physicsandmathstutor.com

Size: px

Start display at page:

Download "physicsandmathstutor.com"

Jeremy Nichols
6 years ago
Views:

1 physicsadmathstutor.com

2 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*

3 8. (a) Fid all the values of, to 1 decimal place, i the iterval 0 < 360 for which 5 si( + 30 ) = 3. (4) 16 *N23552A01620*

4 Questio 8 cotiued (b) Fid all the values of, to 1 decimal place, i the iterval 0 < 360 for which ta 2 = 4. (5) (Total 9 marks) Q8 *N23552A01720* 17 Tur over

5 6. (a) Give that si = 5cos, fid the value of ta. (1) (b) Hece, or otherwise, fid the values of i the iterval 0 < 360 for which si = 5cos, givig your aswers to 1 decimal place. (3) 10 *N23558A01020*

6 6. Fid all the solutios, i the iterval 0 x < 2 of the equatio 2cos 2 x + 1 = 5 si x, givig each solutio i terms of. (6) 10 *N24322A01024*

7 physicsadmathstutor.com Jue (a) Sketch, for 0 x 2 π, the graph of y si x. 6 (b) Write dow the exact coordiates of the poits where the graph meets the coordiate axes. (3) (c) Solve, for 0 x 2 π, the equatio (2) si x, givig your aswers i radias to 2 decimal places. (5) 20 *H26108A02024*

8 physicsadmathstutor.com Jue 2007 Questio 9 cotiued Q9 (Total 10 marks) *H26108A02124* 21 Tur over

9 4. (a) Show that the equatio 3 si 2 2 cos 2 = 1 ca be writte as 5 si 2 = 3. (2) (b) Hece solve, for 0 < 360, the equatio 3 si 2 2 cos 2 = 1, givig your aswers to 1 decimal place. (7) 8 *H26320B0824*

10 Questio 4 cotiued Q4 (Total 9 marks) *H26320B0924* 9 Tur over

11 9. Solve, for 0 x < 360, (a) 1 si ( x 20 ) = 2 (4) (b) cos 3x = 1 2 (6) 24 *H30722A02428*

12 Questio 9 cotiued Q9 (Total 10 marks) TOTAL FOR PAPER: 75 MARKS END *H30722A02728* 27

13 8. (a) Show that the equatio 4 si 2 x + 9 cos x 6 = 0 ca be writte as 4 cos 2 x 9 cos x + 2 = 0. (2) (b) Hece solve, for 0 x < 720, 4 si 2 x + 9 cos x 6 = 0, givig your aswers to 1 decimal place. (6) 20 *H30957A02028*

14 Questio 8 cotiued Q8 (Total 8 marks) *H30957A02128* 21 Tur over

15 7. (i) Solve, for 180 < 180, ( ) ( ) 1+ taθ 5siθ 2 = 0. (4) 18 *H34263A01824*

16 (ii) Solve, for 0 x 360, 4si x = 3ta x (6) Q7 (Total 10 marks) *H34263A01924* 19 Tur over

17 2. (a) Show that the equatio 5 si x = cos 2 x ca be writte i the form 2 si 2 x + 5 si x 3 = 0 (2) (b) Solve, for 0 x < 360, 2 si 2 x + 5 si x 3 = 0 (4) (Total 6 marks) *N35101A0324* Q2 3 Tur over

18 5. (a) Give that 5si = 2cos, fid the value of ta. (b) Solve, for 0 x < 360, 5si 2x 2cos 2x, (1) givig your aswers to 1 decimal place. (5) 10 *H35384A01028*

19 7. (a) Show that the equatio 2 2 3si x+ 7si x= cos x 4 ca be writte i the form 2 4si x+ 7si x+ 3 = 0 (2) (b) Hece solve, for 0 x < 360, 2 2 3si x+ 7si x= cos x 4 givig your aswers to 1 decimal place where appropriate. (5) 16 *H35403A01628*

20 Questio 7 cotiued Q7 (Total 7 marks) *H35403A01728* 17 Tur over

21 7. (a) Solve for 0 x 360, givig your aswers i degrees to 1 decimal place, 3 si (x + 45 ) = 2 (4) (b) Fid, for 0 x 2, all the solutios of 2 2si x+ 2= 7cos x givig your aswers i radias. You must show clearly how you obtaied your aswers. (6) 20 *P38158A02032*

22 Questio 7 cotiued *P38158A02132* 21 Tur over

23 o 1 9. (i) Fid the solutios of the equatio si( 3x 15 ) =, for which 0 x o (6) (ii) y O P Q R x Figure 4 Figure 4 shows part of the curve with equatio y = si( ax b), where a> 0, 0< b< ϖ The curve cuts the x-axis at the poits P, Q ad R as show. Give that the coordiates of P, Q ad R are ϖ ( 10 ) ( ), 0, 3ϖ, 0 ad 11 5 ( 10 ), 0 fid the values of a ad b. ϖ respectively, (4) 26 *P40083A02628*

24 Questio 9 cotiued Q9 (Total 10 marks) TOTAL FOR PAPER: 75 MARKS END 28 *P40083A02828*

25 6. (a) Show that the equatio ta 2x = 5 si 2x ca be writte i the form (1 5 cos 2x) si 2x = 0 (2) (b) Hece solve, for 0 x 180, ta 2x = 5 si 2x givig your aswers to 1 decimal place where appropriate. You must show clearly how you obtaied your aswers. (5) 16 *P40685A01628*

26 4. Solve, for 0 x 180, o cos( 3x 10 ) = 04. givig your aswers to 1 decimal place. You should show each step i your workig. (7) 10 *P41487A01032*

27 9. (i) Solve, for 0 θ 180 si (2 30 ) + 1 = 0.4 givig your aswers to 1 decimal place. (5) (ii) Fid all the values of x, i the iterval 0 x 360, for which 9cos 2 x 11cos x + 3si 2 x = 0 givig your aswers to 1 decimal place. (7) You must show clearly how you obtaied your aswers. 28 *P42826A02832*

28 Questio 9 cotiued Q9 (Total 12 marks) END TOTAL FOR PAPER: 75 MARKS 32 *P42826A03232*

29 physicsadmathstutor.com Jue (i) Solve, for 180 x < 180, ta(x 40 ) = 1.5 givig your aswers to 1 decimal place. (3) (ii) (a) Show that the equatio ca be writte i the form si ta = 3cos + 2 4cos 2 + 2cos 1 = 0 (3) (b) Hece solve, for 0 < 360, si ta = 3cos + 2 showig each stage of your workig. (5) 22 *P41859A02232*

30 physicsadmathstutor.com Jue 2013 Questio 8 cotiued *P41859A02332* 23 Tur over

31 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 =

32 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 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