(4 ,2)(6,3)

B


Megan says,‘The point B has coordinates (11,5).’

Use the graph to explain why she cannot be correct.

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Q12 Here is a graph.

0 x

y

A

(4 ,2)(6,3)

B


Megan says,‘The point B has coordinates (11,5).’Use the graph to explain why she cannot be correct.

(b) Explanation which either implies that B has the coordinates (12, 6) OR that (11, 5) cannot be on the line because of the general relationship between the points, eg:

· ‘Because it’s 12, 6’· ‘If you count up in 2’s and 1’s it doesn’t come to 11, 5’· ‘The first numbers are always even’· ‘First should be twice the second number’Do not accept arbitrary or vague reasons, such as:‘She miscounted’;‘Because the bottom line doesn’t go up to 11’;‘Because it’s in a pattern’.

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Q13a This table shows the distances in kilometres between five towns.

Birm ingham

Cardiff

London

M anchester

Newcastle

179 188 127 334

269 278 489

298 441

212

334 489 441 212

127 278 298

188 269

179 Use the table to find the distance from London to Manchester in km.

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Q13b This table shows the distances in kilometres between five towns.

Birm ingham

Cardiff

London

M anchester

Newcastle

179 188 127 334

269 278 489

298 441

212

334 489 441 212

127 278 298

188 269

179

James goes from Newcastle to Birmingham, and then on to Cardiff.How many kilometres does he travel?

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Q13a Gavin was ill in March.

This is his temperature chart.

5 6 7 8 9 10 11 12 13 14 15 16 17 18

36

38

40

Tem

pe

ratu

re º

C

Date in M arch

G avin 's tem perature chart

For how many days was his temperature marked as more than 37°C?

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Q13b Gavin was ill in March.


5 6 7 8 9 10 11 12 13 14 15 16 17 18

36

38

40

Tem

pe

ratu

re º

C

Date in M arch


Which date showed the largest change in temperature from the day before? It was the _ th of March.



Q13c Gavin was ill in March.


5 6 7 8 9 10 11 12 13 14 15 16 17 18

36

38

40

Tem

pe

ratu

re º

C

Date in M arch


Estimate Gavin’s highest

temperature shown on the graph.

Give your answer to 1

decimal place.

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Q13 Gavin was ill in March.


5 6 7 8 9 10 11 12 13 14 15 16 17 18

36

38

40

Tem

pe

ratu

re º

C

Date in M arch


(a) For how many days was his temperature marked as more than 37°C? (b) Which date showed the largest change in temperature from the day before? It was the _ th of March. © Estimate Gavin’s highest temperature shown on the graph.Give your answer to 1 decimal place.

(a) 9(b) 8th of March

Accept 8.Accept ‘7th – 8th’ or similar.Do not accept 7th.

(c) 39.1 OR 39.2

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Q14 Here are the ingredients for fish pie for two people.

F ish pie

(f or 2 people)

2 5 0 g f ish

4 0 0 g pot at o

2 5 g but t er

Omar makes fish pie for 3 people.How many grams of fish should he use?

Ratio XL File



Q15 Sima thinks of a number.She divides it by 12. Her answer is 26.

What is the number Sima thinks of?





? ÷ 12 = 26

Simpler version:

? ÷ 2 = 3 ? =

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? ÷ 12 = 26

Simpler version:

? ÷ 2 = 3 ? = 6

What did you do with 2 and 3 to get 6

You multiplied them together.

So on the actual question multiply 12 and 26 together to get the answer of

312

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Q 16 Write the missing number.

= 37910233


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Q16 Write the missing number.


10233 ÷ ? = 379

Simpler version:

6 ÷ ? = 3 ? = 2

What did you do with 6 and 3 to get 2

You divided them.

So on the actual question divide 10233

by 379 to get the answer of 27

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Q17a Fill in the empty boxes to complete the pattern.

n + 6 7n + 6

4n + 3 7n + 3

n 4n

First

Second

Third

Which formula should be in the First box?

A. n + 7B. 4n + 3C. 4n + 7D. n + 3E. 7nF. 4n + 6

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Q17b Fill in the empty boxes to complete the pattern.

n + 6 7n + 6

4n + 3 7n + 3

n 4n

First

Second

Third

Which formula should be in the Second box?

A. n + 7B. 4n + 3C. 4n + 7D. n + 3E. 7nF. 4n + 6

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Q17c Fill in the empty boxes to complete the pattern.

n + 6 7n + 6

4n + 3 7n + 3

n 4n

First

Second

Third

Which formula should be in the Third box?

A. n + 7B. 4n + 3C. 4n + 7D. n + 3E. 7nF. 4n + 6

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Q17a Fill in the empty boxes to complete the pattern.

n + 6 7n + 6

4n + 3 7n + 3

n 4n

n + 3

7n

What are the patterns?If all three boxes are correct, award TWO marks.If only two boxes are correct, award ONE mark.No marks are awarded for only one correct box.Accept ‘1n’ for ‘n’.Accept ‘7n + 0’ for ‘7n’ and similar alternatives.Accept ‘3 + n’ for ‘n + 3’ and similar alternatives.

A. n + 7B. 4n + 3C. 4n + 7D. n + 3E. 7nF. 4n + 6

4n + 6 Pattern = +3n (unit = 6)

Pattern = +3n (unit = 3)

Pattern = +3n (no unit added)

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Q18a Write the missing digits.

= 371X

What is this digit?

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Q18b Write the missing digits.

= 371X

What is this number?

(Put both digits in and send).

XL File

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Q19a Which letter should go into this sentence.Shape ? is a reflection of shape A.

A

B

C

D

Correct answer = ?

Check – where is the mirror line? Pen tool?



Q19b Shape A is rotated 180° about the point P.Draw shape A in its new position on the diagram below.

In the actual SAT, you may use tracing paper or an angle measurer.

A

P

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Q19b Shape A is rotated 180° about the point P.Draw shape A in its new position on the diagram below.

In the actual SAT, you may use tracing paper or an angle measurer.

(b) Award TWO marks for the lower triangle in the position as shown

below. up to 2

A

P

If the answer is incorrect, award ONE mark for the correct rotation, but incorrect position drawn anywhere on the grid, eg:

A

P



Q20a Kelly chooses a section of a newspaper.It has 50 words in it.

She draws a bar chart of the number of letters in each word.

12

10

8

6

4

2

01 2 3 4 5 6 7 8 9 10

num berof words

num ber of letters in word

N ew spaper w ords

What fraction of the 50 words have more than 6 letters?

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Q20a Kelly chooses a section of a newspaper.It has 50 words in it.


12

10

8

6

4

2

01 2 3 4 5 6 7 8 9 10

num berof words


N ew spaper w ords

What fraction of the 50 words have more than 6 letters?

(a) 1/5 OR 10/50Accept other equivalent fractions, eg: 20/100

3+1+3+3 = 10

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Q20b Kelly chooses a section of a newspaper.It has 50 words in it.


12

10

8

6

4

2

01 2 3 4 5 6 7 8 9 10

num berof words


N ew spaper w ords

Kelly says,23 of the 50 words have less than 5 letters.This shows that nearly half of all the words used in the newspaper have less than 5 letters in them.Explain why she could be wrong.

End of paper


Q20b Kelly says,23 of the 50 words have less than 5 letters.

This shows that nearly half of all the words used in the newspaper have less than 5 letters in them.

Explain why she could be wrong.

(b) Explanations which imply that the results from a small sample cannot safelybe applied to a large one, eg:

· ‘You could be wrong because every section is different’· ‘The article is only a small proportion of the whole newspaper’· ‘The rest could be different’· ‘You can’t judge a whole newspaper by one article’Do not accept vague or arbitrary explanations such as:‘She might not have counted right’;‘The words in the newspaper might be big’;‘There are more bigger words than small’.

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1997 mathematics paper b

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