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FM1 Sept practice assessment.docx - Further Maths year 1...

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Further Maths year 1 practice September assessment1.Answer this question without the use of a calculator and show all yourworking.Show that422(23)226  (4)2.f(x) =x3+x2− 12x− 18(a) Use the factor theorem to show that (x+ 3) is a factor of f(x).(2)(b) Factorise f(x).(2)(c)Hence find exact values for all the solutions of the equation f(x) = 0(3)3.The equationk(3x2+ 8x+ 9) = 2 – 6x, wherekis a real constant, has noreal roots.(a) Show thatksatisfies the inequality11k2– 30k– 9 > 0(4)(b) Find the range of possible values fork.(4)4.Solve the simultaneous equationsy– 2x– 4 = 04x2+y2+ 20x= 0(7)5.Given thaty= 2x,
(a) express 4xin terms ofy.(1)(b) Hence, or otherwise, solve8(4x) – 9(2x) + 1 = 0.
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Term
Fall
Professor
NoProfessor
Tags
Elementary algebra, Euclidean geometry, line L1, curve C

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