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Vectors (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

41 mins15 questions
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1
Sme Calculator2 marks

A is the point open parentheses 1 comma space 2 close parentheses and stack A B with rightwards arrow on top equals open parentheses negative 1 3 close parentheses.

Find the coordinates of the point B.

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2
Sme Calculator2 marks

Work out 2 open parentheses space 2 space 3 close parentheses minus open parentheses negative 3 space space space 5 close parentheses.

open parentheses space space space space space space space close parentheses

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3
Sme Calculator1 mark

Ahmed finds the magnitude of the vector open parentheses space space space space 2 minus 3 close parentheses.
From this list, select the correct calculation.  

square root of 2 squared space plus space minus 3 squared end root space space space space space space space space space space 2 to the power of 2 space end exponent minus space 3 squared space space space space space space space space space space square root of 2 squared space minus space 3 squared end root space space space space space space space space space space 2 to the power of 2 space end exponent plus space open parentheses negative 3 squared close parentheses space space space space space space space space space space square root of 2 squared space plus space open parentheses negative 3 close parentheses squared end root

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4
Sme Calculator1 mark

bold m equals open parentheses table row 5 row 7 end table close parentheses
Find 3 bold m.

open parentheses table row cell space space space space space space end cell row blank end table close parentheses  

How did you do?

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5
Sme Calculator2 marks

Find the magnitude of the vector open parentheses table row cell negative 1 end cell row 7 end table close parentheses.

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6
Sme Calculator3 marks
cie-igcse-2018-oct-nov-p4-tz3-q1b

i) Find the column vector stack A B with rightwards arrow on top.

 

 stack A B with rightwards arrow on top equals open parentheses table row cell space space space space end cell row cell space space space space space space end cell end table close parentheses [1]

ii) Find  vertical line stack A B with rightwards arrow on top vertical line.

  

vertical line stack A B with rightwards arrow on top vertical line equals................................................. [2]

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1
Sme Calculator2 marks

Find the magnitude of the vector open parentheses negative 6 space space space 8 close parentheses .

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2
Sme Calculator2 marks

stack V W with rightwards arrow on top equals open parentheses table row 10 row cell negative 24 end cell end table close parentheses
Find  open vertical bar stack V W with rightwards arrow on top close vertical bar.

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3a
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bold u bold space equals space open parentheses table row 3 row cell negative 2 end cell end table close parentheses space space space space space space space space space space space bold italic v space equals space open parentheses table row cell negative 12 end cell row 5 end table close parentheses

Find bold u space – space 2 bold v.

3b
Sme Calculator2 marks

Find space vertical line bold v vertical line space .

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4
Sme Calculator4 marks

bold p equals open parentheses table row 4 row 5 end table close parentheses       bold q equals open parentheses table row cell negative 2 end cell row 7 end table close parentheses

i) Find 2 bold p plus bold q.  

open parentheses table row cell space space space space space end cell row blank end table close parentheses [2]

ii) Find open vertical bar bold p close vertical bar.  

[2]

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5
Sme Calculator1 mark

bold m equals open parentheses table row 5 row 7 end table close parentheses
Find 3 bold m.

open parentheses table row cell space space space space space space end cell row blank end table close parentheses  

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6
Sme Calculator4 marks

bold a equals open parentheses table row cell negative 3 end cell row 2 end table close parentheses space space space space space space space bold b equals open parentheses table row 5 row 4 end table close parentheses space space space space space space space bold c equals open parentheses table row 14 row 9 end table close parentheses

i) Find  3 bold a minus 2 bold b .

 

 open parentheses table row cell space space space space space end cell row cell space space space space space end cell end table close parentheses [2]

ii) Find  vertical line space bold a bold space vertical line.

  

[2]

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1
Sme Calculator5 marks

bold p equals open parentheses space space space space 3 minus 2 close parentheses space space space space space space space space space space bold q equals open parentheses negative 5 space space space 1 close parentheses

(i) Work out bold p plus 2 bold q.

[2]

(ii) Ais the point open parentheses 2 comma space 6 close parentheses and B is the image of point Aafter a translation by the vector bold p.

Find the coordinates of B.

( ...................... , ...................... ) [1]

(iii) Find the magnitude of bold q.

[2]

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2
Sme Calculator5 marks

bold a equals open parentheses table row cell negative 3 end cell row 2 end table close parentheses space space space space space space space bold b equals open parentheses table row 5 row 4 end table close parentheses space space space space space space space bold c equals open parentheses table row 14 row 9 end table close parentheses

m bold a plus n bold b equals text bold c end text  

Write down two simultaneous equations and solve them to find the value of m and the value of n. Show all your working.  

m = ................................................     
n = ................................................      

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3
Sme Calculator3 marks

stack M T with rightwards arrow on top space space equals space open parentheses 2 k minus k close parentheses  and  open vertical bar stack M T with rightwards arrow on top space close vertical bar equals space square root of 180.  
Find the positive value of k.

k space equals ..............................................

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