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2 8. The circle C, with cetre at the poit A, has equatio x 2 + y 2 10x + 9 = 0. Fid (a) the coordiates of A, (b) the radius of C, (c) the coordiates of the poits at which C crosses the x-axis. (2) (2) (2) 7 Give that the lie l with gradiet 2 is a taget to C, ad that l touches C at the poit T, (d) fid a equatio of the lie which passes through A ad T. (3) 16 *N23492B01628*

3 Questio 8 cotiued *N23492B01728* 17 Tur over

4 3. Figure 1 y B C P O A x I Figure 1, A(4, 0) ad B(3, 5) are the ed poits of a diameter of the circle C. Fid (a) the exact legth of AB, (b) the coordiates of the midpoit P of AB, (c) a equatio for the circle C. (2) (2) (3) 6 *N23552A0620*

5 Questio 3 cotiued Q3 (Total 7 marks) *N23552A0720* 7 Tur over

6 7. Figure 1 y y = 3x 4 C O P (2, 2) Q x The lie y = 3x 4 is a taget to the circle C, touchig C at the poit P (2, 2), as show i Figure 1. The poit Q is the cetre of C. (a) Fid a equatio of the straight lie through P ad Q. (3) Give that Q lies o the lie y = 1, (b) show that the x-coordiate of Q is 5, (c) fid a equatio for C. (1) (4) 12 *N23558A01220*

7 Questio 7 cotiued Q7 (Total 8 marks) *N23558A01320* 13 Tur over

8 3. The lie joiig the poits ( 1, 4) ad (3, 6) is a diameter of the circle C. Fid a equatio for C. (6) Q3 (Total 6 marks) 6 *N24322A0624*

9 physicsadmathstutor.com Jue y B M (3, 1) O A (1, 2) P x l Figure 3 The poits A ad B lie o a circle with cetre P, as show i Figure 3. The poit A has coordiates (1, 2) ad the mid-poit M of AB has coordiates (3, 1). The lie l passes through the poits M ad P. (a) Fid a equatio for l. (4) Give that the x-coordiate of P is 6, (b) use your aswer to part (a) to show that the y-coordiate of P is 1, (c) fid a equatio for the circle. (1) (4) 14 *H26108A01424*

10 physicsadmathstutor.com Jue 2007 Questio 7 cotiued *H26108A01524* 15 Tur over

11 5. The circle C has cetre (3, 1) ad passes through the poit P(8, 3). (a) Fid a equatio for C. (4) (b) Fid a equatio for the taget to C at P, givig your aswer i the form ax + by + c = 0, where a, b ad c are itegers. (5) 10 *H30722A01028*

12 5. y (9, 10) R(a, 4) P( 3, 2) O x C Figure 2 The poits P( 3, 2), (9, 10) ad R(a, 4) lie o the circle C, as show i Figure 2. Give that PR is a diameter of C, (a) show that a = 13, (3) (b) fid a equatio for C. (5) 10 *H30957A01028*

13 Questio 5 cotiued *H30957A01128* 11 Tur over

14 6. The circle C has equatio x 2 + y 2 6x + 4y = 12 (a) Fid the cetre ad the radius of C. (5) The poit P( 1, 1) ad the poit (7, 5) both lie o C. (b) Show that P is a diameter of C. (2) The poit R lies o the positive y-axis ad the agle PR = 90. (c) Fid the coordiates of R. (4) 14 *H34263A01424*

15 Questio 6 cotiued *H34263A01524* 15 Tur over

16 8. y C O x A 12 B P Figure 3 Figure 3 shows a sketch of the circle C with cetre (a) Write dow the coordiates of. (b) Fid the radius of C (x 2) + (y + 1) = 4 ad equatio (2) (1) The chord AB of C is parallel to the x-axis, lies below the x-axis ad is of legth 12 uits as show i Figure 3. (c) Fid the coordiates of A ad the coordiates of B (d) Show that agle A B = 134.8, to the earest 0.1 of a degree. (5) (2) The tagets to C at the poits A ad B meet at the poit P (e) Fid the legth AP, givig your aswer to 3 sigificat figures. (2) 18 *N35101A01824*

17 Questio 8 cotiued *N35101A01924* 19 Tur over

18 10. The circle C has cetre A (2,1) ad passes through the poit B (10, 7). (a) Fid a equatio for C. (4) The lie 1 is the taget to C at the poit B. (b) Fid a equatio for 1. (4) The lie 2 is parallel to 1 ad passes through the mid-poit of AB. Give that 2 itersects C at the poits P ad, (c) fid the legth of P, givig your aswer i its simplest surd form. (3) 26 *H35384A02628*

19 Questio 10 cotiued Q10 (Total 11 marks) TOTAL FOR PAPER: 75 MARKS END 28 *H35384A02828*

20 9. The poits A ad B have coordiates ( 2, 11) ad (8, 1) respectively. Give that AB is a diameter of the circle C, (a) show that the cetre of C has coordiates (3, 6), (b) fid a equatio for C. (c) Verify that the poit (10, 7) lies o C. (1) (4) (1) (d) Fid a equatio of the taget to C at the poit (10, 7), givig your aswer i the form y = mx + c, where m ad c are costats. (4) 22 *H35403A02228*

21 Questio 9 cotiued *H35403A02328* 23 Tur over

22 4. The circle C has equatio 2 2 x + y + 4x 2y 11 = 0 Fid (a) the coordiates of the cetre of C, (b) the radius of C, (2) (2) (c) the coordiates of the poits where C crosses the y-axis, givig your aswers as simplified surds. (4) 8 *P38158A0832*

23 2. A circle C has cetre ( 1, 7 ) ad passes through the poit (, 0 0 ). Fid a equatio for C. (4) 4 *P40083A0428*

24 physicsadmathstutor.com Jue y C T r P Q O L Figure 1 x The circle C with cetre T ad radius r has equatio x 2 + y 2 20x 16y = 0 (a) Fid the coordiates of the cetre of C. (b) Show that r = 5 (3) (2) The lie L has equatio x = 13 ad crosses C at the poits P ad Q as show i Figure 1. (c) Fid the y coordiate of P ad the y coordiate of Q. (3) Give that, to 3 decimal places, the agle PTQ is radias, (d) fid the perimeter of the sector PTQ. (3) 6 *P40685A0628*

25 physicsadmathstutor.com Jue 2012 Questio 3 cotiued *P40685A0728* 7 Tur over

26 physicsadmathstutor.com Jauary The circle C has equatio 2 2 x + y 20x 24y+ 195 = 0 The cetre of C is at the poit M. (a) Fid (i) the coordiates of the poit M, (ii) the radius of the circle C. (5) N is the poit with coordiates (25, 32). (b) Fid the legth of the lie MN. (2) The taget to C at a poit P o the circle passes through poit N. (c) Fid the legth of the lie NP. (2) 12 *P41487A01232*

27 physicsadmathstutor.com Jauary 2013 Questio 5 cotiued *P41487A01332* 13 Tur over

28 10. C physicsadmathstutor.com Jue 2013 y 9 O x Figure 4 The circle C has radius 5 ad touches the y-axis at the poit (0, 9), as show i Figure 4. (a) Write dow a equatio for the circle C, that is show i Figure 4. (3) A lie through the poit P(8, 7) is a taget to the circle C at the poit T. (b) Fid the legth of PT. (3) 30 *P41859A03032*

29 physicsadmathstutor.com Jue 2013 Questio 10 cotiued Q10 (Total 6 marks) END TOTAL FOR PAPER: 75 MARKS 32 *P41859A03232*

30 Edexcel AS/A level Mathematics Formulae List: Core Mathematics C2 Issue 1 September Core Mathematics C2 Cadidates sittig C2 may also require those formulae listed uder Core Mathematics C1. Cosie rule a 2 = b 2 + c 2 2bc cos A Biomial series 2 1 ) ( r r b b a r b a b a a b a = + K K ( N) where )!!(! C r r r r = = < = + x x r r x x x r 1, ( 2 1 1) ( 1) ( 2 1 1) ( 1 ) (1 2 K K K K R) Logarithms ad expoetials a x x b b a log log log = Geometric series u = ar 1 S = r r a 1 ) (1 S = r a 1 for r < 1 Numerical itegratio The trapezium rule: b a x y d 21 h{(y 0 + y ) + 2(y 1 + y y 1 )}, where a b h =

31 Core Mathematics C1 Mesuratio Surface area of sphere = 4π r 2 Area of curved surface of coe = π r slat height Arithmetic series u = a + ( 1)d S = 2 1 (a + l) = 2 1 [2a + ( 1)d] 4 Edexcel AS/A level Mathematics Formulae List: Core Mathematics C1 Issue 1 September 2009

physicsandmathstutor.com

physicsandmathstutor.com physicsadmathstutor.com 5. Solve, for 0 x 180, the equatio 3 (a) si( x + 10 ) =, 2 (b) cos 2x = 0.9, givig your aswers to 1 decimal place. (4) (4) 10 *N23492B01028* 8. (a) Fid all the values of, to 1 decimal