2014年Alevel数学真题(精排版)VIP免费

11 . Find the first 3 terms in ascending powers of x of226−⎛⎝⎜⎞⎠⎟xgiving each term in its simplest form.2 . f(x),x8=− 43+xx − 1x  02Giving your answers in their simplest form, find (a) fƍ(x)(3 )(b) ∫ ( )fdxx(4 )3 .f (x) = 10x3 + 27x2 – 13x – 12(a) Find the remainder when f (x) is divided by (i) x – 2 (ii) x + 3(3 ) (b) Hence factorise (f x) completely.(4 )(4)4 . Answer this question without the use of a calculator and show all your working.(i) Show that42 262 2(2 +3−=)(4 ) (ii) Show that 272163= 8 3+×7 −(3 )25 . A sequence is defined by1 3uuunn+12=− 4 ,n . 1Find the exact values of (a) u2, u3 and u4(3 ) (b) u61(1 ) (c) uii=∑19 9(3 )6 . Given that a and b are positive constants, solve the simultaneous equationsab = 25log4a – log4b = 3Show each step of your working, giving exact values for a and b.(6)7 . (a) Show that12sin2x – cosx – 11 = 0may be expressed in the form12cos2x + cosx – 1 = 0(1 )(b) Hence, using trigonometry, find all the solutions in the interval 0 - x - 360° of 12sin2x – cosx – 11 = 0Give each solution, in degrees, to 1 decimal place.(4)8 . Find the range of values of k for which the quadratic equationkx2 + 8x + 2(k + 7) = 0has no real roots.(7)39 . In the first month after opening, a mobile phone shop sold 300 phones. A model for futuresales assumes that the number of phones sold will increase by 5% per month, so that300 × 1.05 will be sold in the second month, 300 × 1.05 2 in the third month, and so on.Using this model, calculate(a) the number of phones sold in the 24th month,(2 )(b) the total number of phones sold over the whole 24 months.(2 )This model predicts that, in the Nth month, the number...