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
(1)
(b) Expand
Give your answer in the form a + b where a and b are integers.
(Total 3 marks)
Q3.
(a) Write down the value of k
(1)
(b) Expand and simplify (2 + 3)(1 + 3)
Give your answer in the form a + b 3
where a and b are integers
(Total 3 marks)
Q4. Tarish says,
`The sum of two prime numbers is always an even number'.
He is wrong.
Explain why.
(Total 2 marks)
Q5. The nth even number is 2n.
The next even number after 2n is 2n + 2
(a) Explain why.
(b) Write down an expression, in terms of n, for the next even number after 2n + 2
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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 shows a pentagon.
Diagram NOT accurately drawn
All measurements are in centimetres.
Show that the area of this pentagon can be written as 5x + x ­ 6 2
(Total 4 marks)
Q8.…read more

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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
(i)
(ii)
Given that = 8b
(b) Show that AQX is a straight line.
(Total 7 marks)
Q9.
Diagram NOT accurately drawn
= 2a + b
= 4a + 3b
(a) Express the vector in terms of a and b.
Give your answer in its simplest form.…read more

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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)
Q10.
Diagram NOT accurately drawn
OAB is a triangle.
= a
= b
(a) Find the vector in terms of a and b.
P is the point on AB such that AP : PB = 3 : 2
(b) Show that (2a + 3b)
(3)
(Total 4 marks)
Q11.…read more

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Comments

T.A

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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