interactive voting - 1996 mathematics 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 MATHS PAPER B

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1996 Mathematics Paper B

Q1 Write what the missing numbers could be.

- = 77

x = 54

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1996 Mathematics Paper BQ1 Write what the missing numbers could be.

- = 77

x = 54

(a) Any two numbers which have a difference of 77, eg:80 -3

Numbers must be in the correct order.

Accept 77 – 0.Accept negative answers, eg:·70 - -7Answers must be in the form of

only two numbers (one number in each box). Do not accept, eg:

·90 – 10 – 3 = 77·



Q2 Tim buys a 19p postcard.

He pays exactly 19p with five coins.What could the five coins be?

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Q2 Tim buys a 19p postcard.

He pays exactly 19p with five coins.What could the five coins be?

10p 5p 2p 1p 1p

5p 5p 5p 2p 2p

orAll must be correct.

Accept any number in any order.Award mark even if ‘p’ is missing.

Accept answers elsewhere on the page if boxes are blank.

Accept coins drawn.

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Q3a Anne makes a graph of buses passing a school in 1 hour.

Num ber 8 Num ber 11 Num ber 27 N um ber 39 Num ber 50

Bus

Num berof tim es B uses passing in one hour

0

5

10

How many times does a Number 27 bus pass in the hour?

Q3bAnne says,“Bus number 39 passes least often in the hour.”

Explain how the graph shows this.

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Q3c How many more Number 8 buses pass in the hour than Number 11 buses?

Num ber 8 Num ber 11 Num ber 27 N um ber 39 Num ber 50

Bus

N um berof tim es B uses passing in one hour

0

5

10

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Q4a Here is a calculation with one sign missing.

4 x 3 x 2 1 = 25

4 3 2 1 = 23What is the missing sign?

A. +

B. -

C. X

D. ÷

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1996 Mathematics Paper BQ4b Here is a calculation with one sign missing.

4 x 3 x 2 1 = 25

4 3 2 1 = 23What is the missing sign?

A. +

B. -

C. X

D. ÷

XL File

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Q5 What is in the missing three-digit number?

10 = 20

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Q5 What is in the missing three-digit number?

10 = 20

Keep It Simple Stupid!

? ÷ 10 = 20

? ÷ 3 = 2

6 ÷ 3 = 2

What did you do with 3 and 2 to get 6?

You multiplied so do the same for the harder numbers: 10 * 20 = 200

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Q6 What is the first missing number?

= 3 1593 – 20

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Q6 What is the second missing number?

= 3 1593 – 20

XL File

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Q7a Leon’s grid has two shaded shapes.

A B

Leon says,“Shape A has a larger area than shape B.”

Explain how he could have worked this out.

12

3

45

6

12

34

5

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Q7b On the board draw a different shape. It must have the same area as shape A.

A1

23

45

6

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Q8 Here is an equilateral triangle drawn on a circle.

Use straight lines draw a regular hexagon on this circle.

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Q7b Here is an equilateral triangle drawn on a circle.

Use straight lines draw a regular hexagon on this circle.

How many sides does a hexagon have?

It has 6 sides.

How many dots are there around the circle?

There are 12

Each side of the regular hexagon must be two dots wide

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Q9a This is an open top box.

A B C D

For each shape, you must say whether it is a net of the box

Is “A” a net of the box?

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Q9b This is an open top box.

A B C D


Is “B” a net of the box?

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Q9c This is an open top box.

A B C D


Is “C” a net of the box?

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Q9d This is an open top box.

A B C D


Is “D” a net of the box?

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Q9 This is an open top box.

A B C D


Is “D” a net of the box?

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1996 Mathematics Paper BQ10 The rule for this number sequence is

“double and subtract 1”What is the missing number?

2 3 5 9

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2 3 5 9

Here is part of another sequence with the same rule.What is the missing number?

13 25 49

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2 3 5 9

Here is part of another sequence with the same rule.What is the missing number?

13 25 49

(2 * 2 = 4)-1=3 (3 * 2 = 6)-1=5(5 * 2 = 10)-1=9

(9 * 2 = 18)-1=17

(? * 2 = ??)-1=13

Work backwards: ?? – 1 = 13 ?? = 14 so ? * 2 = 14 ? Must be 7



Q11 Use a ruler to draw 2 more lines to make an isosceles triangle. Draw in books or board?

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Q11 Use a ruler to draw 2 more lines to make an isosceles triangle.

Any isosceles triangle made by drawing two more lines, eg: (Isosceles = triangle with 2 sides the same length)

or orVertices need not be exactly on the dots provided intention is clear.There is no requirement to use the dots.

Lines may go outside grid.Any triangle that uses the given line and has at least two sides equal to within

2mm is acceptable.Accept equilateral triangles.

Keep It Simple Stupid!4 across 1 down

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Q12a Here is a graph of guitar sales.

M onth

Num berof guitars

0

G uitar sales

20

40

60

80

100

Jan Feb M arch A pril M ay June

The table below shows the change in sales from month to month.

Use the graph to complete the table.

Change in G uitar sales

January to February

February to M arch

M arch to April

A pril to M ay

M ay to June

Down 40

Up 50

Up 40Did the March to April sales go:

A. Up

B. Or Down?

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Q12b Here is a graph of guitar sales.

M onth

Num berof guitars

0

G uitar sales

20

40

60

80

100





January to February

February to M arch

M arch to April

A pril to M ay

M ay to June

Down 40

Up 50

Up 40How much did the March to April sales go down by?

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Q12c Here is a graph of guitar sales.

M onth

Num berof guitars

0

G uitar sales

20

40

60

80

100





January to February

February to M arch

M arch to April

A pril to M ay

M ay to June

Down 40

Up 50

Up 40Did the May to June sales go:

A. Up

B. Or Down?

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Q12b Here is a graph of guitar sales.

M onth

Num berof guitars

0

G uitar sales

20

40

60

80

100





January to February

February to M arch

M arch to April

A pril to M ay

M ay to June

Down 40

Up 50

Up 40How much did the May to June sales go up by?

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Q12 Here is a graph of guitar sales.

M onth

Num berof guitars

0

G uitar sales

20

40

60

80

100


Which month had the greatest change in sales compared with the month

before?


January to February

February to M arch

M arch to April

A pril to M ay

M ay to June

Down 40

Up 50

Up 40A. January

B. February

C. March

D. April

E. May

F. June

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Q13a There are 2 adults and 3 children in a family.How many pounds does it cost the family to go on the ferry?

Answer like so:

33.20 Two marks for the correct answer. One mark for working out.

2 adults = 2 * £23.00 = £46.00

3 children = 3 * £11.50 = £34.50

£46.00 + £34.50 = £80.50(a) Award TWO marks for the correct answer of £80.50. up to 2

If answer is incorrect, award ONE mark for evidence of appropriate strategysuch as:

· £23 × 2 + £11.50 × 3

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Q13b On the ferry they change pounds for French francs.For every £1 they get 7 francs.How many francs do they get for £150?

x 100 50 0

7 700 350 0 = 1050

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Q14a A, B and C are three corners of a square.What are the co-ordinates of the other corner?

0 1 2 3 4 5 6 7

0

1

2

3

4

5

6

7

y

x

A

B

C

( , )

What is the first co-ordinate?

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Q14b A, B and C are three corners of a square.What are the co-ordinates of the other corner?

0 1 2 3 4 5 6 7

0

1

2

3

4

5

6

7

y

x

A

B

C

( , )

What is the second co-ordinate?

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Q14 A, B and C are three corners of a square.What are the co-ordinates of the other corner?

0 1 2 3 4 5 6 7

0

1

2

3

4

5

6

7

y

x

A

B

C

X co-ordinate y co-ordinate

( 4 , 3 )



Q15 Complete this three-digit number so that it is a multiple of 9.

2

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Q15 Complete this three-digit number so that it is a multiple of 9.

2

Any three-digit number that is a multiple of 9,eg:

If correct, the sum of the digits will be 9 or 18.

2 0 7

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Q16a At a petrol station there is a scale for converting litres and gallons.

0

1

2

3

4

0

5

10

15

G allons

G allons

Litres

Litres

Approximately how many litres are there in 3 gallons?

Give your answer to the nearest litre.

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Q16b At a petrol station there is a scale for converting litres and gallons.

0

1

2

3

4

0

5

10

15

G allons

G allons

Litres

Litres

Approximately how many gallons are there in 7 litres?

Give your answer to 1 decimal place.

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Q16 At a petrol station there is a scale for converting litres and gallons.

0

1

2

3

4

0

5

10

15

G allons

G allons

Litres

Litres

Approximately how many gallons are there in 7 litres?

Give your answer to 1 decimal place.

Approximately how many litres are there in 3 gallons?

Give your answer to the nearest litre.

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Q17 Sarah draws a quadrilateral.It has these properties:

· it has 2 long sides the same length;· it has 2 short sides the same length;· it does NOT have any right angles;

· it does NOT have reflective symmetry.Write the mathematical name for Sarah’s quadrilateral.

Does the quadrilateral have right angles?

Y N

A quadrilateral sorting diagram

Does the quadrilateral have any parallel sides?

Y N

Does the quadrilateral have four equal sides?

Y N

Y N

Does the quadrilateral have four equal sides?

Y N

One pair of parallel sides?

An Irregular quadrilateral

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Q18 Here are some number cards.

9

A Use two of the cards to make a fraction which is less than 2

1

.

B How much less than 1 is your fraction?

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Q18 Here are some number cards.

9

A Use two of the cards to make a fraction which is less than 2

1

. B How much less than 1 is your fraction?

Accept: 3/7 or 3/9 or 3/11 or 5/11

Accept: 4/7 or 6/9 or 8/11 or 6/11 depending on the answer to A

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Q19 In a country dance there are 3 boys and 2 girls in every line.

42 boys take part in the dance.How many girls take part?

.

Two marks for the correct answer. One mark for working out.

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1996 Mathematics Paper BQ19 In a country dance there are 3 boys and 2

girls in every line. 42 boys take part in the dance.

How many girls take part?

.

1 line = 3b + 2g

1 line = 3b + 2g

Total boys

Total girls

3

2

6

4

Number of lines

1 2

How many lines (inc 3 boys) would you need to have 42 boys?

14 So what is 14 lots of 2 girls equal to?

28

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1996 Mathematics Paper BQ20a Mrs Jones prints books.

.


Jon pays £4.35 for his book, including the cover.How many pages are in his book?


1996 Mathematics Paper BQ20b Mrs Jones prints books.

.


Here are the print prices again.3p per page and 75p for the cover.

Write a formula for the total cost of printing a book with cover.t stands for the total cost in pence.

Use n for the number of pages.

t =

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1996 Mathematics Paper BQ20 Mrs Jones prints books.

.

Here are the print prices again.3p per page and 75p for the cover.

Write a formula for the total cost of printing a book with cover.t stands for the total cost in pence.

Use n for the number of pages.

Jon pays £4.35 for his book, including the cover.How many pages are in his book?

(a)Award TWO marks for correct answer of 120 OR 95(if book is assumed to have two covers) up to 2

If the answer is incorrect, award ONE mark for evidence of appropriatestrategy, eg:

·435 – 75 = 360360 ÷ 3

·435 – 150 = 285285 ÷ 3

(b) Award TWO marks for correct algebraic expression equivalent tot = 3n + 75, OR t = 3n + 150, eg: up to 2· t = 3 × n + 75

· t = 75 + n3If expression is incorrect award ONE mark for evidence of 3 × n, eg:

· 3n + 750OR evidence of addition of 75 (or 150) to an expression involving n, eg:

· n + 75No mark is awarded for the expression in words.

Accept inclusion of ‘p’ in expression, eg:· 3p × n + 75p

Accept ‘use of N’ as well as n.Answer to 20b must be consistent with answer to 20a, ie if 2 covers are assumed in 20a, they should be assumed in 20b.

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1996 Mathematics Paper BQ21a Jim draws a graph to show how high two rockets go during their flight.

. 0

50

100

200

150

250

300

350

0 10 20 30 40 50 60 70

rocket A

rocket B

tim e (seconds)

height above ground(m etres)

Estimate how much higher rocket A reaches than rocket B.

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1996 Mathematics Paper BQ21b Jim draws a graph to show how high two rockets go during their flight.

. 0

50

100

200

150

250

300

350

0 10 20 30 40 50 60 70

rocket A

rocket B

tim e (seconds)


Estimate the time after the start when the two rockets are at the same height.


1996 Mathematics Paper BQ21c Jim draws a graph to show how high two rockets go during their flight.

. 0

50

100

200

150

250

300

350

0 10 20 30 40 50 60 70

rocket A

rocket B

tim e (seconds)


Jim says,“The graph shows that rocket A was more than 200 m above the ground for about 23

seconds.”Explain how the graph shows this.

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.

0

50

100

200

150

250

300

350

0 10 20 30 40 50 60 70

rocket A

rocket B

tim e (seconds)


Estimate how much higher rocket A reaches than rocket B.

(a) Any answer in the range 145m to 175m inclusive.

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1996 Mathematics Paper BQ21b Jim draws a graph to show how high two rockets go during their flight.

.

0

50

100

200

150

250

300

350

0 10 20 30 40 50 60 70

rocket A

rocket B

tim e (seconds)


Estimate the time after the start when the two rockets are at the same height.

(b) A time in the range 27 to 29 seconds inclusive.

End of test


. 0

50

100

200

150

250

300

350

0 10 20 30 40 50 60 70

rocket A

rocket B

tim e (seconds)


Jim says,“The graph shows that rocket A was more than 200 m above the ground for about 23

seconds.”Explain how the graph shows this.

(c) Evidence of awareness that the time interval between the points where the200m line cuts the graph for rocket A has been used, eg: 1

· “He could have checked when the rocket went above 200m and when it went under 200m and worked out the time between.”· “Look how high it goes until it gets to 200m then look along the horizontal line until it drops below 200m.”

An appropriate drawing on the graph, identifying the intersection of the 200m line with the curve is acceptable as part of explanation, eg, award mark for:

· “Subtract the two dots” if dots are marked indicating correct intersections.Do not accept vague statements or ones which only repeat information, eg:· “You can draw the graph then draw the things then work it out.”· “Because on the graph the rocket is above 200m for 23 seconds.”

interactive voting - 1996 mathematics paper b

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