gcse foundation maths student licence version 4€¦ · 3a - sequences, functions and graphs 174...

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3 sequences, functions and graphs

3A - sequences LIN 10 MOD 13

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SECTION A

Answer ALL SIX questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

You must NOT use a calculator for this section.

1. Here are some patterns made with dots.

Pattern number 1 Pattern number 2 Pattern number 3 Pattern number 4

(a) In the space below, draw Pattern number 5

(1)

(b) How many dots are used in Pattern number 6?

......................(1) Q1

(Total 2 marks)

1.

3A - sequences, functions and graphs

o Recognisethepatterninasequenceofdiagrams(includingfindingnextinsequence)

o Findandusetheruletocomputetermsinalinearnumbersequence

o Findaterminalinearnumbersequence

o Findmissingnumbersinalinearseries

o Findthenthtermofalinearexpression

GCSE Foundation Maths Student Li60 60 10/11/06 09:33:14

This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited

A02 - n

umber and algebra

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7. (a) The first odd number is 1.

(i) Find the 3rd odd number...........................

(ii) Find the 12th odd number...........................

(2)

(b) Write down a method you could use to find the 100th odd number.

.......................................................................................................................................

.......................................................................................................................................(1)

Here are some patterns made with dots.

(c) In the space below, complete Pattern Number 4.

(1)

The table shows the number of dots used to make each pattern.

(d) Complete the table.

(2)

Pattern Number 1 Pattern Number 2 Pattern Number 3

Pattern Number 1 2 3 4 5

Number of dots 5 8 11

Q7

(Total 6 marks)

2.




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174 GCSE Mathematics 2540/2544 Sample Assessment Material UG017663

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3. Here are some patterns made from matchsticks.


(1)

3.



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3. Here are some patterns made from matchsticks.


(1)



A02 - n

umber and algebra


175GCSE Mathematics 2540/2544 Sample Assessment Material UG017663

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The graph shows the number of matchsticks m in pattern number n.

(b) Mark the point showing the number of matchsticks used in Pattern number 4

(1)

(c) How many matchsticks are used in Pattern number 10?

..........................(1)

(d) Write down a formula for m in terms of n.

.............................................(1) Q3

(Total 4 marks)

(b)

(c) Write down a formula for m (the number of matchsticks) in terms of n (the pattern number)



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3A - sequences, functions and graphsLeaveblank

3. Here are the first five terms of a number sequence.

(a) Write down the next two terms of the number sequence.

…………… , ……………(1)

(b) Explain how you found your answer.

.......................................................................................................................................(1)

The 20th term of the number sequence is 50

(c) Write down the 21st term of the number sequence.

..........................(1)

4. Work out

..........................

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126 122 118 114 110

286 43×

Q3

(Total 3 marks)

Q4

(Total 3 marks)

4.

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10 16 22 28 34

(a) Which one of these numbers is a square number?....................

(1)

(b) Write down the next term of the number sequence.

....................(1)

(c) Explain why 861 is not a term of the number sequence.

.......................................................................................................................................

.......................................................................................................................................(1)

3. (a) Write 0.85 as a percentage.

......................................%(1)

(b) Write as a percentage.

......................................%(1)

(c) Write 60% as a decimal.

.........................................(1)

Q2

(Total 3 marks)

Q3

(Total 3 marks)

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Maths147300_M22881A.indd 4 08/09/2005 19:15:31

5.

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10 16 22 28 34

(a) Which one of these numbers is a square number?....................

(1)

(b) Write down the next term of the number sequence.

....................(1)

(c) Explain why 861 is not a term of the number sequence.

.......................................................................................................................................

.......................................................................................................................................(1)

3. (a) Write 0.85 as a percentage.

......................................%(1)

(b) Write as a percentage.

......................................%(1)

(c) Write 60% as a decimal.

.........................................(1)

Q2

(Total 3 marks)

Q3

(Total 3 marks)

110

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(a)

(b)



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umber and algebra

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4. Here are the first four terms of a number sequence.

2 7 12 17

(a) Write down the 6th term of this number sequence.

....................................(1)

The nth term of a different number sequence is 4n + 5

(b) Work out the first three terms of this number sequence.

.......... .......... ..........(2)

(Total 3 marks)

5. The price of a DVD player was £120In a sale, the price is reduced by 35%.

Work out the sale price of the DVD player.

£ ..................................

(Total 3 marks)

Q5

Q4

Maths147303_M22884A.indd 5 05/09/2005 09:55:31

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2. Here are the first five terms of an arithmetic sequence.

7 11 15 19 23

(a) Write down, in terms of n, an expression for the nth term of this sequence.

....................................(2)

Pat says that 453 is a term in this sequence. Pat is wrong.

(b) Explain why.

......................................................................................................................................

......................................................................................................................................(1)

(Total 3 marks)

3. (a) Simplify p8 ÷ p2

.......................... (1)

(b) Simplify (w4)3

.......................... (1)

(c) Simplify 5e3f × e2f 2

.......................... (2)

4. Write 58 000 in standard form.

..........................

Q3

(Total 4 marks)

Q2

Q4

(Total 1 mark)

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7.

6.




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3. Susan is decorating her bedroom. She buys

1 paint brush costing £2.46 1 paint roller costing £3.08 2 tins of paint costing £5.95 each

She pays with a £20 note.

Work out how much change she should get.

£ ......................................

(Total 3 marks)

4.

(a) Write down the coordinates of the point L.

(............ , ............)(1)

The coordinates of another point are (–4, –1).

(b) Mark this point on the grid. Label it M.

(1)

(Total 2 marks)

Q3

Q4

–4 –3 –2 –1 O 1 2 3 4 x

4

3

2

1

–1

–2

–3

–4

y

×L

–5

1.

3B - Real life graphs LIN 12 MOD 15

3B - Real life graphs

o Plotorreadcoordinatesin4quadrants

o Interpretinformationinareallifegraph

o Drawanduseconversiongraphs

o Interpretatravelgraph

o Completetravelgraphs



A02 - n

umber and algebra

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Tom also travels by car to his meetings.Tom’s company works out the amount it will pay him for the distance he travels.It uses the graph below.

(c) Use the graph to write down

(i) the amount Tom’s company pays him when he travels 200 miles,

£........................

(ii) the distance Tom travels when his company pays him £50.

.................(2)

50 100 150 200 250 300

120

100

80

60

40

20

Amount inpounds (£)

Distance in miles

miles

O

Q9

(Total 9 marks)

2.

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£........................


.................(2)

50 100 150 200 250 300

120

100

80

60

40

20


Distance in miles

miles

O

Q9

(Total 9 marks)

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£........................


.................(2)

50 100 150 200 250 300

120

100

80

60

40

20


Distance in miles

miles

O

Q9

(Total 9 marks)

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£........................


.................(2)

50 100 150 200 250 300

120

100

80

60

40

20


Distance in miles

miles

O

Q9

(Total 9 marks)



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20. A man left home at 12 noon to go for a cycle ride.The travel graph represents part of the man’s journey.

At 12.45pm the man stopped for a rest.

(a) For how many minutes did he rest?

.............(1)

(b) Find his distance from home at 1.30pm.

.....................(1)

The man stopped for another rest at 2pm.He rested for one hour.Then he cycled home at a steady speed. It took him 2 hours.

(c) Complete the travel graph.(2)

minutes

km

Q20

(Total 4 marks)

3.




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6. Here is a conversion graph for changing between kilograms and pounds.

(a) Use the graph to change 22 pounds to kilograms.

........................ kg(1)

(b) Use the graph to change 2.5 kilograms to pounds.

................. pounds(1)

Fabio weighs 110 pounds.

(c) Change 110 pounds to kilograms.

........................ kg(2) Q6

(Total 4 marks)

4.




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Q3

(Total 6 marks)

3. (a) Complete the table of values for y = 3x + 1

(2)

(b) On the grid, draw the graph of y = 3x + 1

(2) (c) Use your graph to find

(i) the value of y when x = – 0.8 y = ................... (ii) the value of x when y = 8.2 x = ...................

(2)

x –2 –1 0 1 2 3

y –5 1

1.

3C - Graphs on coordinate axes LIN 15 MOD 16

3C - Graphs on coordinate axes

o Useatableofvaluestodrawasimplestraightlinegraph

o Drawthegraphofastraightlinebyfindingandplottingpointsandjoining

o Drawatableofvaluesandthegraphofaquadraticfunctionfromatableofvalues

o Usestraightlinegraphstosolveproblems

(2)



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umber and algebra

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(2)(b) On the grid, draw the graph of y = 3x + 2

(2)

x –2 –1 0 1 2

y –1 5

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-1-2 1 2O

y

x

Q9

(Total 4 marks)

2.


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Q3

(Total 6 marks)


(2)

(b) On the grid, draw the graph of y = 3x + 1

(2) (c) Use your graph to find

(i) the value of y when x = – 0.8 y = ................... (ii) the value of x when y = 8.2 x = ...................

(2)

x –2 –1 0 1 2 3

y –5 1



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SECTION B

Answer ALL SIX questions.

Write your answers in the spaces provided.

You must write down all stages of your working.

1. (a) Complete the table of values for y = x2 + x.

(2)

(b) On the grid, draw the graph of y = x2 + x.

(2) Q1

(Total 4 marks)

x –3 –2 –1 0 1 2 3

y 6 2 0 6

s

s

O

y

12

10

8

6

4

2

–2

–4

–6

–8

–10

–12

–3 –2 –1 1 2 3 x

Math147308_M22894A.indd 3 09/09/2005 18:04:16

3.




A02 - n

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Q5

(Total 2 marks)

5.

The diagram shows the graph of the equation y = 2x2 – 4x – 3

Use the graph to find the approximate values of x when 2x2 – 4x – 3 = 0

x = ............................ or x = ...........................

-2 -1 1 2 3 4-2

2

4

6

8

10

12

14

-4

-6

0

y

x

4.

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Q5

(Total 2 marks)

5.

The diagram shows the graph of the equation y = 2x2 – 4x – 3

Use the graph to find the approximate values of x when 2x2 – 4x – 3 = 0

x = ............................ or x = ...........................

-2 -1 1 2 3 4-2

2

4

6

8

10

12

14

-4

-6

0

y

x


(2)


gcse foundation maths student licence version 4€¦ · 3a - sequences, functions and graphs 174...

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