u 2 or GCE A Level H1 Maths Solution Paper 1 2(i) Given 4x 2y i.e. 2x y (i) And..(ii) From (i), substitute y 40 2x into (ii):
|
|
- Oliver Eaton
- 6 years ago
- Views:
Transcription
1 GCE A Level H Maths Solution Paper e e u u u u u or e or (N.A.) ln (i) Given y i.e. y... (i) And y( )..(ii) From (i), substitute y into (ii): shown (ii) From or (N.A) since When, y. Thus y. Therefore, length of HF is cm. (i) (ii) Substitute y k into y k : k k k k k or which are the -coordinates of points of intersection of C & L. k Area Area of under the curve from to k Area of the rectangle with sides and k Note: Alternatively, the area can be epressed as k k k d k
2 k k d k k k k 8 k k k k 6 k (i)(a) d ln = 6 d (i)(b) d 8 = 8 d (ii) d d ln 6 ln 8 ln ln 5(i) y y Note: In general, there is a modulus for the ln in d ln C.767 O Points of intersection with the aes are.767,,.,,,, and 5(ii) From GC, the gradient of C at.5 is.986 =.95 correct to d.p. 5(iii) When.5, y Equation of tangent to C is Note: Equation of a straight line is y m c or we can
3 y y y That is, y correct to d.p. consider the form which is used y y m. here: 5 (iv) At y -ais, coordinates of A,.77 At y B.8,.8 coordinates of Length of AB correct to s.f. 6(i) 6(ii) Systematic sampling is a method of selecting members from an ordered sampling frame in such a way that the first member of the sample is randomly selected out of the first k members in the ordered sampling frame, followed by selecting every subsequent k th member from the ordered sampling frame for inclusion in the sample. number of members in sampling frame Here, k. sample size Advantage This method is cost effective. That is, it takes less time and effort to carry out. 6(iii) Disadvantage Not all adults will go to the supermarket at midday due to various reasons such as work etc. Thus the sample collected may not be representative of the town people. One possible way to carry out a more appropriate systematic sampling is to obtain the list of all adults in that particular town, apply systematic sampling on it and call the adults selected in the sample to do the survey. Note: Since the objective is to survey on usage time on computer, the choice of doing survey outside the supermarket is irrelevant. 7(i) P A B P A PB P A B p p p A & B are independent. 9 p 5 5 p or 9p 8p 5 9
4 7(ii) From (i), p or 5 (N.A.) 8 P A B p 8(i) A M.5 P (ii) P( F ) = A B C M F M F M F 8(iii) 9 (i) P( C M ) = 5 y P C M.5. P M (ii) r.98 Since r.98 (correct to s.f.) is close to, it suggests there is a strong negative linear correlation between the advertised price and the age of Pluto cars. 9(iii) From GC, y That is, y correct to d.p. 9(iv) When, y 6.8 Thus, the estimated advertised price is $6. When 9, y. Thus, the estimated advertised price is $.
5 9(v) Since is within the data range, the estimate obtained in (a) is reliable but 9 is not within the given range of data ( we are doing etrapolation), hence the estimate obtained in (b) is unreliable. Let X be the number of Sunbrite plants that flower out of plants. X ~ B,.8. Then (i) P X.87.8 correct to s.f. (ii) P X 8 X P correct to s.f. (iii) (iv) Let Y be the number of Sunbrite plants that flower out of 96 plants (8 trays). Y ~ B 96,.8. Then n = 96 is large, np & nq 9. 5 Y C.C. ~ N 76.8,5.6 appro. Thus required probability is P Y 75 P Y correct to s.f. Let T be the number of gardeners who have more than 75 of their plants flower. T ~ B,.699. Then T P T P correct to s.f. (i) n, ( ) n ( ) s ( ) n n (ii) Let be the mean length of string in a ball. H : against H : at the 5% significance level X Test statistic, Z S Note: In the manager s claim that the average length is at least m, we test H : 5
6 Using z -test, from GC, p -value.7 correct to s.f. Since p -value =.7 <.5, we reject H at 5% level of significance and conclude that there is sufficient evidence to conclude that. Hence the manager s claim is not valid. (iii) H : against H : at the % significance level. k Test statistic, Z. For manager s claim to be valid, we have H not to be rejected. k Thus Z k (.855) k least k correct to d.p. Let X and Y be the masses of grapefruit of type A and B respectively. N.5,. Y N.5,. Then X and (i) Let the total mass of randomly chosen grapefruit of type A be X X... X. X X... X N.5,. Then X X... X ~ N.5,. Required probability P X X... X correct to s.f. 6
7 (ii) Let M be the total mass of 6 randomly chosen grapefruit of type A and Let M be the total mass of 5 randomly chosen grapefruit of type B. Then M M ~ N , (iii) M M ~ N.5,.69 Required probability is P( M M.) P(. M M.).76.7 correct to s.f. Let $W be the price paid by Mrs Woo. W.5 X X X. Y Y Y Then W ~ N ,.5... W ~ N.65,.85 Let $T be the price paid by Mr Tan. T.5 X X X. Then T T N.75,.9 N.5.5,.5. Therefore, W T N.65.75,.85.9 W T N.5,.75 Note: The phrase type A is within. kg of type B means type A grapefruits weigh at most. kg more than type B and at the same time, type A grapefruits weigh at most. kg less than type B. P( W T) P( W T ).67.6 correct to s.f. 7
The required region is shown in the diagram above. The
011 GCE A Level H1 Maths Solution SECTION A (PURE MATHEMATICS) 1 For x k x k 1 0 to be true for all real x, the discriminant That is, k k k 8k 0 k k8 0 D b 4ac must be negative. 4 1 0 The critical points
More informationNote: Students must indicate that the centre of the circle is at (7, 3) and that the radius is 4.
0 GCE A Level H Maths Solution Paper (a) dy 3 6 3 C d 3 y 8 C D (b) du dt 3u 3u ln 3 8 3u t C Substitute u, t 0 Note: Students must add in the arbitrary constant each time they work out an indefinite integral.
More information2009 GCE A Level H1 Mathematics Solution
2009 GCE A Level H1 Mathematics Solution 1) x + 2y = 3 x = 3 2y Substitute x = 3 2y into x 2 + xy = 2: (3 2y) 2 + (3 2y)y = 2 9 12y + 4y 2 + 3y 2y 2 = 2 2y 2 9y + 7 = 0 (2y 7)(y 1) = 0 y = 7 2, 1 x = 4,
More information2007 Paper 1 Solutions
27 Paper 1 Solutions 2x 2 x 19 x 2 + x + 2 1 = 2x2 x 19 (x 2 + x + 2) x 2 + x + 2 2x 2 x 19 x 2 + x + 2 > 1 2x 2 x 19 x 2 + x + 2 1 > x 2 4x 21 x 2 + x + 2 > (x + )(x 7) (x + 2)(x + 1) > = x2 4x 21 x 2
More informationGCE A Level H2 Mathematics November 2014 Paper 1. 1i) f 2 (x) = f( f(x) )
GCE A Level H Mathematics November 0 Paper i) f () f( f() ) f ( ),, 0 Let y y y y y y y f (). D f R f R\{0, } f () f (). Students must know that f () stands for f (f() ) and not [f()]. Students must also
More information2017 Promotional Examination II Pre-University 2
Class Adm No Candidate Name: 017 Promotional Eamination II Pre-University MATHEMATICS 8865/01 Paper 1 1 September 017 Additional Materials: Answer Paper List of Formulae (MF 6) 3 hours READ THESE INSTRUCTIONS
More information2016 VJC JC2 Prelim Paper 2 Solutions/Comments
6 VJC JC Prelim Paper s/comments Qn i Since speed is decreasing and v is positive, dv kv, where k is a positive constant dt dv k v dt d v k d t v ln v kt C v v Be kt When t = s, v = D m s - B = D Let k
More informationYISHUN JUNIOR COLLEGE 2017 JC2 Preliminary Examination
YISHUN JUNIOR COLLEGE 07 JC Preliminary Examination MATHEMATICS 8864/0 HIGHER 8 AUGUST 07 MONDAY 0800h 00h Additional materials : Answer paper List of Formulae (MF5) TIME 3 hours READ THESE INSTRUCTIONS
More informationThe 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(a) Show that there is a root α of f (x) = 0 in the interval [1.2, 1.3]. (2)
. f() = 4 cosec 4 +, where is in radians. (a) Show that there is a root α of f () = 0 in the interval [.,.3]. Show that the equation f() = 0 can be written in the form = + sin 4 Use the iterative formula
More information2009 GCE A Level Solution Paper 1
2009 GCE A Level Solution Paper i) Let u n = an 2 + bn + c. u = a + b + c = 0 u 2 = 4a + 2b + c = 6 u 3 = 9a + 3b + c = 5 Using GC, a =.5, b = 8.5, c = 7. u n =.5n 2 8.5n + 7. (ii) Let y =.5n 2 8.5n +
More informationSolutionbank Edexcel AS and A Level Modular Mathematics
Page of Exercise A, Question The curve C, with equation y = x ln x, x > 0, has a stationary point P. Find, in terms of e, the coordinates of P. (7) y = x ln x, x > 0 Differentiate as a product: = x + x
More informationAdd 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 informationAdd Math (4047) Paper 2
1. Solve the simultaneous equations 5 and 1. [5]. (i) Sketch the graph of, showing the coordinates of the points where our graph meets the coordinate aes. [] Solve the equation 10, giving our answer correct
More informationd y 2016 PU3H2 Prelims 2 Paper 2 Marking Scheme 1i) Alternatively, e (2) When x=0, y e 1, 2, 4, By Maclaurin Series, 1ii) 1
06 PU3H Prelims Paper Marking Scheme S/N i) ln y sin dy yd dy yd 4 dy d 4 y (shown) () SOLUTION d y dy d 4 y 4 ( 8 ) d d d 0 dy d y When =0, y e,, 4, d d By Maclaurin Series, 4 y... y ii) ln y sin y e
More information(c) Find the gradient of the graph of f(x) at the point where x = 1. (2) The graph of f(x) has a local maximum point, M, and a local minimum point, N.
Calculus Review Packet 1. Consider the function f() = 3 3 2 24 + 30. Write down f(0). Find f (). Find the gradient of the graph of f() at the point where = 1. The graph of f() has a local maimum point,
More informationS2 QUESTIONS TAKEN FROM JANUARY 2006, JANUARY 2007, JANUARY 2008, JANUARY 2009
S2 QUESTIONS TAKEN FROM JANUARY 2006, JANUARY 2007, JANUARY 2008, JANUARY 2009 SECTION 1 The binomial and Poisson distributions. Students will be expected to use these distributions to model a real-world
More informationPAPER A numerical answers. 1 Proof by forming quadratic >0 then sh0w quadratic has no solutions using discriminant b 2 4ac < 0 or similar method
PAPER A numerical answers 1 Proof by forming quadratic >0 then sh0w quadratic has no solutions using discriminant b 4ac < 0 or similar method 9a 51 + 04px + 4608 p x + 576 p x + a 5y + 9x 1 = 0 9b p =
More informationDifferentiation. Each correct answer in this section is worth two marks. 1. Differentiate 2 3 x with respect to x. A. 6 x
Differentiation Paper 1 Section A Each correct answer in this section is worth two marks. 1. Differentiate 2 3 with respect to. A. 6 B. 3 2 3 4 C. 4 3 3 2 D. 2 3 3 2 Ke utcome Grade Facilit Disc. Calculator
More informationu x y reduces the differential equation
CATHOLIC JUNIOR COLLEGE H MATHEMATICS 06 JC PRELIM Paper (i) Prove that the substitution (ii) (i) Given u x y, du dy x y dx dx du dy x y ----------- (I) dx dx Substitute (I) & u x y and into D.E: we get
More information1. (a) B, D A1A1 N2 2. A1A1 N2 Note: Award A1 for. 2xe. e and A1 for 2x.
1. (a) B, D N (b) (i) f () = e N Note: Award for e and for. (ii) finding the derivative of, i.e. () evidence of choosing the product rule e.g. e e e 4 e f () = (4 ) e AG N0 5 (c) valid reasoning R1 e.g.
More informationLINEARIZATION OF GRAPHS
LINEARIZATION OF GRAPHS Question 1 (**) The table below shows eperimental data connecting two variables and y. 1 2 3 4 5 y 12.0 14.4 17.3 20.7 27.0 It is assumed that and y are related by an equation of
More informationSL - Binomial Questions
IB Questionbank Maths SL SL - Binomial Questions 262 min 244 marks 1. A random variable X is distributed normally with mean 450 and standard deviation 20. Find P(X 475). Given that P(X > a) = 0.27, find
More informationA-level MATHEMATICS. Paper 3. Exam Date Morning Time allowed: 2 hours SPECIMEN MATERIAL
SPECIMEN MATERIAL Please write clearly, in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature A-level MATHEMATICS Paper 3 Exam Date Morning Time allowed: 2 hours Materials
More informationACS MATHEMATICS GRADE 10 WARM UP EXERCISES FOR IB HIGHER LEVEL MATHEMATICS
ACS MATHEMATICS GRADE 0 WARM UP EXERCISES FOR IB HIGHER LEVEL MATHEMATICS DO AS MANY OF THESE AS POSSIBLE BEFORE THE START OF YOUR FIRST YEAR IB HIGHER LEVEL MATH CLASS NEXT SEPTEMBER Write as a single
More informationARE YOU READY FOR CALCULUS?? Name: Date: Period:
ARE YOU READY FOR CALCULUS?? Name: Date: Period: Directions: Complete the following problems. **You MUST show all work to receive credit.**(use separate sheets of paper.) Problems with an asterisk (*)
More informationMath Contest Level 2 - March 6, Coastal Carolina University
Math Contest Level 2 - March 6, 2015 Coastal Carolina University 1. Which of one of the following points is on an asymptote to the hyperbola 16x 2 9y 2 = 144? a) (16, 9) b) (12, 16) c) (9, 4) d) (9, 16)
More informationMATHEMATICS 8865/01 Paper 1 13 September hours
Candidate Name: Class: JC PRELIMINARY EXAMINATION Higher 1 MATHEMATICS 8865/01 Paper 1 13 September 017 3 hours Additional Materials: Cover page Answer papers List of Formulae (MF6) READ THESE INSTRUCTIONS
More informationDifferentiating Functions & Expressions - Edexcel Past Exam Questions
- Edecel Past Eam Questions. (a) Differentiate with respect to (i) sin + sec, (ii) { + ln ()}. 5-0 + 9 Given that y =, ¹, ( -) 8 (b) show that = ( -). (6) June 05 Q. f() = e ln, > 0. (a) Differentiate
More informationabc Mathematics Further Pure General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES
abc General Certificate of Education Mathematics Further Pure SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER
More information2. Jan 2010 qu June 2009 qu.8
C3 Functions. June 200 qu.9 The functions f and g are defined for all real values of b f() = 4 2 2 and g() = a + b, where a and b are non-zero constants. (i) Find the range of f. [3] Eplain wh the function
More informationASSIGNMENT COVER SHEET omicron
ASSIGNMENT COVER SHEET omicron Name Question Done Backpack Ready for test Drill A differentiation Drill B sketches Drill C Partial fractions Drill D integration Drill E differentiation Section A integration
More informationExam-style practice: Paper 3, Section A: Statistics
Exam-style practice: Paper 3, Section A: Statistics a Use the cumulative binomial distribution tables, with n = 4 and p =.5. Then PX ( ) P( X ).5867 =.433 (4 s.f.). b In order for the normal approximation
More informationy=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions
AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions. Which of the following integrals correctly corresponds to the area of the shaded region in the figure to the right? (A) (B) (C) (D) (E)
More information5 Find an equation of the circle in which AB is a diameter in each case. a A (1, 2) B (3, 2) b A ( 7, 2) B (1, 8) c A (1, 1) B (4, 0)
C2 CRDINATE GEMETRY Worksheet A 1 Write down an equation of the circle with the given centre and radius in each case. a centre (0, 0) radius 5 b centre (1, 3) radius 2 c centre (4, 6) radius 1 1 d centre
More informationand show that In the isosceles triangle PQR, PQ = 2 and the angle QPR = angle PQR 1 radians. The area of triangle PQR is denoted by A.
H Mathematics 07 Prelim Eam Paper Question Answer all questions [00 marks]. n n Given that k!( k ) ( n )! n, find ( k )!( k k ). [] k k A geometric sequence U, U, U,... is such that T, T, T,... U and has
More information6675/01 Edexcel GCE Pure Mathematics P5 Further Mathematics FP2 Advanced/Advanced Subsidiary
6675/1 Edecel GCE Pure Mathematics P5 Further Mathematics FP Advanced/Advanced Subsidiary Monday June 5 Morning Time: 1 hour 3 minutes 1 1. (a) Find d. (1 4 ) (b) Find, to 3 decimal places, the value of.3
More informationCHAPTER 2 LINEAR LAW FORM 5 PAPER 1. Diagram 1 Diagram 1 shows part of a straight line graph drawn to represent
PAPER. n ( 8, k ) Diagram Diagram shows part of a straight line graph drawn to represent and n.. Find the values of k [4 marks] 2. log ( 3,9 ) ( 7,) log Diagram 2 Diagram 2 shows part of a straight line
More informationCALCULUS AP BC Q301CH5A: (Lesson 1-A) AREA and INTEGRAL Area Integral Connection and Riemann Sums
CALCULUS AP BC Q301CH5A: (Lesson 1-A) AREA and INTEGRAL Area Integral Connection and Riemann Sums INTEGRAL AND AREA BY HAND (APPEAL TO GEOMETRY) I. Below are graphs that each represent a different f()
More informationMathematics Extension 2
009 TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Etension General Instructions o Reading Time- 5 minutes o Working Time hours o Write using a blue or black pen o Approved calculators may be
More informationSummer Review Packet. for students entering. IB Math SL
Summer Review Packet for students entering IB Math SL The problems in this packet are designed to help you review topics that are important to your success in IB Math SL. Please attempt the problems on
More informationMATHEMATICS. NORTH SYDNEY BOYS HIGH SCHOOL 2008 Trial HSC Examination STUDENT NUMBER:... QUESTION Total %
008 Trial HSC Eamination MATHEMATICS General instructions Working time 3 hours. plus 5 minutes reading time) Write on the lined paper in the booklet provided. Each question is to commence on a new page.
More informationCircle. Paper 1 Section A. Each correct answer in this section is worth two marks. 5. A circle has equation. 4. The point P( 2, 4) lies on the circle
PSf Circle Paper 1 Section A Each correct answer in this section is worth two marks. 1. A circle has equation ( 3) 2 + ( + 4) 2 = 20. Find the gradient of the tangent to the circle at the point (1, 0).
More informationCore Mathematics 2 Geometric Series
Core Mathematics 2 Geometric Series Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Geometric Series 1 Geometric series The sum of a finite geometric series; the sum to infinity of
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 Centre Number Mathematics B Paper 1R Candidate Number Monday 8 January 2018 Morning Time: 1 hour 30 minutes Paper Reference 4MB0/01R
More informationIB Math Standard Level 2-Variable Statistics Practice SL 2-Variable Statistics Practice from Math Studies
IB Math Standard Level -Variable Statistics Practice SL -Variable Statistics Practice from Math Studies 1. The figure below shows the lengths in centimetres of fish found in the net of a small trawler.
More informationSection A : Pure Mathematics [40 Marks]
H1 Mathematics 017 Preliminary Eam Paper Question Section A : Pure Mathematics [40 Marks] 1. Whole Food Grocer was having sales and some food items were on offer. Organic feed eggs were having a 1% discount.
More informationFP1 PAST EXAM QUESTIONS ON NUMERICAL METHODS: NEWTON-RAPHSON ONLY
FP PAST EXAM QUESTIONS ON NUMERICAL METHODS: NEWTON-RAPHSON ONLY A number of questions demand that you know derivatives of functions now not included in FP. Just look up the derivatives in the mark scheme,
More informationb (3 s.f.). b Make sure your hypotheses are clearly written using the parameter ρ:
Review exercise 1 1 a Produce a table for the values of log s and log t: log s.31.6532.7924.8633.959 log t.4815.67.2455.3324.4698 which produces r =.9992 b Since r is very close to 1, this indicates that
More informationNAME: PAPER I Date to be handed in: MARK (out of 60):
NAME: PAPER I Date to be handed in: MARK (out of 60): Qu 1 2 3 4 5 6 7 TOTAL Paper 2: Statistics and Mechanics Time 1 hour 15 minutes Practice Paper I Questions to revise: 1 SECTION A: Statistics 1. An
More information1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.
Higher Maths Non Calculator Practice Practice Paper A. A sequence is defined b the recurrence relation u u, u. n n What is the value of u?. The line with equation k 9 is parallel to the line with gradient
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 information1. Given the function f (x) = x 2 3bx + (c + 2), determine the values of b and c such that f (1) = 0 and f (3) = 0.
Chapter Review IB Questions 1. Given the function f () = 3b + (c + ), determine the values of b and c such that f = 0 and f = 0. (Total 4 marks). Consider the function ƒ : 3 5 + k. (a) Write down ƒ ().
More informationMath 10 - Compilation of Sample Exam Questions + Answers
Math 10 - Compilation of Sample Exam Questions + Sample Exam Question 1 We have a population of size N. Let p be the independent probability of a person in the population developing a disease. Answer the
More informationThe normal distribution Mixed exercise 3
The normal distribution Mixed exercise 3 ~ N(78, 4 ) a Using the normal CD function, P( 85).459....4 (4 d.p.) b Using the normal CD function, P( 8).6946... The probability that three men, selected at random,
More informationSolutions to O Level Add Math paper
Solutions to O Level Add Math paper 4. Bab food is heated in a microwave to a temperature of C. It subsequentl cools in such a wa that its temperature, T C, t minutes after removal from the microwave,
More informationy=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions
AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions. Which of the following integrals correctly corresponds to the area of the shaded region in the figure to the right? (A) (B) (C) (D) (E)
More informationSolutionbank Edexcel AS and A Level Modular Mathematics
Page of Exercise A, Question Use the binomial theorem to expand, x
More informationTopic 6: Calculus Integration Markscheme 6.10 Area Under Curve Paper 2
Topic 6: Calculus Integration Markscheme 6. Area Under Curve Paper. (a). N Standard Level (b) (i). N (ii).59 N (c) q p f ( ) = 9.96 N split into two regions, make the area below the -ais positive RR N
More informationIB Practice - Calculus - Differentiation Applications (V2 Legacy)
IB Math High Level Year - Calc Practice: Differentiation Applications IB Practice - Calculus - Differentiation Applications (V Legacy). A particle moves along a straight line. When it is a distance s from
More informationLesson 18 - Solving & Applying Exponential Equations Using Logarithms
Lesson 18 - Solving & Applying Exponential Equations Using Logarithms IB Math HL1 - Santowski 1 Fast Five! Solve the following:! (a) 5 x = 53! (b) log 3 38=x! (c) Solve 2 x = 7. HENCE, ALGEBRAICALLY solve
More informationNational Quali cations
National Quali cations AH017 X70/77/11 Mathematics of Mechanics MONDAY, 9 MAY 1:00 PM :00 PM Total marks 100 Attempt ALL questions. You may use a calculator. Full credit will be given only to solutions
More informationVersion 1,0. General Certificate of Education (A-level) June 2012 MPC3. Mathematics. (Specification 6360) Pure Core 3. Mark Scheme
Version,0 General Certificate of Education (A-level) June 0 Mathematics MPC (Specification 660) Pure Core Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together with the
More informationAdditional Math (4047) Paper 1(80 marks)
Aitional Math (07) Prepare b Mr Ang, Nov 07 A curve is such that 6 8 an the point P(, 8) lies on the curve. The graient of the curve at P is. Fin the equation of the curve. [6] C where C is an integration
More information1. Calculate the gradients of the lines AB and CD shown below. (2) (a) Find the gradient of the line AB. (2)
DETERMINING the EQUATION of a STRAIGHT LINE 1. alculate the gradients of the lines AB and D shown below. (2) A B 0 x D 2. A line passes through the points A( 2, 4) and B(8, 1). (a) Find the gradient of
More informationMATH 236 ELAC FALL 2017 CA 9 NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
MATH 236 ELAC FALL 207 CA 9 NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ) 27 p 3 27 p 3 ) 2) If 9 t 3 4t 9-2t = 3, find t. 2) Solve the equation.
More informationMath : Analytic Geometry
7 EP-Program - Strisuksa School - Roi-et Math : Analytic Geometry Dr.Wattana Toutip - Department of Mathematics Khon Kaen University 00 :Wattana Toutip wattou@kku.ac.th http://home.kku.ac.th/wattou 7 Analytic
More informationMathematics (JAN13MPC301) General Certificate of Education Advanced Level Examination January Unit Pure Core TOTAL
Centre Number Candidate Number For Eaminer s Use Surname Other Names Candidate Signature Eaminer s Initials Mathematics Unit Pure Core Wednesday January General Certificate of Education Advanced Level
More informationEdexcel GCE A Level Maths. Further Maths 3 Coordinate Systems
Edecel GCE A Level Maths Further Maths 3 Coordinate Sstems Edited b: K V Kumaran kumarmaths.weebl.com 1 kumarmaths.weebl.com kumarmaths.weebl.com 3 kumarmaths.weebl.com 4 kumarmaths.weebl.com 5 1. An ellipse
More informationAnglo-Chinese Junior College H2 Mathematics JC 2 PRELIM PAPER 1 Solutions
Anglo-Chnese Junor College H Mathematcs 97 8 JC PRELIM PAPER Solutons ( ( + + + + + 8 range of valdty: > or < but snce number, reject < wll result n the sq rt of a negatve . no. of
More informationGeneral Certificate of Education Advanced Level Examination January 2010
General Certificate of Education Advanced Level Eamination January 00 Mathematics MPC3 Unit Pure Core 3 Friday 5 January 00.30 pm to 3.00 pm For this paper you must have: an 8-page answer book the blue
More information1. Joseph runs along a long straight track. The variation of his speed v with time t is shown below.
Kinematics 1. Joseph runs along a long straight track. The variation of his speed v with time t is shown below. After 25 seconds Joseph has run 200 m. Which of the following is correct at 25 seconds? Instantaneous
More informationComplete Solutions to Examination Questions Complete Solutions to Examination Questions 16
Complete Solutions to Examination Questions 16 1 Complete Solutions to Examination Questions 16 1. The simplest way to evaluate the standard deviation and mean is to use these functions on your calculator.
More informationE Math (4016/01) Total marks : 80. x 1. Solve Answer x = [1]
Requirement : Answer all questions Total marks : 80 Duration : hours x 1. Solve 14 8. 5 8 14 30 x 5 Answer x = [1]. Frank bought an antique vase for $345. One year later he sold it for a profit of 180%
More informationFormulae to Learn. The Rules for Differentiation are. The instructions are to either: Find ( or ), or
Differentiation Formulae to Learn The Rules for Differentiation are The instructions are to either: Find ( or ), or Differentiate, or Find the derived function, or Find the derivative. the curve. finds
More informationANOTHER FIVE QUESTIONS:
No peaking!!!!! See if you can do the following: f 5 tan 6 sin 7 cos 8 sin 9 cos 5 e e ln ln @ @ Epress sin Power Series Epansion: d as a Power Series: Estimate sin Estimate MACLAURIN SERIES ANOTHER FIVE
More information8864/01 October/November MATHEMATICS (H1) Paper 1 Suggested Solutions. 3. Topic: Graphs
MATHEMATICS (H1) Paper 1 Suggested Solutions 8864/01 October/November 2010 3. Topic: Graphs (i) y = ln(2x 3) Equation of asymptote: 2x 3 = 0 x = 3 2 Using G. C. (refer to Appendix for detailed steps),
More information4024 MATHEMATICS 4024/02 Paper 2, maximum raw mark 100
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level www.xtremepapers.com MARK SCHEME for the May/June 009 question paper for the guidance of teachers 404 MATHEMATICS 404/0 Paper, maimum
More informationHALF YEARLY EXAMINATIONS 2015/2016
FORM 4 SECONDARY SCHOOLS HALF YEARLY EXAMINATIONS 2015/2016 MATHS NON-CALCULATOR PAPER Track 3 Time: 20 min Name: Non-Calculator Paper Class: Answer all questions. Each question carries 1 mark. Question
More information2001 Higher Maths Non-Calculator PAPER 1 ( Non-Calc. )
001 PAPER 1 ( Non-Calc. ) 1 1) Find the equation of the straight line which is parallel to the line with equation x + 3y = 5 and which passes through the point (, 1). Parallel lines have the same gradient.
More informationHWA CHONG INSTITUTION JC2 PRELIMINARY EXAMINATION Wednesday 14 September hours. List of Formula (MF15)
1 HWA CHONG INSTITUTION JC PRELIMINARY EXAMINATION 016 MATHEMATICS Higher 1 8864/01 Paper 1 Wednesday 14 September 016 3 hours Additional materials: Answer paper List of Formula (MF15) READ THESE INSTRUCTIONS
More informationMATHEMATICS AS/P2/M18 AS PAPER 2
Surname Other Names Candidate Signature Centre Number Candidate Number Examiner Comments Total Marks MATHEMATICS AS PAPER 2 March Mock Exam (Edexcel Version) CM Time allowed: 1 hour and 15 minutes Instructions
More information2015 CCHY Midyear 4E5N Additional Maths P2 Marking Scheme [M1] [M1] [A1] [M1] [A1]
05 CCHY Midear 4E5N Additional Maths P Marking Scheme (i) Side 4 8 8 6 [M] 8 8 6 48 [M] 0 0 6 [A] (ii) B Pthagoras Theorem, Longest side 0 6 [M] 00 0 08 [A] f ( ) (i) Divisible b f 0 7 8 () 7 8 9 6 0 0
More informationPractice Lesson 11-1 Practice Algebra 1 Chapter 11 "256 "32 "96. "65 "2a "13. "48n. "6n 3 "180. "25x 2 "48 "10 "60 "12. "8x 6 y 7.
Practice 11-1 Simplifying Radicals Simplify each radical epression. 1. "32 2. "22? "8 3. "147 4. 17 5. "a 2 b 5 Ä 144 6. 2 "256 7. "80 8. "27 9. 10. 8 "6 "32 "7 "96 11. "12 4 12. 13. "200 14. 12 15. "15?
More informationIntegration Past Papers Unit 2 Outcome 2
Integration Past Papers Unit 2 utcome 2 Multiple Choice Questions Each correct answer in this section is worth two marks.. Evaluate A. 2 B. 7 6 C. 2 D. 2 4 /2 d. 2. The diagram shows the area bounded b
More information2 nd ORDER O.D.E.s SUBSTITUTIONS
nd ORDER O.D.E.s SUBSTITUTIONS Question 1 (***+) d y y 8y + 16y = d d d, y 0, Find the general solution of the above differential equation by using the transformation equation t = y. Give the answer in
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 000 MATHEMATICS /3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of equal
More informationAS Level / Year 1 Edexcel Maths / Paper 2
AS Level / Year 1 Edexcel Maths / Paper 2 March 2018 Mocks 2018 crashmaths Limited 1 (a) For every (extra) 1 mile per hour Callum travels in his car, his car s average fuel consumption decreases by 0.46
More informationSAMPLE. paper provided. Each question carries 2 marks. Marks will not be. from any one option. Write your answers on the answer paper provided.
UNIVERSITY ENTRANCE EXAMINATION 2017 MATHEMATICS ( A LEVEL EQUIVALENT) Duration: 2 hours INSTRUCTIONS TO CANDIDATES 1. This examination paper has TWO (2) sections A and B, and comprises SIXTEEN (16) printed
More informationPaper Reference. Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes. Mathematical Formulae (Orange or Green)
Centre No. Candidate No. Paper Reference(s) 6665/01 Edecel GCE Core Mathematics C3 Advanced Thursday 11 June 009 Morning Time: 1 hour 30 minutes Materials required for eamination Mathematical Formulae
More informationFor use only in [your school] Summer 2012 IGCSE-F1-02f-01 Fractions-Addition Addition and Subtraction of Fractions (Without Calculator)
IGCSE-F1-0f-01 Fractions-Addition Addition and Subtraction of Fractions (Without Calculator) 1. Calculate the following, showing all you working clearly (leave your answers as improper fractions where
More information= f (x ), recalling the Chain Rule and the fact. dx = f (x )dx and. dx = x y dy dx = x ydy = xdx y dy = x dx. 2 = c
Separable Variables, differential equations, and graphs of their solutions This will be an eploration of a variety of problems that occur when stuing rates of change. Many of these problems can be modeled
More informationHigher. Specimen NAB Assessment
hsn.uk.net Higher Mathematics UNIT Specimen NAB Assessment HSN0 This document was produced speciall for the HSN.uk.net website, and we require that an copies or derivative works attribute the work to Higher
More informationCore Mathematics C3 Advanced Level
Paper Reference(s) 666/0 Edecel GCE Core Mathematics C Advanced Level Wednesda 0 Januar 00 Afternoon Time: hour 0 minutes Materials required for eamination Mathematical Formulae (Pink or Green) Items included
More informationDifferentiation Past Papers Unit 1 Outcome 3
PSf Differentiation Past Papers Unit 1 utcome 3 1. Differentiate 2 3 with respect to. A. 6 B. 3 2 3 4 C. 4 3 3 2 D. 2 3 3 2 2 2. Given f () = 3 2 (2 1), find f ( 1). 3 3. Find the coordinates of the point
More informationSolutions to O Level Add Math paper
Solutions to O Level Add Math paper 04. Find the value of k for which the coefficient of x in the expansion of 6 kx x is 860. [] The question is looking for the x term in the expansion of kx and x 6 r
More informationMATHEMATICS 9740/02 Paper 2 16 Sep hours
Candidate Name: Class: JC2 PRELIMINARY EXAM Higher 2 MATHEMATICS 9740/02 Paper 2 6 Sep 206 3 hours Additional Materials: Cover page Answer papers List of Formulae (MF5) READ THESE INSTRUCTIONS FIRST Write
More informationThird Annual NCMATYC Math Competition November 16, Calculus Test
Third Annual NCMATYC Math Competition November 6, 0 Calculus Test Please do NOT open this booklet until given the signal to begin. You have 90 minutes to complete this 0-question multiple choice calculus
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)
N E W S O U T H W A L E S HIGHER SCHOOL CERTIFICATE EXAMINATION 996 MATHEMATICS /3 UNIT (COMMON) Time allowed Three hours (Plus minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL
More information2. Topic: Series (Mathematical Induction, Method of Difference) (i) Let P n be the statement. Whenn = 1,
GCE A Level October/November 200 Suggested Solutions Mathematics H (9740/02) version 2. MATHEMATICS (H2) Paper 2 Suggested Solutions 9740/02 October/November 200. Topic:Complex Numbers (Complex Roots of
More information