C2 Paper

Paper Reference(s) 6664 Edexcel GCE Core maths C2 Advanced Subsidiary Tuesday 10 January 2006 ? Afternoon Time 1 instant 30 minutes Materials required for examination Mathematical Formulae (Green) Items included with interview papers Nil Candidates may use any calculator save those with the facility for symbolic algebra, differentiation and/or integration. Thus candidates may non use calculators such as the Texas Instruments TI 89, TI 92, Casio CFX 9970G, Hewlett Packard HP 48G.operating instructions to Candidates In the boxes on the answer book, write the name of the examining body (Edexcel), your summation number, candidate number, the unit title (Core Mathematics C2), the paper reference (6664), your surname, separate name and signature. When a calculator is used, the answer should be given to an separate degree of accuracy. Information for Candidates A booklet Mathematical Formulae and Statistical Tables is provided. practiced marks may be obtained for answers to ALL que stions.The marks for individual questions and the move of questions be shown in round brackets e. g. (2). There are 9 questions on this paper. The total mark for this paper is 75. Advice to Candidates You must ensure that your answers to parts of questions are go byly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers without working may gain no credit. N23552A This publication may only when be reproduced in accordance with Edexcel Limited copyright policy. 2006 Edexcel Limited. 1. Given that f(1) = 0, (x) = 23 + x2 5x + c, where c is a constant. (a) move up the observe of c, (2) (b) factorise f(x) completely, (4) (c) find the remainder when f(x) is divided by (2x 3). (2) 2. (a) Find the first 3 terms, in asc shuttinging powers of x, of the binomial expansion of (1 + px)9, where p is a constant. (2) The first 3 terms are 1, 36x and qx2, where q is a constant. (b) Find the protect of p and the value of q. (4) N23552A 2 3. y B num eral 1 C P O A x In Figure 1, A(4, 0) and B(3, 5) are the end points of a diameter of the circle C.Find (a) the exact length of AB, (2) (b) the coordinates of the nub P of AB, (2) (c) an equation for the circle C. (3) 4. The first term of a geometrical series is 120. The sum to infinity of the series is 480. (a) Show that the common ration, r, is 3 . 4 (3) (b) Find, to 2 decimal places, the difference between the 5th and sixth terms. (2) (c) Calculate the sum of the first 7 terms. (2) The sum of the first n terms of the series is greater than 300. (d) Calculate the smallest possible value of n. (4) N23552A 3 5. Figure 2 A 6m 5m 5m BO In Figure 2 OAB is a sector of a circle, radius 5 m. The chord AB is 6 m long. 7 ? . (a) Show that cos AOB = 25 (2) ? (b) Hence find the angle AOB in radians, giving your answer to 3 decimal places. (1) (c) Calculate the field of battle of the sector OAB. (2) (d) Hence calculate the shaded area. (3) 6. The speed, v m s1, of a pack at time t seconds is given by v = ? (1. 2t 1), 0 ? t ? 30. The following disconcert shows the speed of the train at 5 second separations. t v 0 0 5 1. 22 10 2. 28 15 20 6. 11 25 30 (a) Complete the table, giving the set of v to 2 decimal places. 3) The distance, s metres, travelled by the train in 30 seconds is given by ? s = ? ? (1. 2 t ? 1) dt . ?0 (b) Use the trapezium rule, with all the values from your table, to estimate the value of s. (3) 30 N23552A 4 7. The curve C has equation y = 23 52 4x + 2. (a) Find dy . dx (2) (b) Using the get out from part (a), find the coordinates of the turning points of C. (4) d2 y (c) Find . dx 2 (2) (d) Hence, or otherwise, determine the nature of the turning points of C. (2) 8. (a) Find all the values of ? to 1 decimal place, in the interval 0? ? ? 360? for which 5 sin (? + 30? ) = 3. (4) (b) Find all the values of ? , to 1 decimal place, in the interval 0? ? ? 360? for which tan2 ? = 4. (5) N23552A 5 9. y Figure 3 3 2 A R B O x Figure 3 shows the shade d region R which is bounded by the curve y = 22 + 4x and the 3 line y = . The points A and B are the points of intersection of the line and the curve. 2 Find (a) the x-coordinates of the points A and B, (4) (b) the exact area of R. (6) TOTAL FOR PAPER 75 MARKS END N23552A 6