SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 2008

 Marshall Perry
 8 months ago
 Views:
Transcription
1 SULIT 47/ Matematik Tambahan Kertas Sept 008 Jam Name :.. Form :.. SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 008 MATEMATIK TAMBAHAN Kertas Dua jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU This question paper consists of 5 questions.. Answer all questions.. Give only one answer for each question. 4. Write your answers clearly in the spaces provided in the question paper. 5. Show your working. It may help you to get marks. 6. If you wish to change your answer, cross out the work that you have done. Then write down the new answer. 7. The diagrams in the questions provided are not drawn to scale unless stated. 8. The marks allocated for each question and subpart of a question are shown in brackets. 9. A list of formulae is provided on pages to. 0. A booklet of fourfigure mathematical tables is provided.. You may use a nonprogrammable scientific calculator. This question paper must be handed in at the end of the examination. Question For examiner s use only Total Marks TOTAL 80 Marks Obtained Kertas soalan ini mengandungi 5 halaman bercetak 47/ 008 Hak Cipta Zon A Kuching [Lihat Sebelah Sarawak Zon A Trial SPM 008 SULIT
2 SULIT 47/ The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. b x = b 4ac a ALGEBRA 8 log a b = log log c c b a a m a n = a m + n a m a n = a m n 4 (a m ) n = a nm 5 log a mn = log a m + log a n m 6 log a = log a m log a n n 7 log a m n = n log a m 9 T n = a + (n )d n 0 S n = [a ( n ) d] T n = ar n n n a( r ) a( r ) S n = r r a S, r < r, (r ) dy dv du y = uv, u v dx dx dx du dv v u u dy y, dx dx, v dx v dy dx dy du du dx CALCULUS 4 Area under a curve b = y dx or a b = x dy a 5 Volume generated b = y dx or a b = x dy a GEOM ETRY Distance = Midpoint x (x, y) = x ( x x ) ( y y ) y, y 5 A point dividing a segment of a line nx mx ny my (x, y) =, m n m n 6. Area of triangle = r x y ( ) ( ) x y x y x y x y x y x y x i yj 4 r x y 47/ Sarawak Zon A Trial SPM Hak Cipta Zon A Kuching SULIT
3 SULIT 47/ STATISTICS x = N x = = 4 = x fx f ( x x) = N f ( x x) f = x N x fx f x wi i 7 I i wi 8 9 n P r n C r n! ( n r)! n! ( n r)! r! 0 P(A B) = P(A) + P(B) P(A B) P(X = r) = r C p q n r n r, p + q = N F 5 m = L C fm P 6 I 00 P 0 Mean, = np npq x 4 z = TRIGONOMETRY Arc length, s = r Area of sector, A = sin A + cos A = 4 sec A = + tan A 5 cosec A = + cot A 6 sin A = sinacosa r 7 cos A = cos A sin A = cos A = sin A 8 tana = tan A tan A 9 sin (A B) = sinacosb cosasinb 0 cos (A B) = cos AcosB sinasinb tan (A B) = a sin A b sin B tan A tan B tan Atan B c sinc a = b +c bc cosa 4 Area of triangle = absin C 47/ 008 Hak Cipta Zon A Kuching Lihat sebelah Sarawak Zon A Trial SPM 008 SULIT
4 SULIT 4 47/ Answer all questions. For examiner s use only Diagram shows the linear function f. x f f(x) n 4 DIAGRAM (a) State the value of n. (b) Using the function notation, express f in terms of x. [ marks ] Answer : (a)... Two functions are defined by f : x x and gf : x x ax b, find the value of a and of b. (b)... g : x x x. Given that [ marks ] Answer :... Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT
5 For examiner s use only SULIT 5 47/ x The function of p is defined as p(x), x h. x Find (a) the value of h, (b) p ( x ). [ marks ] Answer : (a).. (b)... 4 Find the range of values of t if the following quadratic equation has no roots (t + ) x + 6x + = 0. [ marks ] 4 Answer :... 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [ Lihat sebelah SULIT
6 SULIT 6 47/ 5 Given that and are the roots of the quadratic equation x x 7. Form the quadratic equation whose roots are and. For examiner s use only [ marks ] 5 Answer :... 6 Diagram shows the graph of a curve y = a(x + p)² + q that passes through the point (0, 5) and has the minimum point (, ). Find the values of a, p and q. y [ marks ] (0, 5) O (, ) DIAGRAM x Answer : p =... q =... 6 a =... Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT
7 For examiner s use only SULIT 7 47/ 7 Find the range of values of x for which x(x ) 5. [ marks] 7 Answer :... x 8 Solve 7 x 9 [ marks ] 8 Answer :... 9 Given that lg 0 and lg7, find, without using scientific calculator or mathematical tables, find the value of log 4. [ marks ] 9 Answer :... 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [ Lihat sebelah SULIT
8 SULIT 8 47/ th 0 The n term of an arithmetic progression is given by T n 5n. Find For examiner s use only (a) the first term and the common difference, (b) the sum of the first 5 terms of the progression. [4 marks] Answer : (a). (b) The first three terms of a geometric progression are 968, 656, 87,.... Find the three consecutive terms whose product is [ marks ] Answer :... Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT
9 For examiner s use only SULIT 9 47/ Diagram shows the straight line obtained by plotting log 0 y against log 0 x. log 0 y (4, h ) (0, 6) 0 DIAGRAM log 0 x 4 The variables x and y are related by the equation y kx, where k is a constant. Find the value of (a) k, (b) h. [ 4 marks ] Answer : (a) (b)... The coordinates of the vertices of a triangle PQR are P(, h), Q(, 0) and R(5, h). If the area of the PQR is 9 units, find the values of h. [ marks ] Answer : h =. 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [ Lihat sebelah SULIT
10 SULIT 0 47/ x y 4 If the straight line is perpendicular to the straight line 5 p 0x y 0, find the value of p. [ marks ] For examiner s use only 4 Answer :. 5 Given the vectors a i mj, b 8 i j and c 5 i j. If vector a b vector c, find the value of the constant m. ~ is parallel to [ marks ] 5 Answer :.. Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT
11 For examiner s use only SULIT 47/ 6 The diagram 4 shows a parallelogram ABCD drawn on a Cartesian plane. y B A O x C D It is given that AB i j and BC 4 i j. Find DIAGRAM 4 (a) BD, (b) AC. [ 4 marks ] 6 Answer : (a) (b).. 7 Solve the equation sin 5cos cos for [ marks ] 7 Answer : / Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [ Lihat sebelah SULIT
12 SULIT 47/ 8 Given that sin x = 5 and 90 < x < 70, find the value of sec x. [ marks ] For examiner s use only Answer : The diagram 5 shows a semicircle of centre O and radius r cm. C A O B DIAGRAM 5 The length of the arc AC is 7 cm and the angle of COB is 69 radians. Calculate (a) the value of r, (b) the area of the shaded region. [Use π =.4] [ 4 marks ] Answer : (a).. (b).. Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT
13 For examiner s use only SULIT 47/ 0 Find the coordinates of the turning points of the curve y = x + x. [4 marks] 0 Answer : Given that y = m and m = x +. Find dy (a) in terms of x, dx (b) the small change in y when x increases from to 0. [ 4 marks ] Answer : (a).. 4 (b).. Find x dx [ marks ] Answer :.. 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [Lihat Sebelah SULIT
14 SULIT 4 47/ Ben and Shafiq are taking driving test. The probability that Ben and Shafiq pass the test are 5 and respectively. For examiner s use only Calculate the probability that at least one person passes the test. [ marks ] Answer :.. 4 A committee of 5 members is to be selected from 6 boys and 4 girls. Find the number of ways in which this can be done if (a) the committee has no girls, (b) the committee has exactly boys. [ marks ] 4 Answer : (a).. (b).. 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 SULIT
15 For examiner s use only SULIT 5 47/ 5 A random variable X has a normal distribution with mean 50 and variance. Given that P[X > 5] = 088, find the value of. [ marks ] 5 Answer : END OF QUESTION PAPER 47/ Sarawak 008 Hak Zon Cipta A Zon Trial A Kuching SPM 008 [Lihat Sebelah SULIT SULIT
16 SULIT 47/ 47/ Matematik Tambahan Kertas ½ jam Sept 008 SEKOLAHSEKOLAH ZON A KUCHING LEMBAGA PEPERIKSAAN SEKOLAH ZON A PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 008 MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. This question paper consists of three sections : Section A, Section B and Section C.. Answer all question in Section A, four questions from Section B and two questions from Section C.. Give only one answer / solution to each question.. 4. Show your working. It may help you to get marks. 5. The diagram in the questions provided are not drawn to scale unless stated. 6. The marks allocated for each question and subpart of a question are shown in brackets.. 7. A list of formulae is provided on pages to. 8. A booklet of fourfigure mathematical tables is provided. 9. You may use a nonprogrammable scientific calculator. Kertas soalan ini mengandungi halaman bercetak 47/ 008 Hak Cipta Zon A Kuching [Lihat sebelah Sarawak Zon A Trial SPM 008 SULIT
17 SULIT 47/ The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. b x = b 4ac a ALGEBRA 8 log a b = log log c c b a a m a n = a m + n a m a n = a m n 4 (a m ) n = a nm 5 log a mn = log a m + log a n m 6 log a = log a m log a n n 7 log a m n = n log a m 9 T n = a + (n )d n 0 S n = [a ( n ) d] T n = ar n n n a( r ) a( r ) S n = r r a S, r < r, (r ) dy dv du y = uv, u v dx dx dx du dv v u u dy y, dx dx, v dx v dy dx dy du du dx CALCULUS 4 Area under a curve b = y dx or a b = x dy a 5 Volume generated b = y dx or a b = x dy a GEOM ETRY Distance = Midpoint x (x, y) = x ( x x ) ( y y ) y, y 5 A point dividing a segment of a line nx mx ny my (x, y) =, m n m n 6. Area of triangle = r x y ( ) ( ) x y x y x y x y x y x y x i yj 4 r x y 47/ Sarawak Zon A Trial SPM Hak Cipta Zon A Kuching SULIT
18 SULIT 47/ STATISTICS x = N x = = 4 = x fx f ( x x) = N f ( x x) f = x N x fx f x wi i 7 I i wi 8 9 n P r n C r n! ( n r)! n! ( n r)! r! 0 P(A B) = P(A) + P(B) P(A B) P(X = r) = r C p q n r n r, p + q = N F 5 m = L C fm P 6 I 00 P 0 Mean, = np npq x 4 z = TRIGONOMETRY Arc length, s = r Area of sector, A = sin A + cos A = 4 sec A = + tan A 5 cosec A = + cot A 6 sin A = sinacosa r 7 cos A = cos A sin A = cos A = sin A 8 tana = tan A tan A 9 sin (A B) = sinacosb cosasinb 0 cos (A B) = cos AcosB sinasinb tan (A B) = a sin A b sin B tan A tan B tan Atan B c sin C a = b +c bc cosa 4 Area of triangle = absin C 47/ 008 Hak Cipta Zon A Kuching [Lihat sebelah Sarawak Zon A Trial SPM 008 SULIT
19 SULIT 4 47/ SECTION A [40 marks] Answer all questions in this section. Solve the simultaneous equations p m and p m pm 8. Give your answers correct to three decimal places. [5 marks] (a) Given that the surface area, S cm, of a sphere with radius r is 4 r. Find ds dr. Hence, determine the rate of increase of the surface area of the sphere if the radius is increasing at the rate of 0 cm s when r =. [ marks] (b) Given that y = x d y x +, find the values of x if dx + dy + 4x = y. dx [4 marks] Table shows the distribution of scores obtained by a group of students in a competition. Score 4 5 Number of students TABLE (a) Calculate the standard deviation of the distribution. [ marks] (b) If each score of the distribution is multiplied by and then subtracted by c, the mean of the new distribution of scores is 8, calculate (i) the value of c, (ii) the standard deviation of the new distribution of scores. [ marks] 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT
20 SULIT 5 47/ 4 Diagram shows a sector AOB with centre O and a radius of cm. C A O DIAGRAM B Point C lies on OA such that OC : OA = : 4 and OCB = 90. [Use π =.4] Find (a) the value of COB, in radian, (b) the perimeter of the shaded region, (c) the area of the shaded region. [ marks] [ marks] [ marks] 5 Diagram shows a square with side of length a cm was cut into four equal squares and then every square was cut into another four equal squares for the subsequent stages. a cm a cm Stage Stage Stage DIAGRAM Given that the sum of the perimeters of the squares in every stage form a geometric progression. (a) If the sum of the perimeters of the squares cut in stage 0 is 0 40 cm, find the value of a. [ marks] (b) Calculate the number of squares cut from stage 5 until stage 0. [4 marks] 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT
21 SULIT 6 47/ 6 In Diagram, ABC is a triangle. The point P lies on AC and the point Q lies on BC. The straight lines BP and AQ intersect at R. C P A R Q DIAGRAM B It is given that AB 4x, AC 6y, AP PC and BC BQ. (a) Express in terms of x and y (i) BP, (ii) CQ. (b) Given that BR ( x y) and RP mbr. 4 [ marks] (i) State BR in terms of m, x and y. (ii) Hence, find the value of m. [5 marks] Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT
22 SULIT 7 47/ 7 Use graph paper to answer this question. SECTION B [40 marks] Answer four questions from this section. Table shows the values of two variables, x and y, obtained from an experiment. c The variables x and y are related by the equation y where c and d are x d constants. (a) Plot xy against y, by using a scale of cm to 0.4 unit on the xaxis and cm to unit on the yaxis. Hence, draw the line of best fit. [ 5 marks ] (b) Use your graph from 7(a) to find the value of (i) c, (ii) d, x 4 5 y TABLE (iii) x when y = 5 x. [ 5 marks ] 8 (a) Prove that cosec x tan x cot x. (b) (i) Sketch the graph of y sin x for 0 x. [4 marks] [ marks] (ii) Hence, sketch a suitable straight line on the same axes, and state the number of solutions to the equation sin x x for 0 x. [ marks] 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT
23 SULIT 8 47/ 9 (a) The results of a study shows that 0% of the residents of a village are farmers. If residents from the village are chosen at random, find the probability that (i) exactly 5 of them are farmers, (ii) less than of them are farmers. [5 marks] (b) The age of a group of teachers in a town follows a normal distribution with a mean of 40 years and a standard deviation of 5 years. Find (i) the probability that a teacher chosen randomly from the town is more than 4 years old. (ii) the value of m if 5% of the teachers in the town is more than m years old. [5 marks] 0 Solutions by scale drawing will not be accepted. Diagram 4 shows a straight line AD meets a straight line BC at point D. y C 8 A(7, 7) D B(, ) O x Given DIAGRAM 4 ADB = 90 and point C lies on the yaxis. (a) Find the equation of the straight line AD. [ marks ] (b) Find the coordinates of point D. [ marks ] (c) The straight line AD is extended to a point E such that AD : DE = :. Find the coordinates of the point E. [ marks ] (d) A point P moves such that its distance from point B is always 5 units. Find the equation of the locus of P. [ marks ] Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT
24 SULIT 9 47/ (a) Diagram 5 shows a curve y = x 4x and a straight line y = x. y y x 4x y x 0 x Find the volume of the solid generated when the shaded region is rotated through 60 about the xaxis. [6 marks] (b) The gradient of the curve y = px qx at the point (, ) is 5. Find (i) the value of p and of q. DIAGRAM 5 (ii) the equation of the normal to the curve at the point (, ). [4 marks] 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT
25 SULIT 0 47/ SECTION C [0 marks] Answer two questions from this section. A particle starts moving in a straight line from a fixed point O. Its velocity V ms is given by V 4t 8t, where t is the time in seconds after leaving O. (Assume motion to the right is positive) Find (a) the initial velocity of the particle. (b) the values of t when it is momentarily at rest. (c) the distance between the two positions where it is momentarily at rest. (d) the velocity when its acceleration is 6 m s. [ mark] [ marks] [ marks] [4 marks] In the diagram, ABC and EDC are straight lines. E cm D 0 cm 7 cm 6 cm A B 5 cm C Given that AE = 0 cm, BD = 7 cm, BC = 5 cm, CD = 6 cm and DE = cm. Calculate (a) BCD, (b) AEC, (c) AC, (d) the area of triangle BDE. [ marks] [ marks] [ marks] [ marks] Sarawak Zon A Trial SPM / 008 Hak Cipta Zon A Kuching SULIT
26 SULIT 47/ 4 Use the graph paper provided to answer this question. Mr. Simon has RM 600 to buy x scientific calculators and y reference books. The total number of scientific calculators and reference books is not less than 60. The number of reference books is at least half the number of scientific calculators. The price of a scientific calculator is RM 40 and the price of a reference book is RM 0. (a) Write three inequalities other than x 0 and y 0 that satisfy the conditions above. [ marks] (b) By using a scale of cm to 0 units on both axes, construct and shade the region R that satisfies all the conditions above. [ marks] (c) If Mr. Simon buys 50 reference books, what is the maximum balance of money after the purchase? [4 marks] 5 Table shows the monthly expenditure and weightage of Mohd Amirul for the year 005 and 007. Item Expenditure (RM) Year 005 Year 007 Price Index Weightage Food Rental p 5 Transport q 50 5 Others 60 r 5 4 TABLE (a) Find the values of p, q and r. (b) Find the composite index for the year 007 based on the year 005. [ marks] [ marks] (c) Given the composite index for the year 008 based on the year 007 is 8, calculate the monthly expenditure of Mohd Amirul for the year 008. [4 marks] END OF QUESTION PAPER 47/ Sarawak 008 Zon Hak Cipta A Zon Trial A Kuching SPM 008 [Lihat sebelah SULIT SULIT
27 SULIT 47/ Additional Mathematics Paper Sept 008 SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM TINGKATAN ADDITIONAL MATHEMATICS Paper MARKING SCHEME This marking scheme consists of 6 printed pages Sarawak Zon A Trial SPM 008
28 PAPER MARKING SCHEME 47/ Number Solution and marking scheme Sub Marks Full Marks (a) (b) 0 x 5 or f : x x 5 or f(x) = x 5 a = and b = gf(x) = x + x (x ) + (x ) + B B (a) (b) x, x x y = x x B 4 t > t < or equivalent (6) (t +)() < 0 B B 5 x + x + 4 = 0 () = 4 and + = 7 and = B B Sarawak Zon A Trial SPM 008
29 Number Solution and marking scheme Sub Marks Full Marks 6 a = a( )² + = 5 p = and q = B B 7 x 5 (x 5)(x + ) 0 x² x 5 0 B B 8 x 4 x x or equivalent x x or x x B B 9 5 lg lg7 lg lg4 lg B B 0 (a) d 5 T = 4 or T = 9 B (b) 585 8, 54, 6 n = or 54 or 8 or equivalent (Solving) a = 968 and r = B B Sarawak Zon A Trial SPM 008
30 4 Number (a) Solution and marking scheme k Sub Marks Full Marks (b) log 0 y 4log 0 x + log 0 k h B 4 h B h 4 p h h h h h h h h B B p or equivalent B p 5 5 m = m or m 5 5 m 5 6 B B 6 (a) a b 5i m j BD i 5 j BD BA AD or BA BC B B 4 (b) 50 AC 7i j B Sarawak Zon A Trial SPM 008
31 5 Number Solution and marking scheme , 9.58 Sub Marks Full Marks cos 5 5cos or equivalent 5 cos x B B B B 9 (a) r = 6 (b) AOC = 0.45 or 7. = r (0.45) or 458 or 46 (6) ( 69) B B 4 0 (, ) and (0, ) x = 0, 4 B 4 dy = 0 or x(x + ) = 0 dx B dy = x + 6x dx B Sarawak Zon A Trial SPM 008
32 6 Number (a) dy dx Solution and marking scheme 4x 6 or equivalent Sub Marks Full Marks dy dm 6m and dm dx B 4 (b) 08 y [4() 6] 0 0 B ( x) c ( x) c B ( x) or B 5 4 or equivalent 5 B 4 (a) 6 4 or 5 B (b) C C B B B Sarawak Zon A Trial SPM 008
33 47/ Matematik Tambahan Kertas ½ jam Sept 008 SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 008 MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU MARKING SCHEME Skema Pemarkahan ini mengandungi 5 halaman bercetak Sarawak Zon A Trial SPM 008
34 QUESTION NO. ADDITIONAL MATHEMATICS MARKING SCHEME TRIAL ZON A KUCHING 007 PAPER SOLUTION MARKS p m p P 5 * m m * m m p p p p * * 8 m.8, p.7, p.67 Eliminate p or m Solve the quadratic equation by using quadratic completing the square p OR p.7, m.8, m.67 Note : OW if the working of solving quadratic equation is not shown. 5 (a) ds ds ds dr = 8 r or = dr dt dr dt 8 () Sarawak Zon A Trial SPM 008
35 QUESTION NO. SOLUTION MARKS (b) dy d y x and dx dx P 4 + (x ) + 4x = x x + (x )( x + ) = 0 x =, 7 (a) x.9 or fx 9 P 9 (.9) 0 Use the formula 58 Or equivalent (b) (i) (.9) c.8 c = (ii).58* = 76* 6 Sarawak Zon A Trial SPM 008
36 4 QUESTION NO. SOLUTION MARKS 4 (a) cos or = 45 4 P 077 rad (b) 797 or (077) or (077) (c) () () (a) 4a() 9 = a = 5 (b) a =, r = 4(both correct) or Sarawak Zon A Trial SPM 008
37 5 QUESTION NO. SOLUTION MARKS 6 (a) (i) BP y 4x P (ii) CQ CB or Equivalent 8 CQ x 4y (b) (i) BR BP m P 5 BR 4x y m P 4x y m = ( x y) 4 4 m m = 5 8 Sarawak Zon A Trial SPM 008
38 6 QUESTION NO. 7 (a) SOLUTION y xy MARKS 0 All values of xy correct (accept correct to decimal places) xy dy c P Refer to the graph. Plot xy against y 6 points mark correctly Line of best fit (b)(i) m = c (ii) p = 5 0 d = 0 (iii) y = Sarawak Zon A Trial SPM 008
39 7 QUESTION NO. SOLUTION MARKS 8 (a) sin x cos x cosx sin x sin x cos x sin x sin x cos x sin x cos x sin x or cosec x (b) (i) & (ii) y 6 x Shape of sine curve Amplitude of and period P P Translation x y 0 P Draw the straight line correctly Number of solutions = Sarawak Zon A Trial SPM 008 0
40 8 QUESTION NO. 9 (a) (i) 0 p 0. q SOLUTION P MARKS 5 P[ X 5] C (0.) (0.7) (ii) P[X = 0] + P[X = ] + P[X = ] = (07) + 0 C (0.) (0.7) + C (0.) (0.7) = 058 (b)(i) PZ (ii) m 0.5 P X m m Sarawak Zon A Trial SPM 008
41 9 QUESTION NO. SOLUTION MARKS 0 (a) m BC = or m AD = or m AD = y 7 = (x 7) or 7 = (7) + c y = x 7 (b) y = x + 8 P x 7 = x + 8 or equivalent D(6, 5) (c) x 7() = 6 or y 7() = 5 E(4, ) (d) ( x) ( y ) 5 x² + y² 4x 4y + = 0 0 Sarawak Zon A Trial SPM 008
42 0 QUESTION NO. (a) x = 0, 5 SOLUTION MARKS (5) (5) x 4 x dx 4 5 x 4 x x (5) (5) (4) (4) (b) (i) dy = px q or 5 = p equivalent or = p q dx 4 p =, q = (ii) Gradient of normal = 5 5y + x = or equivalent Sarawak Zon A Trial SPM 008 0
43 QUESTION NO. (a) SOLUTION MARKS V P o (b) 4t 8t 0 Use v = 0 (t )(t) 0 t,, (c) 4 [ t 4t t] Integrate v dt 4 [ ( ) 4( ) 4 ( )] [ ( ) 4( ) ( )] m (d) a 8t 8 4 t s V 4() 8() 5ms Sarawak Zon A Trial SPM 008 0
44 QUESTION NO. (a) cos BCD (5)(6) SOLUTION MARKS BCD = 788 (b) sin CAE sin * CAE = 57 * AEC 499 (c) AC 0 8 (0)(8)cos 49 9 AC = 7805 (d) Area of BDE = 5 6sin 7846 = Use of the formula ab sin C 0 Sarawak Zon A Trial SPM 008
45 Answer for question 4 y (a) I. x y 60 II. y x III. 4xy 60 (b) Refer to the graph, or straight lines correct st. lines correct Correct shaded area 90 (c) (i) (0, 50) 80 Max balance after purchase = RM[ ] = RM (0) (0, 50) Sarawak Zon A Trial SPM x
46 4 5 (a) Q Use of formula I 00 Q0 5 p = 09. q = 00 N,, 0 r = 486 (b) I = = 4.5 (c) Monthly expenditure for Year 007 = 986 x RM Sarawak Zon A Trial SPM 008
47 Answer for question 7 xy (a) 5 y xy Sarawak Zon A Trial SPM y
SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 2008
SULIT 7/ Matematik Tambahan Kertas Sept 008 Jam Name :.. Form :.. SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 008 MATEMATIK TAMBAHAN Kertas Dua jam JANGAN BUKA KERTAS SOALAN
More informationSULIT 449/ 449/ Mathematics Nama : Kertas September Kelas : 008 jam PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 008 SEKOLAHSEKOLAH ZON A KUCHING MATHEMATICS Kertas Dua jam tiga puluh minit JANGAN BUKA
More informationSEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN LIMA 2007
1449/2 Matematik Kertas 2 Mei 2007 1 2 jam 2 NAMA : TINGKATAN : 1449/2 SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN LIMA 2007 MATEMATIK
More informationSULIT /2 ( 2) ( 2) 4(1)( 12) 2(1) Note: 1. If the solutions of x and y are matched wrongly, then SS1 from full marks.
7/ Modul Peningkatan Prestasi Matematik Tambahan (Kertas ) SPM 6 Zon B Kuching Sarawak y y P Substitute () into () * * y * y y ( ) ( ) ()( ) () ( ) ( ) ()( ) y ().,. y.66,.66 Note:. If the solutions of
More informationMatematik Tambahan Kertas September JABATAN PELAJARAN SELANGOR 009 1 jam PROGRAM PENINGKATAN PRESTASI SAINS DAN MATEMATIK 009 ` MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN
More informationSULIT 3472/1. Nama:.. Tingkatan: 3472/1 NO. KAD PENGENALAN Matematik Tambahan PROGRAM PENINGKATAN PRESTASI SAINS DAN MATEMATIK 2009
SULIT 347/1 Nama:.. Tingkatan: 347/1 NO. KAD PENGENALAN Matematik Tambahan Kertas 1 ANGKA GILIRAN 009 September jam JABATAN PELAJARAN SELANGOR PROGRAM PENINGKATAN PRESTASI SAINS DAN MATEMATIK 009 MATEMATIK
More informationJABATAN PELAJARAN NEGERI PERAK GERAK GEMPUR SIJIL PELAJARAN MALAYSIA SET 2 (Paper 1) Two Hours
347/1 Name: Additional Mathematics Set (P1) Class: 010 hours JABATAN PELAJARAN NEGERI PERAK GERAK GEMPUR SIJIL PELAJARAN MALAYSIA 010 Additional Mathematics SET (Paper 1) Two Hours Question Full Marks
More informationSULIT /2 3472/2 Matematik Tambahan Kertas 2 2 ½ jam 2009 SEKOLAHSEKOLAH MENENGAH ZON A KUCHING
SULIT 1 347/ 347/ Mtemtik Tmbhn Kerts ½ jm 009 SEKOLAHSEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 009 MATEMATIK TAMBAHAN Kerts Du jm tig puluh minit JANGAN BUKA KERTAS
More information47/ NO. KAD PENGENALAN Additional Mathematics Paper ANGKA GILIRAN Hours JABATAN PELAJARAN NEGERI PULAU PINANG ADDITIONAL MATHEMATICS Paper Two Hours J
PROGRAM DIDIK CEMERLANG AKADEMIK SPM ADDITIONAL MATHEMATICS MODULE 9 MODEL SPM QUESTIONS ( PAPER ) ORGANISED BY: JABATAN PELAJARAN NEGERI PULAU PINANG 47/ NO. KAD PENGENALAN Additional Mathematics Paper
More informationNote : This document might take a little longer time to print. more exam papers at : more exam papers at : more exam papers at : more exam papers at : more exam papers at : more exam papers at : more
More information( ) 2 + ( 2 x ) 12 = 0, and explain why there is only one
IB Math SL Practice Problems  Algebra Alei  Desert Academy 0 SL Practice Problems Algebra Name: Date: Block: Paper No Calculator. Consider the arithmetic sequence, 5, 8,,. (a) Find u0. (b) Find the
More informationMOZ@C MATHEMATICS NAMA : KELAS : NO K.P : A. GILIRAN : PAPER 1 AUGUST 008 1 HOUR 15 MINUTES JABATAN PELAJARAN NEGERI SABAH SIJIL PELAJARAN MALAYSIA TAHUN 008 EXCEL MATHEMATICS (MATEMATIK) PAPER 1 (KERTAS1)
More informationPractice Papers Set D Higher Tier A*
Practice Papers Set D Higher Tier A* 1380 / 2381 Instructions Information Use black ink or ballpoint pen. Fill in the boxes at the top of this page with your name, centre number and candidate number.
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
PAPA CAMBRIDGE Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 1 0 4 5 3 8 9 2 1 * ADDITIONAL MATHEMATICS 0606/23 Paper 2 May/June 2014 2 hours
More informationSULIT 1449/1 ppr maths nbk SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN DIAGNOSTIK TINGKATAN
449/ 449/ Matematik Kertas Oktober 007 4 jam SEKTOR SEKOLAH ERASRAMA PENUH AHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN IAGNOSTIK TINGKATAN 4 007 MATEMATIK Kertas Satu jam lima belas minit
More information4) If ax 2 + bx + c = 0 has equal roots, then c is equal. b) b 2. a) b 2
Karapettai Nadar Boys Hr. Sec. School One Word Test No 1 Standard X Time: 20 Minutes Marks: (15 1 = 15) Answer all the 15 questions. Choose the orrect answer from the given four alternatives and write
More informationAll E Maths Formulas for O levels E Maths by Ethan Wu
All E Maths Formulas for O levels E Maths by Ethan Wu Chapter 1: Indices a 5 = a x a x a x a x a a m a n = a m + n a m a n = a m n (a m ) n = a m n (ab) n = a n b n ( a b )n = an b n a 0 = 1 a n = 1 a
More information2016 SEC 4 ADDITIONAL MATHEMATICS CW & HW
FEB EXAM 06 SEC 4 ADDITIONAL MATHEMATICS CW & HW Find the values of k for which the line y 6 is a tangent to the curve k 7 y. Find also the coordinates of the point at which this tangent touches the curve.
More informationabc Mathematics Pure Core General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES
abc General Certificate of Education Mathematics Pure Core SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER MATHEMATICS
More informationExpress g(x) in the form f(x) + ln a, where a (4)
SL 2 SUMMER PACKET 2013 PRINT OUT ENTIRE PACKET, SHOW YOUR WORK FOR ALL EXERCISES ON SEPARATE PAPER. MAKE SURE THAT YOUR WORK IS NEAT AND ORGANIZED. WORK SHOULD BE COMPLETE AND READY TO TURN IN THE FIRST
More information(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2
CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5
More information2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is
. If P(A) = x, P = 2x, P(A B) = 2, P ( A B) = 2 3, then the value of x is (A) 5 8 5 36 6 36 36 2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time
More informationMathematics A Paper 3HR
P45864A 2016 Pearson Education Ltd. 1/1/1/1/ Write your name here Surname Pearson Edexcel International GCSE Mathematics A Paper 3HR Thursday 26 May 2016 Morning Time: 2 hours Centre Number Other names
More informationADDITIONAL MATHEMATICS
ADDITIONAL MATHEMATICS GCE NORMAL ACADEMIC LEVEL (016) (Syllabus 4044) CONTENTS Page INTRODUCTION AIMS ASSESSMENT OBJECTIVES SCHEME OF ASSESSMENT 3 USE OF CALCULATORS 3 SUBJECT CONTENT 4 MATHEMATICAL FORMULAE
More informationSMJK PEREMPUAN CHINA PULAU PINANG
SMJK PEREMPUAN CHINA PULAU PINANG PEPERIKSAAN PERCUBAAN PMR 2011 50/1 TINGKATAN 3 MATEMATIK Kertas 1 September 2011 1 1 jam Satu jam lima belas minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1.
More informationQUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)
QUESTION BANK ON CONIC SECTION (Parabola, Ellipse & Hyperbola) Question bank on Parabola, Ellipse & Hyperbola Select the correct alternative : (Only one is correct) Q. Two mutually perpendicular tangents
More informationAS PURE MATHS REVISION NOTES
AS PURE MATHS REVISION NOTES 1 SURDS A root such as 3 that cannot be written exactly as a fraction is IRRATIONAL An expression that involves irrational roots is in SURD FORM e.g. 2 3 3 + 2 and 32 are
More informationAQA Level 2 Certificate in Further Mathematics. Worksheets  Teacher Booklet
AQA Level Certificate in Further Mathematics Worksheets  Teacher Booklet Level Specification Level Certificate in Further Mathematics 860 Worksheets  Teacher Booklet Our specification is published on
More informationIt is known that the length of the tangents drawn from an external point to a circle is equal.
CBSE MATHSSET 12014 Q1. The first three terms of an AP are 3y1, 3y+5 and 5y+1, respectively. We need to find the value of y. We know that if a, b and c are in AP, then: b a = c b 2b = a + c 2 (3y+5)
More informationMathematics 2017 HSC ASSESSMENT TASK 3 (TRIAL HSC) Student Number Total Total. General Instructions. Mark
Mathematics 017 HSC ASSESSMENT TASK 3 (TRIAL HSC) General Instructions Reading time 5 minutes Working time 3 hours For Section I, shade the correct box on the sheet provided For Section II, write in the
More informationy mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent
Mathematics. The sides AB, BC and CA of ABC have, 4 and 5 interior points respectively on them as shown in the figure. The number of triangles that can be formed using these interior points is () 80 ()
More informationΠ xdx cos 2 x
Π 5 3 xdx 5 4 6 3 8 cos x Help Your Child with Higher Maths Introduction We ve designed this booklet so that you can use it with your child throughout the session, as he/she moves through the Higher course,
More informationPADASALAI CENTUM COACHING TEAM 10 TH MATHS FULL PORTION ONE MARKS ONLY
PADASALAI CENTUM COACHING TEAM 10 TH MATHS FULL PORTION ONE MARKS ONLY CHOOSE THE CORRECT ANSWER 100 X 1 = 100 1. If ACB, then A is (a) B (b) A \ B (c) A (d) B \ A 2. If n(a) = 20, n(b) = 30 and n(aub)
More informationSection I 10 marks (pages 2 5) Attempt Questions 1 10 Allow about 15 minutes for this section
017 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time hours Write using black pen NESA approved calculators may be used A reference sheet is provided
More information1. Peter cuts a square out of a rectangular piece of metal. accurately drawn. x + 2. x + 4. x + 2
1. Peter cuts a square out of a rectangular piece of metal. 2 x + 3 Diagram NOT accurately drawn x + 2 x + 4 x + 2 The length of the rectangle is 2x + 3. The width of the rectangle is x + 4. The length
More informationQUESTION BANK ON STRAIGHT LINE AND CIRCLE
QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,
More informationMathematics, Algebra, and Geometry
Mathematics, Algebra, and Geometry by Satya http://www.thesatya.com/ Contents 1 Algebra 1 1.1 Logarithms............................................ 1. Complex numbers........................................
More informationMATHEMATICS. IMPORTANT FORMULAE AND CONCEPTS for. Summative Assessment II. Revision CLASS X Prepared by
MATHEMATICS IMPORTANT FORMULAE AND CONCEPTS for Summative Assessment II Revision CLASS X 06 7 Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.), B. Ed. Kendriya Vidyalaya GaCHiBOWli
More informationSolving equations UNCORRECTED PAGE PROOFS
1 Solving equations 1.1 Kick off with CAS 1. Polynomials 1.3 Trigonometric symmetry properties 1.4 Trigonometric equations and general solutions 1.5 Literal equations and simultaneous equations 1.6 Review
More informationMATHEMATICS. (Two hours and a half) Answers to this Paper must be written on the paper provided separately.
MATHEMATICS (Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading
More informationADDITIONAL MATHEMATICS
ADDITIONAL MATHEMATICS GCE Ordinary Level (06) (Syllabus 4047) CONTENTS Page INTRODUCTION AIMS ASSESSMENT OBJECTIVES SCHEME OF ASSESSMENT 3 USE OF CALCULATORS 3 SUBJECT CONTENT 4 MATHEMATICAL FORMULAE
More informationMathematics Higher Level
L.7/0 PreLeaving Certificate Examination, 06 Mathematics Higher Level Marking Scheme Paper Pg. Paper Pg. 36 Page of 68 exams PreLeaving Certificate Examination, 06 Mathematics Higher Level Paper Marking
More informationAS and Alevel Mathematics Teaching Guidance
ΑΒ AS and Alevel Mathematics Teaching Guidance AS 7356 and Alevel 7357 For teaching from September 017 For AS and Alevel exams from June 018 Version 1.0, May 017 Our specification is published on our
More informationGCSE MATHEMATICS 43603H. Higher Tier Unit 3 Geometry and Algebra. Morning. (NOV H01) WMP/Nov16/E5
Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature GCSE H MATHEMATICS Higher Tier Unit 3 Geometry and Algebra Tuesday 8 November 2016 Materials
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Tuesday 19 January 2016 Morning Time: 2 hours Candidate Number
More informationIB Math SL 1: Trig Practice Problems: MarkScheme Circular Functions and Trig  Practice Problems (to 07) MarkScheme
IB Math SL : Trig Practice Problems: MarkScheme Circular Functions and Trig  Practice Problems (to 07) MarkScheme. (a) Evidence of using the cosine rule p + r q eg cos P Qˆ R, q p + r pr cos P Qˆ R pr
More informationCAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level General Certificate of Education Advanced Level
CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level General Certificate of Education Advanced Level MATHEMATICS 9709/1 PAPER 1 Pure Mathematics 1 (P1) Additional
More information9/ 9/ Matematik Kertas Mei 007 jam SEKTOR SEKOLH ERSRM PENUH HGIN SEKOLH KEMENTERIN PELJRN MLYSI PEPERIKSN PERTENGHN THUN TINGKTN 5 007 MTEMTIK Kertas Satu jam lima belas minit JNGN UK KERTS SOLN INI SEHINGG
More informationKENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 (201718) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit
More informationKertas soalan ini mengandungi 11 halaman bercetak
SULIT 1 4531/3 4531/3 Fizik Kertas 3 Mei 2007 1 ½ jam SEKTOR SEKOLAH BERASRAMA PENUH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 5 2007 FIZIK Kertas 3 Satu jam tiga puluh minit
More informationMARK SCHEME for the November 2004 question paper 4037 ADDITIONAL MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level MARK SCHEME for the November 004 question paper 4037 ADDITIONAL MATHEMATICS 4037/01 Paper 1, maximum raw
More informationMethods in Mathematics
Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Methods in Mathematics Unit 1: Methods 1 For Approved Pilot Centres ONLY Higher Tier Monday 11 November 013
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *9418659189* MATHEMATICS 0580/42 Paper 4 (Extended) May/June 2017 Candidates answer on the Question
More informationMathematics (Modular) 43055/2H (Specification B) Module 5
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier June 0 Mathematics (Modular) 43055/H
More informationCore Mathematics 3 Trigonometry
Edexcel past paper questions Core Mathematics 3 Trigonometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Maths 3 Trigonometry Page 1 C3 Trigonometry In C you were introduced to radian measure
More informationADVANCED PROGRAMME MATHEMATICS: PAPER I MODULE 1: CALCULUS AND ALGEBRA
GRADE 1 EXAMINATION NOVEMBER 017 ADVANCED PROGRAMME MATHEMATICS: PAPER I MODULE 1: CALCULUS AND ALGEBRA Time: hours 00 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists
More informationSo, eqn. to the bisector containing (1, 4) is = x + 27y = 0
Q.No. The bisector of the acute angle between the lines x  4y + 7 = 0 and x + 5y  = 0, is: Option x + y  9 = 0 Option x + 77y  0 = 0 Option x  y + 9 = 0 Correct Answer L : x  4y + 7 = 0 L :x 5y
More informationCambridge International Examinations CambridgeInternationalGeneralCertificateofSecondaryEducation
PAPA CAMBRIDGE Cambridge International Examinations CambridgeInternationalGeneralCertificateofSecondaryEducation * 7 0 2 4 7 0 9 2 3 8 * ADDITIONAL MATHEMATICS 0606/22 Paper2 May/June 2014 2 hours CandidatesanswerontheQuestionPaper.
More informationMATHEMATICS SYLLABUS SECONDARY 4th YEAR
European Schools Office of the SecretaryGeneral Pedagogical Development Unit Ref.:010D591en Orig.: EN MATHEMATICS SYLLABUS SECONDARY 4th YEAR 6 period/week course APPROVED BY THE JOINT TEACHING COMMITTEE
More informationMockTime.com. (b) 9/2 (c) 18 (d) 27
212 NDA Mathematics Practice Set 1. Let X be any nonempty set containing n elements. Then what is the number of relations on X? 2 n 2 2n 2 2n n 2 2. Only 1 2 and 3 1 and 2 1 and 3 3. Consider the following
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
PAPA CAMBRIDGE Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 7 8 0 7 1 0 6 7 7 * ADDITIONAL MATHEMATICS 0606/11 Paper 1 May/June 014 hours
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION. Mathematics
009 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Boardapproved calculators may be used A table of standard
More information+ 2gx + 2fy + c = 0 if S
CIRCLE DEFINITIONS A circle is the locus of a point which moves in such a way that its distance from a fixed point, called the centre, is always a constant. The distance r from the centre is called the
More information8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.
8. Quadrilaterals Q 1 Name a quadrilateral whose each pair of opposite sides is equal. Mark (1) Q 2 What is the sum of two consecutive angles in a parallelogram? Mark (1) Q 3 The angles of quadrilateral
More informationOC = $ 3cos. 1 (5.4) 2 θ = (= radians) (M1) θ = 1. Note: Award (M1) for identifying the largest angle.
4 + 5 7 cos α 4 5 5 α 0.5. Note: Award for identifying the largest angle. Find other angles first β 44.4 γ 4.0 α 0. (C4) Note: Award (C) if not given to the correct accuracy.. (a) p (C) 4. (a) OA A is
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *41476759* ADDITIONAL MATHEMATICS 0606/ Paper February/March 017 hours Candidates answer on the Question
More informationSAMPLE QUESTION PAPER MATHEMATICS
SAMPLE QUESTION PAPER 078 MATHEMATICS Time allowed : 3 hrs Maximum marks : 80 General Instructions : All questions are compulsory. The question paper consists of 30 questions divided into four sections
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Edexcel Certificate Edexcel International GCSE Mathematics A Paper 3H Friday 10 May 2013 Afternoon Time: 2 hours Centre Number Candidate Number Higher Tier Paper
More informationKENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 04 (201718) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit
More informationC3 Revision Questions. (using questions from January 2006, January 2007, January 2008 and January 2009)
C3 Revision Questions (using questions from January 2006, January 2007, January 2008 and January 2009) 1 2 1. f(x) = 1 3 x 2 + 3, x 2. 2 ( x 2) (a) 2 x x 1 Show that f(x) =, x 2. 2 ( x 2) (4) (b) Show
More informationCLASS X FORMULAE MATHS
Real numbers: Euclid s division lemma Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r, 0 r < b. Euclid s division algorithm: This is based on Euclid s division
More informationAiming for Grade 68: Study Programme
Aiming for Grade 68: Study Programme Week A1: Similar Triangles Triangle ABC is similar to triangle PQR. Angle ABC = angle PQR. Angle ACB = angle PRQ. Calculate the length of: i PQ ii AC Week A: Enlargement
More informationAS Mathematics Assignment 9 Due Date: Friday 22 nd March 2013
AS Mathematics Assignment 9 Due Date: Friday 22 nd March 2013 NAME GROUP: MECHANICS/STATS Instructions to Students All questions must be attempted. You should present your solutions on file paper and submit
More informationGrade 11 November Examination 2015 Mathematics: Paper 2 Time: 3 hours Marks: 150
Grade 11 November Examination 2015 Mathematics: Paper 2 Time: 3 hours Marks: 150 Instructions and Information: Read the following instructions carefully before answering the questions. 1. This question
More informationSixth Form Entrance Mathematics
Sixth Form Entrance 2016 Mathematics 1 hour Attempt all questions if possible. Do not worry if there are topics you have never covered; do your best on whatever you can attempt. Questions are not necessarily
More informationSURA's Guides for 3rd to 12th Std for all Subjects in TM & EM Available. MARCH Public Exam Question Paper with Answers MATHEMATICS
SURA's Guides for rd to 1th Std for all Subjects in TM & EM Available 10 th STD. MARCH  017 Public Exam Question Paper with Answers MATHEMATICS [Time Allowed : ½ Hrs.] [Maximum Marks : 100] SECTION 
More informationGCSE 185/05. MATHEMATICS (2 Tier) HIGHER TIER PAPER 2. A.M. WEDNESDAY, 12 November hours. Candidate Name. Centre Number.
Candidate Name Centre Number 0 Candidate Number GCSE 185/05 MATHEMATICS (2 Tier) HIGHER TIER PAPER 2 A.M. WEDNESDAY, 12 November 2008 2 hours For Examiner s use Question Maximum Mark Mark Awarded ADDITIONAL
More informationINSTRUCTION: This section consists of THREE (3) structured questions. Answer ALL questions.
DBM0: ENGINEERING MATHEMATICS SECTION A : 7 MARKS BAHAGIAN A : 7 MARKAH INSTRUCTION: This section consists of THREE () structured questions. Answer ALL questions. ARAHAN : Bahagian ini mengandungi TIGA
More informationChapter 1. Functions 1.3. Trigonometric Functions
1.3 Trigonometric Functions 1 Chapter 1. Functions 1.3. Trigonometric Functions Definition. The number of radians in the central angle A CB within a circle of radius r is defined as the number of radius
More informationPRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES
PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES 1. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k.. Find the points where the graph of the equation
More informationContact hour per week: 04 Contact hour per Semester: 64 ALGEBRA 1 DETERMINANTS 2 2 MATRICES 4 3 BINOMIAL THEOREM 3 4 LOGARITHMS 2 5 VECTOR ALGEBRA 6
BOARD OF TECHNICAL EXAMINATION KARNATAKA SUBJECT: APPLIED MATHEMATICS I For I semester DIPLOMA COURSES OF ALL BRANCHES Contact hour per week: 04 Contact hour per Semester: 64 UNIT NO. CHAPTER TITLE CONTACT
More informationCambridge IGCSE MATHEMATICS 0580/04 * * Paper 4 (Extended) For examination from hours 30 minutes SPECIMEN PAPER
Cambridge IGCSE *0123456789* MATHEMATICS 0580/04 Paper 4 (Extended) For examination from 2020 SPECIMEN PAPER 2 hours 30 minutes You must answer on the question paper. You will need: Geometrical instruments
More informationS.S.L.C.  MATHS BOOK BACK ONE MARK STUDY MATERIAL
1 S.S.L.C.  MATHS BOOK BACK ONE MARK STUDY MATERIAL DEAR STUDENTS, I have rearranged MATHSone mark book questions in the order based on value of the answer so that, you can understand easily Totally
More informationNATIONAL SENIOR CERTIFICATE GRADE 11
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 06 MARKS: 50 TIME: 3 hours This question paper consists of 3 pages and a page answer book. Mathematics/P DBE/November 06 INSTRUCTIONS AND INFORMATION
More informationMathematics and Further Mathematics PreU June 2010
Mathematics and Further Mathematics PreU June 2010 The following question papers for Mathematics and Further Mathematics are the first papers to be taken by PreU students at the end of the twoyear course.
More informationMATHEMATICS: SPECIALIST UNITS 3C AND 3D FORMULA SHEET 2015
MATHEMATICS: SPECIALIST UNITS 3C AND 3D FORMULA SHEET 05 Copyright School Curriculum and Standards Authority, 05 This document apart from any third party copyright material contained in it may be freely
More informationa Write down the coordinates of the point on the curve where t = 2. b Find the value of t at the point on the curve with coordinates ( 5 4, 8).
Worksheet A 1 A curve is given by the parametric equations x = t + 1, y = 4 t. a Write down the coordinates of the point on the curve where t =. b Find the value of t at the point on the curve with coordinates
More informationALGEBRA 2 /TRIGONOMETRY
ALGEBRA 2/TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2 /TRIGONOMETRY Wednesday, January 25, 2017 1:15 to 4:15 p.m., only Student Name: School Name: The
More informationMATHEMATICS Compulsory Part PAPER 1 (Sample Paper)
Please stick the barcode label here. HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION MATHEMATICS Compulsory Part PAPER 1 (Sample Paper) QuestionAnswer
More informationMAT1035 Analytic Geometry
MAT1035 Analytic Geometry Lecture Notes R.A. Sabri Kaan Gürbüzer Dokuz Eylül University 2016 2 Contents 1 Review of Trigonometry 5 2 Polar Coordinates 7 3 Vectors in R n 9 3.1 Located Vectors..............................................
More informationMath Review for AP Calculus
Math Review for AP Calculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet
More informationPage 1 of 15. Website: Mobile:
Exercise 10.2 Question 1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5
More informationb) The trend is for the average slope at x = 1 to decrease. The slope at x = 1 is 1.
Chapters 1 to 8 Course Review Chapters 1 to 8 Course Review Question 1 Page 509 a) i) ii) [2(16) 12 + 4][2 3+ 4] 4 1 [2(2.25) 4.5+ 4][2 3+ 4] 1.51 = 21 3 = 7 = 1 0.5 = 2 [2(1.21) 3.3+ 4][2 3+ 4] iii) =
More informationNo Calc. 1 p (seen anywhere) 1 p. 1 p. No Calc. (b) Find an expression for cos 140. (c) Find an expression for tan (a) (i) sin 140 = p A1 N1
IBSL /4 IB REVIEW: Trig KEY (0points). Let p = sin 40 and q = cos 0. Give your answers to the following in terms of p and/or q. (a) Write down an expression for (i) sin 40; (ii) cos 70. (b) Find an expression
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 3HR Friday 10 January 2014 Morning Time: 2 hours Centre Number Candidate Number Higher Tier Paper Reference
More informationPaper Reference. Core Mathematics C2 Advanced Subsidiary. Thursday 22 May 2014 Morning Time: 1 hour 30 minutes
Centre No. Candidate No. Paper Reference 6 6 6 4 0 1 Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C2 Advanced Subsidiary Thursday 22 May 2014 Morning Time: 1 hour 30 minutes Materials required
More informationMathematics Paper Sept. 8 4 hours PEPERIKSN PERCUBN SIJIL PELJRN MLYSI 8 SEKOLHSEKOLH MENENGH ZON KUCHING MTHEMTICS Paper One hour fifteen minutes DO NOT OPEN THIS BOOKLET UNTIL YOU RE TOLD TO DO SO.
More informationMODEL QUESTION PAPERS WITH ANSWERS SET 1
MTHEMTICS MODEL QUESTION PPERS WITH NSWERS SET 1 Finish Line & Beyond CLSS X Time llowed: 3 Hrs Max. Marks : 80 General Instructions: (1) ll questions are compulsory. (2) The question paper consists of
More informationTest Codes : MIA (Objective Type) and MIB (Short Answer Type) 2007
Test Codes : MIA (Objective Type) and MIB (Short Answer Type) 007 Questions will be set on the following and related topics. Algebra: Sets, operations on sets. Prime numbers, factorisation of integers
More informationWeek beginning Videos Page
1 M Week beginning Videos Page June/July C3 Algebraic Fractions 3 June/July C3 Algebraic Division 4 June/July C3 Reciprocal Trig Functions 5 June/July C3 Pythagorean Identities 6 June/July C3 Trig Consolidation
More information