1) x = 2p, y = 2q
(a) Express in terms of x and/or y,
(i) 2p + q
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(ii) 2^2q
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(iii) 2p–1
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(3 marks)
2) (a) Show that (2a – 1)^2– (2b – 1)^2 = 4(a – b)(a + b – 1) (3 marks)
(b) Prove that the difference between the squares of any two odd numbers is a multiple of 8.
(You may assume that any odd number can be written in the form 2r – 1, where r is an integer). (3 marks)
3) Bill invests £500 on 1st January 2004 at a a compound interest of R% per annum. The Value, £V, of this investment after n years is given by the formula V= 500 x (1.045)^n
a) Write down the value of R (1 mark)
b) Use your calculator to find the value of Bill's investment after 20 years
(2 marks)
4) rationalise the denominator of 1 divided by 8 square root 8
give your answer in the form square root 2 divided by p
where p is a positive integer
5) solve this quadratic equation x^2 - 5x - 8 = 0
answers in 3 sig fig
6) Two prisms, A and B are mathematically similar. The volume of prism A is 12000cm^3. The volume of prism B is 49152cm^3. The total surface area of prism B is 9728cm^2. Calculate the surface area of prism A