SULIT 47/ The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. x b ± b 4ac a ALGEBRA 8 log

Size: px
Start display at page:

Download "SULIT 47/ The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. x b ± b 4ac a ALGEBRA 8 log"

Transcription

1 SULIT 47/ 47/ Matematik Tambahan Kertas ½ jam 009 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 009 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 sub-part of a question are shown in brackets.. 7. A list of formulae is provided on pages to. 8. A booklet of four-figure mathematical tables is provided. 9. You may use a non-programmable scientific calculator. Kertas soalan ini mengandungi halaman bercetak 47/ ZON A KUCHING 009 SULIT

2 SULIT 47/ The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. x b ± 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 mn 5 log a mn log a m + log a n 6 m log a n log a m log a n 7 log a m n n log a m 9 T n a + (n )d 0 n S n [a + ( n ) d] T n ar n n n a( r ) a( r ) S n r r a S r, r <, (r ) y uv, dy dx dv u dx du v + du v dx dv 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 π y dx or a b π x dy a GEOM ETRY Distance Midpoint x + (x, y) x 4 r x + y xi + r x yj + y ( 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 ( ) ( ) x y + x y + x y x y + x y + x y 47/ ZON A KUCHING 009 SULIT

3 SULIT 47/ x N x σ x fx f ( x x ) N x N x STATISTICS w I I w n n! P r ( n r)! n n! C r ( n r)! r! 0 P(A B) P(A) + P(B) P(A B) 4 σ f ( x x) f fx f x P(X r) Mean µ np r C p q n r n r, p + q N F 5 m L + C fm Q I 00 Q 6 0 σ npq 4 z x µ σ TRIGONOMETRY Arc length, s rθ Area of sector, A sin A + cos A 4 sec A + tan A 5 cosec A + cot A 6 sin A sina cosa r θ 7 cos A cos A sin A cos A sin A tan A 8 tan A tan A 9 sin (A ± B) sina cosb ± cosa sinb 0 cos (A ± B) cosa cosb m sina sinb tan A ± tan B tan (A ± B) m tan Atan B a sin A b sin B c sin C a b + c bc cos A 4 Area of triangle absin C 47/ ZON A KUCHING 009 SULIT

4 SULIT / SECTION A [40 marks] Answer all questions in this section. Solve the simultaneous equations x y and x + xy 0 0. Give your answer correct to decimal places. [5 marks] Diagram shows a circle with centre O. 00 O S R DIAGRAM P T Q PTQ is a tangent to the circle at T and PQ OQ 0 cm. Calculate the length of the arc STR, [4 marks] the area of the shaded region. [4 marks] Table shows the frequency distribution of scores of a group of players in a game. Score Number of players 0 0 w 6 TABLE It is given that the median of the distribution is 7. Calculate the value of w. [ marks] Hence, calculate the variance of the distribution. [4 marks] 47/ ZON A KUCHING 009 SULIT

5 SULIT 5 47/ 4 If the volume of a cube decreases from 5 cm to 4.4 cm, find the small change in the sides of the cube. [ marks] x + 4 Given that f ( x), find the value of f (). x [ marks] 5 Prove that sin x sin x cot x. [ marks] Sketch the graph of y sin x for 0 x π. Hence, using the same axes, sketch a suitable straight line to find the number of solutions of the equation x π for 0 x π. State the number of solutions. sin x [6 marks] 6 cm 5 cm 8 cm... DIAGRAM A piece of wire is cut into 5 parts which are bent to form circles as shown in Diagram. The radius of each circle increases by cm consecutively. Calculate (i) the radius of the last circle, [ marks] the area of the last circle. [ mark] Diagram shows a rectangular geometric pattern. A M B P N D Diagram The first rectangle is ABCD and followed by MBNP and so on. The length and width of the next rectangle is half of the length and width of the previous rectangle. Given that AB 0 cm and BC 0 cm. Find the perimeter of the seventh rectangle. [ marks] 47/ ZON A KUCHING 009 SULIT C DIAGRAM

6 SULIT 6 47/ SECTION B [40 marks] Answer four questions from this section. 7 Use graph paper to answer this question. Table shows the values of two variables x and y which are related by and q are constants. y pq x+, where p x y TABLE Convert x+ y pq to a linear form of mx c Y +. [ marks] Plot log 0 y against ( x + ) by using a scale of cm to unit on the Y-axis and cm to unit on the X-axis. Hence, draw the line of best fit. [4 marks] (c) From the graph in, find the value of p and of q. [4 marks] 8 Diagram 4 shows a triangle OPQ. The point R lies on OP and the point S lies on PQ. The straight line QR intersects the straight line OS at point T. Q T S O R P DIAGRAM 4 Given OP : OR 4 :, PQ : PS :, OP x % and OQ 9y. % Express, in terms of x and / or y, (i) QR, OS. [ marks] If OT hos and QT k QR, where h and k are constants, find the values of h and k. (c) Given that x % units, y 5 % units and POQ 90 o, find PQ. 47/ ZON A KUCHING 009 SULIT [5 marks] [ marks]

7 SULIT 7 47/ 9 In a certain area, 0% of the trees are rubber trees. (i) If 8 trees in the area are chosen at random, find the probability that at least two of the trees are rubber trees. If the variance of the rubber trees is 5, find the number of rubber trees in the area. [5 marks] The masses of the children in the Primary One in the school have a normal distribution with mean.5 kg and variance 5 kg. 50 of the children have masses between 0 kg and 6.5 kg. Calculate the total number of children in Primary One in that school. [5 marks] 0 Solution by scale drawing is not accepted. In Diagram 5, point T lies on the perpendicular bisector of AB. y D A (, 4) T B(, ) C O DIAGRAM 5 x Find the equation of straight line AB. [ marks] A point P moves such that PA AB. Find the equation of locus of P. [ marks] (c) Locus of P intersects the x-axis at points Y and Z. State the coordinates of Y and Z. [ marks] (d) Find the x-intercept of CD. [ marks] 47/ ZON A KUCHING 009 SULIT

8 SULIT 8 47/ Given that a curve has a gradient function px + x such that p is a constant. y 6 x is the equation of tangent to the curve at the point (, q). Find the value of p and of q. [ marks] Diagram 6 shows the curve y (x ) and the straight line y x + intersect at point (, 4). y y x + Calculate O (, 4) y (x ) DIAGRAM 6 x (i) the area of the shaded region, [4 marks] the volume of revolution, in terms of π, when the region bounded by the curve, the x-axis, the y-axis and the straight line x is revolved through 60 about the x-axis. [ marks] 47/ ZON A KUCHING 009 SULIT

9 SULIT 9 47/ SECTION C [0 marks] Answer two questions from this section. A particle moves along a straight line and passes through a fixed point O. Its velocity, v ms, is given by v t 6t + 5, where t is the time, in seconds, after passing through O. (Assume motion to the right is positive). Find the initial velocity, in ms, the minimum velocity, in ms, [ mark] [ marks] (c) the range of values of t at which the particles moves to the left, [ marks] (d) the total distance, in m, travelled by the particle in the first 5 seconds. [4 marks] In Diagram 7, ABC is a triangle. BMC and AM are straight lines. A B M DIAGRAM 7 C Calculate (i) AMB, the area, in cm, of triangle ABC. [7 marks] A new triangle A B M is formed with A B AB, B M BM and B A M BAM, find the length of A M. [ marks] 47/ ZON A KUCHING 009 SULIT

10 SULIT 0 47/ 4 Use the graph paper provided to answer this question. A factory produces two types of school bags M and N using two types of machines A and B. Given that machine A requires 0 minutes to produce a bag M and 0 minutes to produce a bag N while machine B requires 5 minutes to produce a bag M and 40 minutes to produce a bag N. The machines produce x units of M and y units of N in a particular day according to the following conditions. I : Machine A is operated for not more than 8 hours. II : Machine B is operated for at least 4 hours. III : The number of units of bag M produced is not more than twice the number of units of bag N. Write the three inequalities for the above conditions. [ marks] (c) Using a scale of cm to units for both axes, construct and shade the region R which satisfies all the above conditions. [ marks] Use the graph constructed in 4, to find (i) the maximum number of units of bag M that can be produced if the factory produces units of bag N. the maximum profit obtained if the profit from one unit of bag M and bag N are RM 8 and RM 0 respectively. [4 marks] 47/ ZON A KUCHING 009 SULIT

11 SULIT 47/ 5 Table shows the price indices and percentage of usage of four components, P, Q, R and S, which are the number of parts in the making of an electronic device. Item Price index for the year 000 based on the year 997 Percentage of usage (%) P 5 0 Q 40 0 R x 0 S 0 40 Calculate TABLE (i) the price of Q in the year 997 if its price in the year 000 is RM 50.40, the price index of P in the year 000 based on the year 994 if its price index in the year 997 based on the year 994 is 0. [5 marks] The composite index number for the cost of production in the year 000 based on the year 997 is. Calculate (i) the value of x, the price of an electronic device in the year 997 if the corresponding price in the year 000 was RM 88. [5 marks] END OF QUESTION PAPER 47/ ZON A KUCHING 009 SULIT

12 47/ Matematik Tambahan Kertas ½ jam Sept 009 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 009 MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU MARKING SCHEME Skema Pemarkahan ini mengandungi 4 halaman bercetak

13 QUESTION NO. ADDITIONAL MATHEMATICS MARKING SCHEME TRIAL SBP 009 PAPER SOLUTION MARKS x y 6 P 5 (y 6) + (y 6) y 0 0 Eliminate x or y y 5y Solve the quadratic equation by using the quadratic completing the square must be shown y , y x 4.786, x.786 Note : OW- if the working of solving quadratic equation is not shown. 5 OT 7.05 cm π 4 s STR π 7.05 Use the formula s rθ s 8.80 cm STR

14 QUESTION NO. SOLUTION MARKS Area OPQ 0 0 sin 7.05cm o 4 Area OSTR cm 0 0 sin 60 o cm w (5) 0 w 7 P Lower boundary OR 4 + w 5 (5) 0 Score Frequency, f Midpoint, x fx fx Variance f 50 P fx 865 fx OR P

15 4 QUESTION NO. SOLUTION MARKS 4 δv 0.6 OR dv dx x OR x (5) δ x δ x f ( x) ( x )() (x + 4)( x) ( x ) f () [ ] + () () () (() 4)( ()) sin cos x x sin x sin x cos x sin x y x π Sketch straight line correctly P Sine curve P 6 y y sin x x y π Period Amplitude P P O π x Modulus P Number of solutions 4 8

16 5 QUESTION NO. SOLUTION MARKS 6 (i) T 5 + 4() 44 cm Area of the fifteenth circle 96π cm 00, 50, 5, a 00 AND r T

17 6 log 0 y x log 0 y Each set of values correct (log 0 y must be at least decimal places), Y mx + c log 0 y (x + ) log 0 q + log 0 p where Y log 0 y, X (x + ), m log 0 q and c log 0 p (c) log 0 q gradient 4. ( 0.6) log 0 q 7 0 q 4.85 Correct both axes (Uniform scale) All points are plotted correctly Line of best fit 4 log p Y-intercept log p 0.6 p x +

18 7 QUESTION NO. SOLUTION MARKS 8 (i) uuur QR 9x 9y % % uuur OS 9y + 9y + x % % % 9 6x + y % % ( ) uuur uuur OT hos 9 6hx + hy % % OR uuur uuur QT kqr 9kx 9ky % % uuur uuur uuur QT QO + OT 9 9y + 6hx + hy % % % 9 6hx h y % uuur % Comparing QT, 9k 6h k h () OR 9 9k 9 + h k h () 5 (d) Solving the simultaneous equations 6 4 h, k 7 7 uuur PQ x + 9y uuur % % PQ () + 9(5) ( ) ( ) 57.6 units 0

19 8 QUESTION NO. SOLUTION MARKS 9 (i) p 0., q 0.7, n 8 (0.7) 8 8 C (0.)(0.7) n(0.)(0.7) 5 n 500 (i) P < Z < 5 5 n OR 50 P[ 0.7 < Z < 0.6] n 5 P[Z > 0.7] P[Z > 0.6] 50 n n n 0. Total number 0 0

20 9 QUESTION NO. SOLUTION MARKS 0 Get m ( x ) y 4 y + x 5 0 ( x ) + ( y 4) ( 4 ) + ( ) ( 8) x x y y x y x y (c) x x 5 0 ( x )( x ) x 5, x Get both ( ) ( ) Y / Z 5,0 and Z / Y,0 (d) ( ) GetT,, x intercept 0

21 0 QUESTION NO. SOLUTION MARKS px + x p() + p, q (i) Area of the shaded region ( x 8x + 7) dx 0 ( x 6x + 9) dx (x + ) dx 0 0 x 8x + 7x unit. 0 7 Volume of revolution π y dx 0 π 0 ( x ) 4 dx 5 π ( x ) ( ) (0 ) π π unit. 5 0

22 QUESTION NO. SOLUTION MARKS v 5 ms P a t 6 and a 0 or dv dt 0 t v min 4 ms (c) (t )(t 5) < 0 < t < 5 (d) t s t + 5t 4 s s 0 + s 5 s OR 5 v dt + 0 v dt OR 5 () + 5() 0 + (5) + 5(5) () + 5() m 0

23 QUESTION NO. SOLUTION MARKS (i) cos AMB (5)(8) 6' sin ACM sin ACM 65 4' 5 MAC Area of AMB Area of ACM (5)(8)sin.4 (5)(4)sin 68. OR 9.87 cm 4.5 cm Area of ABC cm Get B 'M 'M B 'MM ' M 'B 'M MM ' sin sin MM ' cm A'M ' cm 0

24 Answer for question 4 I. x + y 48 II. 5x + 8y 48 III. y x Refer to the graph, or graph(s) correct graphs correct Correct area 6 (c) i) 6 ii) max point (, 8) 4 k 8x + 0y Maximum Profit RM 8() + RM 0(8) RM R (, 8) 6 4

25 4 QUESTION NO. SOLUTION MARKS 5 (i) RM Q 97 5 Q 97 RM 6 I 00,97 I00,94 00 I 97,94 I00, (i) I 00, x x x 0 RM Q 997 Q 997 RM

SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 2008

SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 2008 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

More information

3472/1 Name :.. Matematik Tambahan

3472/1 Name :.. Matematik Tambahan 7/1 Name :.. Matematik Tambahan Kertas 1 Form :.. Ogos 008 Jam SEKOLAH BERASRAMA PENUH BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH / KLUSTER KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN

More information

SEKOLAH MENENGAH ZON A KUCHING LEMBAGA PEPERIKSAAN PEPERIKSAAN PERCUBAAN SPM 2008

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 information

SULIT / / Matematik Tambahan Kertas ½ jam 0 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 0 MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS

More information

SULIT 47/ 47/ Matematik Tambahan Kertas ½ jam Ogos 008 SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH / KLUSTER KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN

More information

SULIT /2 3472/2 Matematik Tambahan Kertas 2 2 ½ jam 2009 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING

SULIT /2 3472/2 Matematik Tambahan Kertas 2 2 ½ jam 2009 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING SULIT 1 347/ 347/ Mtemtik Tmbhn Kerts ½ jm 009 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 009 MATEMATIK TAMBAHAN Kerts Du jm tig puluh minit JANGAN BUKA KERTAS

More information

SMS MUZAFFAR SYAH, MELAKA

SMS MUZAFFAR SYAH, MELAKA SULIT 7/ ADDITIONAL MATHEMATICS PAPER AUGUST 008 HOURS NAMA : KELAS : NO K.P : A. GILIRAN : - JABATAN PELAJARAN NEGERI SABAH SIJIL PELAJARAN MALAYSIA TAHUN 008 EXCEL ADDITIONAL MATHEMATICS PAPER (KERTAS

More information

SULIT 449/ 449/ Mathematics Nama : Kertas September Kelas : 008 jam PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 008 SEKOLAH-SEKOLAH ZON A KUCHING MATHEMATICS Kertas Dua jam tiga puluh minit JANGAN BUKA

More information

Nama Pelajar : 347/ Additional Mathematics Paper September 00 Tingkatan 5 :. PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN PEPERIKSAAN PERCUBAAN SPM 00 ADDITIONAL MATHEMATICS

More information

1 Nama:... Kelas :... MAKTAB SABAH, KOTA KINABALU PEPERIKSAAN PERTENGAHAN TAHUN 2009 MATEMATIK TAMBAHAN TINGKATAN 4 Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. This question

More information

Matematik 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 information

UNTUK KEGUNAAN PEMERIKSA SAHAJA

UNTUK KEGUNAAN PEMERIKSA SAHAJA SULIT PROGRAM GEMPUR KECEMERLANGAN SIJIL PELAJARAN MALAYSIA 08 NEGERI PERLIS SIJIL PELAJARAN MALAYSIA 08 MATEMATIK TAMBAHAN Kertas Peraturan Pemarkahan Ogos 47/(PP) UNTUK KEGUNAAN PEMERIKSA SAHAJA Peraturan

More information

SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN LIMA 2007

SEKTOR 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 information

Sec 4 Maths SET D PAPER 2

Sec 4 Maths SET D PAPER 2 S4MA Set D Paper Sec 4 Maths Exam papers with worked solutions SET D PAPER Compiled by THE MATHS CAFE P a g e Answer all questions. Write your answers and working on the separate Answer Paper provided.

More information

47/ NO. KAD PENGENALAN Additional Mathematics Paper ANGKA GILIRAN Hours JABATAN PELAJARAN NEGERI PULAU PINANG ADDITIONAL MATHEMATICS Paper Two Hours J

47/ 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 information

SULIT 3472/1. Nama:.. Tingkatan: 3472/1 NO. KAD PENGENALAN Matematik Tambahan PROGRAM PENINGKATAN PRESTASI SAINS DAN MATEMATIK 2009

SULIT 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 information

JABATAN PELAJARAN NEGERI PERAK GERAK GEMPUR SIJIL PELAJARAN MALAYSIA SET 2 (Paper 1) Two Hours

JABATAN 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 information

Sec 4 Maths. SET A PAPER 2 Question

Sec 4 Maths. SET A PAPER 2 Question S4 Maths Set A Paper Question Sec 4 Maths Exam papers with worked solutions SET A PAPER Question Compiled by THE MATHS CAFE 1 P a g e Answer all the questions S4 Maths Set A Paper Question Write in dark

More information

TABLE OF CONTENTS 2 CHAPTER 1

TABLE OF CONTENTS 2 CHAPTER 1 TABLE OF CONTENTS CHAPTER 1 Quadratics CHAPTER Functions 3 CHAPTER 3 Coordinate Geometry 3 CHAPTER 4 Circular Measure 4 CHAPTER 5 Trigonometry 4 CHAPTER 6 Vectors 5 CHAPTER 7 Series 6 CHAPTER 8 Differentiation

More information

( ) 2 + ( 2 x ) 12 = 0, and explain why there is only one

( ) 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 information

Core Mathematics C1 (AS) Unit C1

Core Mathematics C1 (AS) Unit C1 Core Mathematics C1 (AS) Unit C1 Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, factorisation. Graphs of functions; sketching curves defined by simple equations.

More information

MOZ@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 information

SULIT /2 3472/2 Matematik Tambahan Kertas 2 2 ½ jam 2010 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING

SULIT /2 3472/2 Matematik Tambahan Kertas 2 2 ½ jam 2010 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING SULIT / / Mtemtik Tmhn Kerts ½ jm 00 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 00 MATEMATIK TAMBAHAN Kerts Du jm tig puluh minit JANGAN BUKA KERTAS SOALAN INI

More information

Possible C2 questions from past papers P1 P3

Possible C2 questions from past papers P1 P3 Possible C2 questions from past papers P1 P3 Source of the original question is given in brackets, e.g. [P1 January 2001 Question 1]; a question which has been edited is indicated with an asterisk, e.g.

More information

IYGB. Special Paper U. Time: 3 hours 30 minutes. Created by T. Madas. Created by T. Madas

IYGB. Special Paper U. Time: 3 hours 30 minutes. Created by T. Madas. Created by T. Madas IYGB Special Paper U Time: 3 hours 30 minutes Candidates may NOT use any calculator Information for Candidates This practice paper follows the Advanced Level Mathematics Core Syllabus Booklets of Mathematical

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level *8790810596* ADDITIONAL MATHEMATICS 4037/13 Paper 1 October/November 2017 2 hours Candidates answer on the Question Paper. No Additional Materials

More information

SULIT 1449/1 ppr maths nbk SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN DIAGNOSTIK TINGKATAN

SULIT 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 information

2016 SEC 4 ADDITIONAL MATHEMATICS CW & HW

2016 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 information

Practice Papers Set D Higher Tier A*

Practice Papers Set D Higher Tier A* Practice Papers Set D Higher Tier A* 1380 / 2381 Instructions Information Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number.

More information

Answer all the questions

Answer all the questions SECTION A ( 38 marks) Answer all the questions 1 The following information refer to the set A and set B. Set A = { -3, -2, 2, 3 } Set B = { 4, 9 } The relations between set A and set B is defined by the

More information

3472/2 Additional Mathematics Paper 2 [Lihat sebelah SULIT

3472/2 Additional Mathematics Paper 2 [Lihat sebelah SULIT 008 SPM TRIAL EXAMINATION Question Solution and marking scheme. y y P Make y as the subject y y y y 0 0 9 6y y 6y y y 0 0 Eliminate y 9 0 0 y.,..07, 0.07.07 /.08, 0.07 / 0.08 y. /.,. /. Solve quadratic

More information

International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS PAPER 2 MAY/JUNE SESSION 2002

International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS PAPER 2 MAY/JUNE SESSION 2002 International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS ADDITIONAL MATHEMATICS 0606/2 PAPER 2 MAY/JUNE SESSION 2002 2 hours Additional materials: Answer paper Electronic

More information

ADDITIONAL MATHEMATICS 4037/01

ADDITIONAL MATHEMATICS 4037/01 Cambridge O Level *0123456789* ADDITIONAL MATHEMATICS 4037/01 Paper 1 For examination from 2020 SPECIMEN PAPER 2 hours You must answer on the question paper. No additional materials are needed. INSTRUCTIONS

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/02 Paper 2 Examination from 2013 SPECIMEN PAPER 2 hours Candidates

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level * 3 1 3 1 7 3 6 3 6 2 * ADDITIONAL MATHEMATICS 4037/11 Paper 1 May/June 2015 2 hours Candidates answer on the Question Paper. No Additional

More information

Mathematics Paper Sept. 8 4 hours PEPERIKSN PERCUBN SIJIL PELJRN MLYSI 8 SEKOLH-SEKOLH MENENGH ZON KUCHING MTHEMTICS Paper One hour fifteen minutes DO NOT OPEN THIS BOOKLET UNTIL YOU RE TOLD TO DO SO.

More information

DEPARTMENT OF MATHEMATICS

DEPARTMENT OF MATHEMATICS DEPARTMENT OF MATHEMATICS AS level Mathematics Core mathematics 1 C1 2015-2016 Name: Page C1 workbook contents Indices and Surds Simultaneous equations Quadratics Inequalities Graphs Arithmetic series

More information

Further Mathematics Summer work booklet

Further Mathematics Summer work booklet Further Mathematics Summer work booklet Further Mathematics tasks 1 Skills You Should Have Below is the list of the skills you should be confident with before starting the A-Level Further Maths course:

More information

International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS PAPER 1 MAY/JUNE SESSION 2002

International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS PAPER 1 MAY/JUNE SESSION 2002 International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS ADDITIONAL MATHEMATICS 0606/1 PAPER 1 MAY/JUNE SESSION 2002 2 hours Additional materials: Answer paper Electronic

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/01

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/01 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/01 Paper 1 Additional Materials: Answer Booklet/Paper Electronic

More information

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)

QUESTION 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 information

Time: 1 hour 30 minutes

Time: 1 hour 30 minutes Paper Reference (complete below) Centre No. Surname Initial(s) Candidate No. Signature Paper Reference(s) 6663 Edexcel GCE Pure Mathematics C Advanced Subsidiary Specimen Paper Time: hour 30 minutes Examiner

More information

Calculus first semester exam information and practice problems

Calculus first semester exam information and practice problems Calculus first semester exam information and practice problems As I ve been promising for the past year, the first semester exam in this course encompasses all three semesters of Math SL thus far. It is

More information

Paper1Practice [289 marks]

Paper1Practice [289 marks] PaperPractice [89 marks] INSTRUCTIONS TO CANDIDATE Write your session number in the boxes above. Do not open this examination paper until instructed to do so. You are not permitted access to any calculator

More information

Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)

Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0) Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0) First teaching from September 2017 First certification from June 2018 2

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *1406924476* ADDITIONAL MATHEMATICS 0606/21 Paper 2 May/June 2010 Additional

More information

Candidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required.

Candidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required. Revision Checklist Unit C2: Core Mathematics 2 Unit description Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation;

More information

Name: Index Number: Class: CATHOLIC HIGH SCHOOL Preliminary Examination 3 Secondary 4

Name: Index Number: Class: CATHOLIC HIGH SCHOOL Preliminary Examination 3 Secondary 4 Name: Inde Number: Class: CATHOLIC HIGH SCHOOL Preliminary Eamination 3 Secondary 4 ADDITIONAL MATHEMATICS 4047/1 READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work

More information

MATHEMATICS Unit Pure Core 2

MATHEMATICS Unit Pure Core 2 General Certificate of Education June 2008 Advanced Subsidiary Examination MATHEMATICS Unit Pure Core 2 MPC2 Thursday 15 May 2008 9.00 am to 10.30 am For this paper you must have: an 8-page answer book

More information

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge 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 information

Created by T. Madas. Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications.

Created by T. Madas. Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications. IYGB Special Paper Q Time: 3 hours 30 minutes Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications. Information for Candidates This practice paper follows

More information

DEPARTMENT OF MATHEMATICS

DEPARTMENT OF MATHEMATICS DEPARTMENT OF MATHEMATICS AS level Mathematics Core mathematics 2 - C2 2015-2016 Name: Page C2 workbook contents Algebra Differentiation Integration Coordinate Geometry Logarithms Geometric series Series

More information

Possible C4 questions from past papers P1 P3

Possible C4 questions from past papers P1 P3 Possible C4 questions from past papers P1 P3 Source of the original question is given in brackets, e.g. [P January 001 Question 1]; a question which has been edited is indicated with an asterisk, e.g.

More information

Mathematics, Algebra, and Geometry

Mathematics, Algebra, and Geometry Mathematics, Algebra, and Geometry by Satya http://www.thesatya.com/ Contents 1 Algebra 1 1.1 Logarithms............................................ 1. Complex numbers........................................

More information

1. 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. 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 information

MATHEMATICS 2017 HSC Course Assessment Task 4 (Trial Examination) Thursday, 3 August 2017

MATHEMATICS 2017 HSC Course Assessment Task 4 (Trial Examination) Thursday, 3 August 2017 MATHEMATICS 2017 HSC Course Assessment Task 4 (Trial Examination) Thursday, 3 August 2017 General instructions Working time 3 hours. (plus 5 minutes reading time) Write using blue or black pen. Where diagrams

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level *054681477* ADDITIONAL MATHEMATICS 407/11 Paper 1 May/June 017 hours Candidates answer on the Question Paper. No Additional Materials are required.

More information

December 2012 Maths HL Holiday Pack. Paper 1.2 Paper 1 from TZ2 Paper 2.2 Paper 2 from TZ2. Paper 1.1 Paper 1 from TZ1 Paper 2.

December 2012 Maths HL Holiday Pack. Paper 1.2 Paper 1 from TZ2 Paper 2.2 Paper 2 from TZ2. Paper 1.1 Paper 1 from TZ1 Paper 2. December 2012 Maths HL Holiday Pack This pack contains 4 past papers from May 2011 in the following order: Paper 1.2 Paper 1 from TZ2 Paper 2.2 Paper 2 from TZ2 Paper 1.1 Paper 1 from TZ1 Paper 2.1 Paper

More information

MODULE 1 PAPER 1 (3472/1)

MODULE 1 PAPER 1 (3472/1) MODULE 1 PAPER 1 (347/1) FUNCTIONS 1. Given that h(x) =, x 0 and v(x) = 3x +, find hv 1 ) x ( x. p : t t + qp : t t + 4t + 1. Based on the above information, find the function of q. QUADRATIC FUNCTIONS

More information

Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions Pure Mathematics Year (AS) Unit Test : Algebra and Functions Simplify 6 4, giving your answer in the form p 8 q, where p and q are positive rational numbers. f( x) x ( k 8) x (8k ) a Find the discriminant

More information

Paper2Practice [303 marks]

Paper2Practice [303 marks] PaperPractice [0 marks] Consider the expansion of (x + ) 10. 1a. Write down the number of terms in this expansion. [1 mark] 11 terms N1 [1 mark] 1b. Find the term containing x. evidence of binomial expansion

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *7560400886* ADDITIONAL MATHEMATICS 0606/22 Paper 2 May/June 2011 2 hours

More information

a 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).

a 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 information

MOBILE NO : X_STD MATHS RVS - TRICHY R.VETRIVEL

MOBILE NO : X_STD MATHS RVS - TRICHY R.VETRIVEL 10 MOBILE NO : 986545111 ONE MARK - FIRST TEST TIME:10 MINUTES 1. If A B, then A B is a) B b) A/B c) A d) B/A. If the product of the first four consecutive terms of a G.P is 56 and if the common ratio

More information

MATHEMATICS. 24 July Section 1 10 marks (pages 3-7) Attempt Questions 1 10 Allow about 15 minutes for this section

MATHEMATICS. 24 July Section 1 10 marks (pages 3-7) Attempt Questions 1 10 Allow about 15 minutes for this section MATHEMATICS 24 July 2017 General Instructions Reading time 5 minutes Working time 3 hours Write using black pen. NESA approved calculators may be used. Commence each new question in a new booklet. Write

More information

Express g(x) in the form f(x) + ln a, where a (4)

Express g(x) in the form f(x) + ln a, where a (4) SL 2 SUMMER PACKET 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 DAY

More information

CBSE CLASS-10 MARCH 2018

CBSE CLASS-10 MARCH 2018 CBSE CLASS-10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION & ANSWER Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level *054681477* ADDITIONAL MATHEMATICS 4037/11 Paper 1 May/June 017 hours Candidates answer on the Question Paper. No Additional Materials are

More information

ADDITIONAL MATHEMATICS

ADDITIONAL MATHEMATICS 005-CE A MATH HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 005 ADDITIONAL MATHEMATICS :00 pm 5:0 pm (½ hours) This paper must be answered in English 1. Answer ALL questions in Section A and any FOUR

More information

Solutionbank C1 Edexcel Modular Mathematics for AS and A-Level

Solutionbank C1 Edexcel Modular Mathematics for AS and A-Level Heinemann Solutionbank: Core Maths C Page of Solutionbank C Exercise A, Question Find the values of x for which f ( x ) = x x is a decreasing function. f ( x ) = x x f ( x ) = x x Find f ( x ) and put

More information

Practice Assessment Task SET 3

Practice Assessment Task SET 3 PRACTICE ASSESSMENT TASK 3 655 Practice Assessment Task SET 3 Solve m - 5m + 6 $ 0 0 Find the locus of point P that moves so that it is equidistant from the points A^-3, h and B ^57, h 3 Write x = 4t,

More information

4) If ax 2 + bx + c = 0 has equal roots, then c is equal. b) b 2. a) b 2

4) 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 information

Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document

Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document Background knowledge: (a) The arithmetic of integers (including HCFs and LCMs), of fractions, and of real numbers.

More information

National Quali cations

National Quali cations H 2017 X747/76/11 FRIDAY, 5 MAY 9:00 AM 10:10 AM National Quali cations Mathematics Paper 1 (Non-Calculator) Total marks 60 Attempt ALL questions. You may NOT use a calculator. Full credit will be given

More information

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 2 4 2 8 1 9 0 7 2 * ADDITIONAL MATHEMATICS 0606/12 Paper 1 February/March 2016 2 hours Candidates

More information

Core Mathematics C12

Core Mathematics C12 Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C12 Advanced Subsidiary Tuesday 10 January 2017 Morning Time: 2 hours

More information

Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours

Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours 1. Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Mark scheme Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *0050607792* ADDITIONAL MATHEMATICS 0606/21 Paper 2 May/June 2012 2 hours

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level * 9 4 5 1 6 2 0 9 2 4 * ADDITIONAL MATHEMATICS 4037/12 Paper 1 October/November 2015 2 hours Candidates answer on the Question Paper. No Additional

More information

C3 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) 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 information

Mathematics. Caringbah High School. Trial HSC Examination. Total Marks 100. General Instructions

Mathematics. Caringbah High School. Trial HSC Examination. Total Marks 100. General Instructions Caringbah High School 014 Trial HSC Examination Mathematics General Instructions Total Marks 100 Reading time 5 minutes Working time 3 hours Write using a blue or black pen. Black pen is preferred. Board

More information

Express g(x) in the form f(x) + ln a, where a (4)

Express 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

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 0 8 7 6 9 0 5 1 6 * ADDITIONAL MATHEMATICS 0606/11 Paper 1 October/November 016 hours Candidates

More information

DISCRIMINANT EXAM QUESTIONS

DISCRIMINANT EXAM QUESTIONS DISCRIMINANT EXAM QUESTIONS Question 1 (**) Show by using the discriminant that the graph of the curve with equation y = x 4x + 10, does not cross the x axis. proof Question (**) Show that the quadratic

More information

1. SETS AND FUNCTIONS

1. SETS AND FUNCTIONS . SETS AND FUNCTIONS. For two sets A and B, A, B A if and only if B A A B A! B A + B z. If A B, then A + B is B A\ B A B\ A. For any two sets Pand Q, P + Q is " x : x! P or x! Q, " x : x! P and x b Q,

More information

ICSE Solved Paper, 2018

ICSE Solved Paper, 2018 ICSE Solved Paper, 018 Class-X Mathematics (Maximum Marks : 80) (Time allowed : Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to

More information

Core Mathematics 2 Coordinate Geometry

Core Mathematics 2 Coordinate Geometry Core Mathematics 2 Coordinate Geometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Coordinate Geometry 1 Coordinate geometry in the (x, y) plane Coordinate geometry of the circle

More information

The region enclosed by the curve of f and the x-axis is rotated 360 about the x-axis. Find the volume of the solid formed.

The region enclosed by the curve of f and the x-axis is rotated 360 about the x-axis. Find the volume of the solid formed. Section A ln. Let g() =, for > 0. ln Use the quotient rule to show that g ( ). 3 (b) The graph of g has a maimum point at A. Find the -coordinate of A. (Total 7 marks) 6. Let h() =. Find h (0). cos 3.

More information

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time) HIGHER SCHOOL CERTIFICATE EXAMINATION 998 MATHEMATICS / UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of equal value.

More information

x n+1 = ( x n + ) converges, then it converges to α. [2]

x n+1 = ( x n + ) converges, then it converges to α. [2] 1 A Level - Mathematics P 3 ITERATION ( With references and answers) [ Numerical Solution of Equation] Q1. The equation x 3 - x 2 6 = 0 has one real root, denoted by α. i) Find by calculation the pair

More information

H2 MATHS SET D PAPER 1

H2 MATHS SET D PAPER 1 H Maths Set D Paper H MATHS Exam papers with worked solutions SET D PAPER Compiled by THE MATHS CAFE P a g e b The curve y ax c x 3 points, and, H Maths Set D Paper has a stationary point at x 3. It also

More information

REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS

REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS The Department of Applied Mathematics administers a Math Placement test to assess fundamental skills in mathematics that are necessary to begin the study

More information

2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is

2. 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 information

, correct to 4 significant figures?

, correct to 4 significant figures? Section I 10 marks Attempt Questions 1-10 Allow about 15 minutes for this section Use the multiple-choice answer sheet for Questions 1-10. 1 What is the basic numeral for (A) 0.00045378 (B) 0.0004538 (C)

More information

Add Math (4047/02) Year t years $P

Add Math (4047/02) Year t years $P Add Math (4047/0) Requirement : Answer all questions Total marks : 100 Duration : hour 30 minutes 1. The price, $P, of a company share on 1 st January has been increasing each year from 1995 to 015. The

More information

Here is a link to the formula booklet:

Here is a link to the formula booklet: IB MATH SL2 SUMMER ASSIGNMENT review of topics from year 1. We will be quizzing on this when you return to school. This review is optional but you will earn bonus points if you complete it. Questions?

More information

Mathematics Extension 2

Mathematics Extension 2 Northern Beaches Secondary College Manly Selective Campus 010 HIGHER SCHOOL CERTIFICATE TRIAL EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time 3 hours Write using

More information

6. Show appropriate working in its correct place. Full marks will not necessarily be given for answers only.

6. Show appropriate working in its correct place. Full marks will not necessarily be given for answers only. Mathematics Exam Grade Paper eptember 06 3 hours 50 marks Instructions. This paper consists of questions. Answer all questions.. A booklet containing Diagram heets, Answer heets and an Information heet

More information

Percubaan PMR 2010 Pahang MATEMATIK 50/1

Percubaan PMR 2010 Pahang MATEMATIK 50/1 Percubaan PMR 2010 Pahang MATEMATIK 50/1 1 Percubaan PMR 2010 Pahang MATEMATIK 50/1 2 Percubaan PMR 2010 Pahang MATEMATIK 50/1 3 Percubaan PMR 2010 Pahang MATEMATIK 50/1 4 Percubaan PMR 2010 Pahang MATEMATIK

More information

1. Let g(x) and h(x) be polynomials with real coefficients such that

1. Let g(x) and h(x) be polynomials with real coefficients such that 1. Let g(x) and h(x) be polynomials with real coefficients such that g(x)(x 2 3x + 2) = h(x)(x 2 + 3x + 2) and f(x) = g(x)h(x) + (x 4 5x 2 + 4). Prove that f(x) has at least four real roots. 2. Let M be

More information