Surds, Vectors and Proof Questions

Some Maths questions to attempt.

One you have completed them I can give you the answers if you wish. Just email me here and I will be happy to give you the answers, or comment below asking for the answers. 

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Q1. Expand and simplify

(2 + )(7 ­ )

Give your answer in the form a + , where a and b are integers.
(Total 3 marks)

Q2. (a) Rationalise the denominator of

(b) Expand

Give your answer in the form a + b where a and b are…

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(c) Show algebraically that the sum of any 3 consecutive even numbers is always a
multiple of 6
(Total 5 marks)

Q6. Prove that (3n + 1) ­ (3n ­1) is a multiple of 4, for all positive integer values of n.
2 2

(Total 3 marks)

Q7. The diagram…

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= 4a and = 4b

OAC, OBX and BQC are all straight lines

AC = 2OA and BQ:QC = 1:3

(a) Find, in terms of a and b, the vectors which represent



Given that = 8b

(b) Show that AQX is a straight line.

(Total 7 marks)


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Diagram NOT accurately drawn

XYZ is a straight line.
XY : YZ = 2 : 3.

(b) Express the vector in terms of a and b.
Give your answer in its simplest form.

(Total 5 marks)


Diagram NOT accurately drawn

OAB is a triangle.

= a

= b


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Page 5




this is really good! thankyou! can i have the awnsers?

William Addy


Can I have the answers please, thanks a lot !

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