PRE-LEAVING CERTIFICATE EXAMINATION, 2015 MARKING SCHEME MATHEMATICS HIGHER LEVEL
|
|
- Ruby Malone
- 5 years ago
- Views:
Transcription
1 PRE-LEAVING CERTIFICATE EXAMINATION, 05 MARKING SCHEME MATHEMATICS HIGHER LEVEL Page of 40
2 OVERVIEW OF MARKING SCHEME Scale label A B C D E No of categories mark scale 0, 5 0,, 5 0,,, 5 0 mark scale 0, 0 0, 5, 0 0,, 7, 0 0,, 5, 8, 0 5 mark scale 0, 5 0, 7, 5 0, 5, 0, 5 0, 4, 7,, 5 0 mark scale 0, 0 0, 0, 0 0, 7,, 0 0, 5, 0, 5, 0 5 mark scale 0, 5 0,, 5 0, 8, 7, 5 0, 6,, 9, 5 0, 5, 0, 5, 0, 5 A general descriptor of each point on each scale is given below. More specific directions in relation to interpreting the scales in the context of each question are given in the body of the scheme, where necessary. Marking scales level descriptors A-scales (two categories) incorrect response (no credit) correct response (full credit) B-scales (three categories) response of no substantial merit (no credit) partially correct response (partial credit) correct response (full credit) C-scales (four categories) response of no substantial merit (no credit) response with some merit (low partial credit) almost correct response (high partial credit) correct response (full credit) D-scales (five categories) response of no substantial merit (no credit) response with some merit (low partial credit) response about half-right (middle partial credit) almost correct response (high partial credit) correct response (full credit) E-scales (six categories) response of no substantial merit (no credit) response with some merit (low partial credit) response about half-right (lower middle partial credit) response more than half-right (upper middle partial credit) almost correct response (high partial credit) correct response (full credit) Marking categories for all questions are shown throughout the solutions. In certain cases, typically involving rounding or omission of units, a mark that is one mark below the full-credit mark may also be awarded. Such cases are flagged with an asterisk. Thus, for example, Scale 0C* indicates that 9 marks may be awarded. Page of 40
3 Part (a) Part (b) Part (c) Part (d) PAPER QUESTION Scale 0C (a) What is a proof by contradiction? A proof by contradiction is a proof that establishes the validity of a proposition by showing that the proposition being false would imply a contradiction Or similar. Partial Credit ( Marks) Partially correct (b) What is an irrational number? Give an example of an irrational number. Cannot be written in the form b a where a, b Z and b 0. i.e. cannot be written as a fraction Partial Credit ( Marks) Partially correct Page of 40
4 (c) Shade in the region of the following Venn diagram that represents the set of irrational numbers. R Z N Partial Credit ( Marks) Partially correct (d) Use a proof by contradiction to prove that is an irrational number. Full Credit (0 Marks) High Partial Credit (7 Marks) error in proof Low Partial Credit ( Marks) in proof Page 4 of 40
5 Part (a) Part (b) Part (c) QUESTION Scale 5C Scale 0C Scale 0C (a) Simplify: x y 4 y y y + y x + x 6 x 4 y y y y + y x + x 6 ( x )( x + ) y y + y y( y + ) ( x + )( x ) ( x + )( y ) x + ( ) ( )( ) High Partial Credit ( Marks) No more than error Low Partial Credit ( Marks) x (b) Solve the inequality, <, x 4 x + 4 and x R. ( x )( x + 4) ( x + 4) < x + 4 x + 0x 8 < x + 6x + x 6x 40 < 0 x = 4 x = 0 4 < x < 0 or on a graph correctly indicated Full Credit (0 Marks) High Partial Credit (7 Marks) error and continues to end correctly Low Partial Credit ( Marks) x + 4 but continues Does not multiply by ( ) Page 5 of 40
6 (c) Solve the simultaneous equations: x + y 4z = x + y + z = x y + z = x =, y =, z = Full Credit (0 Marks) High Partial Credit (7 Marks) No more than errors and continues to end Low Partial Credit ( Marks) Page 6 of 40
7 Part (a) Part (b) Part (c) QUESTION Scale 0C Scale 0C (a) Examine the graph of the polynomial shown. Write down the polynomial for the graph in 4 the form ax + bx + cx + dx + e, where a, b, c, d, e R. x =, x =, x =, x = 4 ( x + )( x )( x )( x 4) = 0 4 x 4x x + 4x 8 = 0 Full Credit (0 Marks) High Partial Credit (7 Marks) No more than errors and continues to end Low Partial Credit ( Marks) (b) Investigate if x is a factor of 6x 5x + 4x + 5. x = 6 5 x is not a factor Partial Credit ( Marks) Partially correct No conclusion = 6 Page 7 of 40
8 (c) Given that x + ax is a factor of + px + qx + r = 0 ( x + ax )( x + t) = x + px + qx + r x + tx + ax + atx x t = x + px + qx + r Equating Coefficients t + a = p t = p a at = q t = r q = a r = ar + ( ) ( ) ***Accept other valid methods for full credit Full Credit (0 Marks) x, show that = ( ar +) High Partial Credit (7 Marks) Correct long division but fails to find correct form Sets up correct equation, multiplies but final answer not in correct form Low Partial Credit ( Marks) q. Page 8 of 40
9 Part (a) Part (b) (i) (ii) QUESTION 4 Scale 5C Scale 0C Scale 0C (a) Label each of the complex numbers given the following information. z = z z 4 = iz z = z High Partial Credit ( Marks) correct Low Partial Credit ( Marks) correct (b) (i) Given ω = + i, write ω in Polar Form. + π π i = 4cos + i sin Full Credit (0 Marks) High Partial Credit (7 Marks) Correct Modulus Correct Angle Low Partial Credit ( Marks) Sketch of ω Page 9 of 40
10 Page 0 of 40 (ii) Hence solve the equation ω = 4 z. + = sin cos 4 4 π π i z 4 sin cos = π π π π n i n z = sin cos π π π π n i n z If = 0 n = i z If = n + + = i z If = n + + = i z If = n + + = i z Full Credit (0 Marks) High Partial Credit (7 Marks) No more than errors and continues to end Low Partial Credit ( Marks)
11 Part (a) Part (b) (i) (ii) Part (c) QUESTION 5 Scale 0C (a) Identify the following functions as injective, surjective or bijective. x f ( x) x f ( x) x f ( x) Bijective Injective Surjective Partial Credit ( Marks) One correct (b) The growth of a certain species of bacteria can be modelled with the equation N = Re kt. A science teacher puts 00 bacteria into nutrient agar plates (agar will act as a food source for the bacteria). Five hours later, there are 600 bacteria. (i) Calculate the value of k correct to four decimal places. 600 = 00e ln6 = k 5 k = k ( 5) Partial Credit ( Marks) Page of 40
12 (ii) After how many hours will the number of bacteria in the plate be,000? ( )t e ,000 = 00 ln0 = k k =.6 hours Partial Credit ( Marks) (c) Solve for x correct to two decimal places: ( ) 8 0 x+ x 0 = x+ x 0( ) 8 = 0 x x ( ) 0( ) 8 = 0 y 0y 8 = 0 ( y + )( y 4) y = or y = 4 x x or = 4 x =.6 Full Credit (0 Marks) High Partial Credit (7 Marks) Correct but fails to cancel incorrect solution No more than error in solving and cancels incorrect solution Low Partial Credit ( Marks) Page of 40
13 Part (a) (i) (ii) Part (b) Part (c) QUESTION 6 Scale 0C (a) Find: (i) ( x 4x ) + dx x + x x + c Partial Credit ( Marks) dx (ii) ( sin x cosx) cosx sin x + c Partial Credit ( Marks) x 8 (b) Evaluate dx x. x 8 = x ( x + x 4) + x + x + 4x ( ) = Partial Credit ( Marks) ( x )( x + x + 4) ( x ) 4 Page of 40
14 (c) Find the area enclosed by the x-axis and the curve y = x + x +. x + x + = 0 x = or x = x + x + x + x + ( ) + = 0 Full Credit (0 Marks) High Partial Credit (7 Marks) Error in solving but continues to end with no further error error in integration Low Partial Credit ( Marks) Page 4 of 40
15 Part (a) Part (b) Part (c) (i) (ii) (iii) QUESTION 7 Scale 0B Scale 5C Scale 0C Scale 0C Scale 5C (a) John wishes to borrow X from his bank over n years. Interest of r% APR will be applied to the loan. He will make an annual repayment of A. Show the amount owing at the end of the first year, P, can be written as: P = X ( + r)a F = P + F = X + P = ( r) t ( r) t X ( + r) A Full Credit (0 Marks) Partial Credit (5 Marks) (b) If P = 0 after the final year of the mortgage, show that the annual repayment A can be n written as P = X P n n = 0 0 = n Xr( + r) ( + r) A. = n n n n ( + r) A( + r) A( + r) A( + r) A n n n X ( + r) A( + r) A( + r) A( + r) A ( ) ( ) ( ) n ( ) n + r + A + r + + A + r + A + r = A( r) n ( + r) n A + A + A A ( ) ( ) n r Xr( + r) + r = n ( ) = X + r n High Partial Credit (0 Marks) Error in geometric progression and continues correctly to end Low Partial Credit (5 Marks) Page 5 of 40
16 (c) John borrows 50,000 over 0 years at 4% compound interest per annum. (i) Calculate the monthly interest rate correct to five significant figures. (.04) = Full Credit (0 Marks) High Partial Credit (7 Marks) Correct calculation but incorrect significant figures Low Partial Credit ( Marks) (ii) Calculate John s monthly repayment correct to the nearest euro. A = ( 50,000)( 0.007)( ) 40 ( ) A = = Full Credit (0 Marks) High Partial Credit (7 Marks) error in calculation Treats as power of 0 with no other error Low Partial Credit ( Marks) Page 6 of 40
17 (iii) After years, John decides to pay off the remainder of the loan in one lump sum. Calculate the remaining balance on the loan correct to the nearest euro. 8 years left = 96 months a = 90 and r = S 96 =.007 S = ( ) ( ) ( ) 95 High Partial Credit (0 Marks) Error in geometric progression and continues correctly to end Low Partial Credit (5 Marks) Page 7 of 40
18 QUESTION 8 Part (a) Scale 0B* Part (b) Scale 0B* Part (c) Scale 0B* Part (d) Scale 0B* Part (e) Scale 0C* A water trough is in the shape of a prism as shown. (a) Calculate the internal volume of the water trough. Vol = = Full Credit (0 Marks) ( )(.5)( 6) 9 m Partial Credit (5 Marks) (b) Write an equation to represent the volume ( V ) of water in the tank at any time t in terms of h and w. V = V = wh m ( w)( h)( 6) Full Credit (0 Marks) Partial Credit (5 Marks) 4 (c) Show that w = h metres. w h =.5 4 w = h metres Full Credit (0 Marks) Partial Credit (5 Marks) Page 8 of 40
19 (d) Show that the volume of the water tank can be expressed as: V = 4h. V = wh 4 V = h h V = 4h m Full Credit (0 Marks) Partial Credit (Marks) (e) If water is being pumped in at a constant rate of 5 m /s, at what rate is the height of the water changing when the water has a height of 0 cm? dh dv = dt dt dv = 8 h dh dh = dt dh dt () 5 dh dv 8. ( ) = 0.5 m/s Full Credit (0 Marks) High Partial Credit (7 Marks) error in calculation Low Partial Credit ( Marks) Page 9 of 40
20 Part (a) Part (b) Part (c) Part (d) Part (e) QUESTION 9 Scale 5C Scale 0B Scale 0C Scale 0B (a) Complete the following table Shape 4 Number of blocks High Partial Credit ( Marks) incorrect Low Partial Credit ( Marks) Any correct (b) Describe how the number of blocks is changing. Full Credit (0 Marks) Partial Credit (5 Marks) (c) How many blocks would be in the 5 th shape? 6 Partial Credit ( Marks) Page 0 of 40
21 (d) Write an expression in n for the number of blocks in the n th pattern in the sequence. nd Diff = 6 a = T n = an + bn + c T n = n + bn + c n = T = () + b() + c = b + c = n = T = ( ) + b( ) + c = 7 b + c = 5 b =, c = = n n + Full Credit (0 Marks) T n High Partial Credit (7 Marks) error solving to end Low Partial Credit ( Marks) (e) What shape will require 97 blocks to build it? n n + = 97 n n 96 = 0 n n = 0 ( n )( n +) n = th shape Full Credit (0 Marks) Partial Credit (5 Marks) Page of 40
22 Part (a) Part (b) Part (c) PAPER QUESTION Scale 0C Scale 0C Two lines make an angle of tan with the line t, where t : x + y =. 4 (a) Write down the slope of the line t. m = Partial Credit ( Marks) Some correct step towards finding the slope (b) Find the values of m, where m is the slope of the lines that intersect the line t. 4 4 m = ± + m = or ( )( m) m + ( )( m) + ( )( m) ( m) = 4( m) or ( m) = 4( m) 4 = m = 8 4m or m = 8 + 4m 9 7 m = or m = 6 Full Credit (0 Marks) High Partial Credit (7 Marks) error and continues to end correctly Low Partial Credit ( Marks) Page of 40
23 (c) Find the equations of both lines given that they both contain the point (, 5). 9 7 y 5 = ( x ) or y 5 = ( x ) 6 y 0 = 9x + 9 or 6 y 0 = 7x x + y 9 = 0 or 7 x + 6y 7 = 0 Full Credit (0 Marks) High Partial Credit (7 Marks) error and continues to end correctly Low Partial Credit ( Marks) Page of 40
24 Part (a) Part (b) Part (c) Part (d) QUESTION Scale 0C In a survey of 80 men and 60 women, 60% of each gender said that they smoked cigarettes. (a) Complete the following tree diagram. Full Credit (0 Marks) High Partial Credit (7 Marks) Correct tree diagram with no probabilities shown Correct tree diagram with incorrect consistent probabilities shown Low Partial Credit ( Marks) A person is chosen at random and sent a follow-up questionnaire. (b) Find the probability that the person chosen is a male who does not smoke. 8 5 Partial Credit ( Marks) Some correct step towards finding the slope 75% of the non-smokers having never smoked. 50% of those who have smoked are males. Page 4 of 40
25 (c) How many females were smokers but have quit? 7 Partial Credit ( Marks) Some correct step towards finding the slope The smoking ban was introduced in Ireland in 004. A government official claims that the number of smokers has fallen steadily since 004 and is significantly lower now than in 004. (d) Discuss the validity of his claim. Regular and heavy smokers numbers on the decline Light and occasional on the increase. Need further figures to determine if numbers have fallen significantly. Partial Credit ( Marks) Partial explanation Page 5 of 40
26 QUESTION Scale 5D Find the equation of a circle which contains the points (, 5) and (,) line x 5y = 4. x + y + gx + fy + c = 0 ( ) + () 5 + g ( ) + f () 5 + c = 0 6g + 0 f + c = 4 eg ( 7) + ( ) + g ( 7) + g( ) + c = 0 Centre ( g, f ) ( g ) 5( f ) = f = f = 4 4g + f + c = 70 eg g + 5 f = 4 eg g ( ) g ( 0) High Partial Credit (9 Marks) Error in equations but continues to end Equation of circle not written at end Mid Partial Credit ( Marks) Sets up two correct equations Low Partial Credit (6 Marks) 60 g + 6 f = g + 00 f = f = 7 f = 7, and whose centre lies on the Page 6 of 40
27 Part (a) Part (b) (i) (ii) (iii) QUESTION 4 Scale 0C The probability of a certain make of car breaking down within two years after it is purchased is 0.8. (a) Write the probability that the car will not break down within the two years. 0.8 = 8% = 4 50 Partial Credit ( Marks) (b) A local car dealer sold 0 of these cars in January 04. Calculate the probability that: (i) None of the cars will break down within the two year period ( 0.8) ( 0.8) = Partial Credit ( Marks) (ii) No more than two of the cars will break down within the two year period Full Credit (0 Marks) ( 0.8) ( 0.8) + ( 0.8) ( 0.8) + ( 0.8) ( 0.8) = High Partial Credit (7 Marks) One error Low Partial Credit ( Marks) Page 7 of 40
28 (iii) At least three of the cars will break down within the two year period = 0.75 Partial Credit ( Marks) Page 8 of 40
29 Part (a) Part (b) Part (c) QUESTION 5 Scale 5C Scale 5C (a) If sin A = 0. 69, find two values of A, correct to the nearest degree, where 0 A 60. A = 9, High Partial Credit ( Marks) Correct reference angle found with work towards finding two values of A Low Partial Credit ( Marks) (b) The lines q makes an acute angle with the x-axis as shown. (i) Write down the slope of the line q. m = 5 Partial Credit ( Marks) Some correct step towards finding the slope Page 9 of 40
30 tan α =. (ii) The line p makes an angle β with the x-axis such that ( + β ) 5 + tan β = β tan 5 Find the slope of the line p. + tan β = tan β tan β = 5 5 tan β = m = tan β = p High Partial Credit (0 Marks) Solves with no more than error Low Partial Credit (5 Marks) Page 0 of 40
31 Part (a) Part (b) QUESTION 6 Scale 0D (a) Prove that the angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc. Examine five sections of answer Diagram: To Prove: Given: CAD = CBD A circle with centre A and Points B, C and D on the circle as shown Construction: Join B to A and extend to E Proof: In the triangle BCE Full Credit (0 Marks) 5 sections fully correct AB = AC Radii ABC = ACB Theorem (isosceles ) X = ABC + ACB Theorem 6 (exterior angle) X = ABC + ABC X = ABC Similarly EAD = ABD CAD = CBD High Partial Credit (5 Marks) or 4 sections fully correct Mid Partial Credit (0 Marks) sections fully correct Low Partial Credit (5 Marks) Page of 40
32 (b) Hence find CGD. CGD = 08 Partial Credit ( Marks) Partially correct Page of 40
33 QUESTION 7 Part (a) Scale 0C* Part (b) Scale 5C Part (c) Scale 5A Part (d) Scale 5C Part (e) Scale 0B Part (f) Scale 5D (a) Calculate the distance from Ballyline to Dun Mór correct to one decimal place. x 6.6 = sin 75 sin 47. x = 8.7 km Full Credit (0 Marks) High Partial Credit (7 Marks) One error Low Partial Credit ( Marks) Due to the installation of water meters, the road from Ballyline to Dun Mór will be closed for a week. Traffic will be diverted via Deepdale. (b) Calculate the percentage increase in the distance motorists will have to travel due to the diversion if travelling from Ballyline to Dun Mór via Deepdale. x = sin 57.8 x = 7.6 % increase = 6.6 sin 47. ( ) High Partial Credit (0 Marks) One error Low Partial Credit (5 Marks) = 6.% 8.7 Each town will receive its water from a central reservoir after the water meters are installed. The reservoir will be equidistant from each town. Page of 40
34 (c) What name is given to the point equidistant from the three vertices of a triangle? Circumcentre. (d) Using a suitable construction, show where the reservoir will be situated on the diagram above. High Partial Credit (0 Marks) One bisector found correctly Low Partial Credit (5 Marks) Page 4 of 40
35 (e) Taking a scale of cm : km, estimate the shortest distance from the reservoir to each town. Accept range of 4. km to 4.8 km Full Credit (0 Marks) Partial Credit (5 Marks) Page 5 of 40
36 The County Planning Officer decides to double-check the above information by overlapping the information with a coordinate plane. (f) By choosing (0., 4.5) as coordinates for Ballyline, find the coordinates of the reservoir and verify your answer from part (e). **Note: Students answers may vary slightly due to rounding of decimals. Correct in Steps:. Two Midpoints. Slopes. equations of perpendicular bisectors 4. Simultaneous equation leading to a suitable x and y value 5. Distance within acceptable limits Deepdale to Dun Mór: Deepdale to Ballyline: m = = m = m = = m = y 0.5 = ( x 4.5) y.5 = ( x 0.55) 65 y.5 = 7x y 8.5 = 9x x + y = 9 x + 65y = 76. Mid =, = ( 4.5, 0.5) Mid =, = ( 0.55,.5) High Partial Credit ( Marks) or 4 correct steps Low Partial Credit (7 Marks) or correct steps 7 x + y = 9 x + 65y = x + 7y = 97 6 x + 455y = y = 8. y =.6 to.8 x =.5 to x =. 9 ( 8.9) + (. 7 ) 4. km Accept range 4. km to 4.8 km 9 65 Low Partial Credit (4 Marks) Any partially correct step Page 6 of 40
37 Part (a) (i) (ii) (iii) Part (b) (i) (ii) (iii) QUESTION 8 Scale 5C Scale 0B Scale 5C (a) A light bulb manufacturer claims that the lengths of the life of its bulbs have a mean of 6 months and a standard deviation of months. An independent research company tests a random sample of 60 bulbs to investigate the company s claim. (i) Calculate an approximate value for the standard deviation of the sample means. = Partial Credit ( Marks) Partially correct (ii) Assuming the company s claim is true, what is the probability that the research company s sample has a mean life of 5 months or less? x μ z = σ n 5 6 z = = P z.58 = P z <.58 = = = 0.49% ( ) ( ) High Partial Credit (0 Marks) Error in z value but continues to end correctly Low Partial Credit (5 Marks) Page 7 of 40
38 (iii) Based on this information, would you agree or disagree with the manufacturing company s claims? Explain your answer fully. As z >, the company s claim we do not agree with the company s claims. The calculated z score suggests the true mean is lower. Full Credit (0 Marks) Partial Credit (5 Marks) Partially correct (b) The manufacturing company claims that 90% of its customers find their bulbs good value for money. Out of 400 customers surveyed, 46 said that the light bulbs were good value for money. (i) State the null hypothesis. H : P 0 = 0.9 Partial Credit ( Marks) Partially correct (ii) State the alternate hypothesis. H : P 0.9 Partial Credit ( Marks) Partially correct Page 8 of 40
39 (iii) Use a hypothesis test to investigate the company s claim. 46 Step : p ˆ = = Step : E = = Step : < p < < p < 0.95 Step 4: population proportion is within the confidence interval. No evidence to reject the company s claims. ***Deduct one mark from a fully correct solution if a candidate states We accept the company s claim High Partial Credit (0 Marks) or correct steps Low Partial Credit (5 Marks) Page 9 of 40
40 QUESTION 9 Part (a) Scale 5C* Part (b) Scale 0C* A ranger in a forest can view two campsites from the top of the lookout tower which is 60 m high. The angle of depression to Campsite is 7. while the angle of depression with Campsite is 8.4. (a) Calculate the distance from the bottom of the tower to each campsite correct to one decimal place tan 7. = tan 8.4 = x x x = 78.8 m x = m High Partial Credit (0 Marks) Both calculated with one error Low Partial Credit (5 Marks) (b) It is intended to open a walking trail that extends through each campsite. Calculate the distance from Campsite to Campsite correct to one decimal place. ( 78.8) + ( 80.4) ( 78.8)( 80.4) cos( ) x = x =. m Full Credit (0 Marks) High Partial Credit (7 Marks) Calculated with one error to end Low Partial Credit ( Marks) Page 40 of 40
Mathematics Higher Level
L.7/0 Pre-Leaving Certificate Examination, 06 Mathematics Higher Level Marking Scheme Paper Pg. Paper Pg. 36 Page of 68 exams Pre-Leaving Certificate Examination, 06 Mathematics Higher Level Paper Marking
More informationMathematics Ordinary Level
L.16/19 Pre-Leaving Certificate Examination, 018 Mathematics Ordinary Level Marking Scheme Paper 1 Pg. Paper Pg. 36 Page 1 of 56 exams Pre-Leaving Certificate Examination, 018 Mathematics Ordinary Level
More informationMathematics. Pre-Leaving Certificate Examination, Paper 1 Higher Level Time: 2 hours, 30 minutes. 300 marks L.17 NAME SCHOOL TEACHER
L.7 NAME SCHOOL TEACHER Pre-Leaving Certificate Examination, 205 Name/v Printed Checke To: Update Name/v Comple Paper Higher Level Time: 2 hours, 30 minutes 300 marks For examiner Question 2 School stamp
More informationMathematics Higher Level
L.7/0 Pre-Leaving Certificate Examination, 07 Mathematics Higher Level Marking Scheme Paper Pg. Paper Pg. 4 Page of 68 exams Pre-Leaving Certificate Examination, 07 Mathematics Higher Level Paper Marking
More information2017 LCHL Paper 1 Table of Contents
3 7 10 2 2017 PAPER 1 INSTRUCTIONS There are two sections in this examination paper. Section A Concepts and Skills 150 marks 6 questions Section B Contexts and Applications 150 marks 3 questions Answer
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 informationActive Maths 4 Book 1: Additional Questions and Solutions
Active Maths 4 Book 1: Additional Questions and Solutions Question 1 (a) Find the vertex of y = f(x) where f(x) = x 6x 7, stating whether it is a minimum or a maximum. (b) Find where the graph of y = f(x)
More informationMathematics (Project Maths Phase 2) Higher Level
L.7/0 Pre-Leaving Certificate Examination, 03 Mathematics (Project Maths Phase ) Higher Level Marking Scheme Paper Pg. Paper Pg. 5 Page of 48 exams Pre-Leaving Certificate Examination, 03 Mathematics (Project
More informationCDS-I 2019 Elementary Mathematics (Set-C)
1 CDS-I 019 Elementary Mathematics (Set-C) Direction: Consider the following for the next three (03) items : A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the
More informationPROJECT MATHS (Phase 3)
PRE-LEAVING CERTIFICATE EXAMINATION, 04 MARKING SCHEME PROJECT MATHS (Phase ) HIGHER LEVEL Page of 9 Table of Contents SOLUTIONS TO PAPER... PAPER I: Question...4 PAPER I: Question...6 PAPER I: Question...7
More informationMathematics (Project Maths Phase 3)
L.20 NAME SCHOOL TEACHER Pre-Leaving Certificate Examination, 2014 Mathematics (Project Maths Phase 3) Paper 2 Higher Level Time: 2 hours, 30 minutes 300 marks For examiner Question Mark 1 2 3 School stamp
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 Board-approved calculators may be used A table of standard
More informationPre-Leaving Certificate Examination, 2017 Triailscrúdú na hardteistiméireachta, Mathematics. Paper 1. Higher Level. 2½ hours.
*P6* Pre-Leaving Certificate Examination, 2017 Triailscrúdú na hardteistiméireachta, 2017 Mathematics Paper 1 Higher Level 2½ hours 300 marks Name: School: Address: Class: Teacher: For examiner Question
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 informationPearson 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 information2016 Mathematics. Advanced Higher. Finalised Marking Instructions
National Qualifications 06 06 Mathematics Advanced Higher Finalised ing Instructions Scottish Qualifications Authority 06 The information in this publication may be reproduced to support SQA qualifications
More informationPossible 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 informationMATHEMATICS (PROJECT MATHS)
Coimisiún na Scrúduithe Stáit State Examinations Commission LEAVING CERTIFICATE 010 MARKING SCHEME MATHEMATICS (PROJECT MATHS) ORDINARY LEVEL Contents Page INTRODUCTION... MARKING SCHEME FOR PAPER 1...
More informationM14/5/MATSD/SP1/ENG/TZ1/XX. Candidate session number. mathematical studies. Examination code Tuesday 13 May 2014 (afternoon)
M14/5/MATSD/SP1/ENG/TZ1/XX 22147403 mathematical studies STANDARD level Paper 1 Tuesday 13 May 2014 (afternoon) 1 hour 30 minutes Candidate session number Examination code 2 2 1 4 7 4 0 3 INSTRUCTIONS
More informationNewington College Mathematics Trial HSC 2012 (D) 2 2
Section I Attempt Questions 1-10 All questions are equal value. Use the multiple choice answer sheet for Questions 1-10 1 Evaluated to three significant figures, 1 e 0.1 is (A) 0.095 (B) 0.095 (C) 0.0951
More informationMATHEMATICS: PAPER I
NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 017 MATHEMATICS: PAPER I Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 11 pages and an Information
More informationFORM VI MATHEMATICS 2 UNIT
CANDIDATE NUMBER SYDNEY GRAMMAR SCHOOL 07 Trial Examination FORM VI MATHEMATICS UNIT Thursday 0th August 07 General Instructions Reading time 5 minutes Writing time 3 hours Write using black pen. Board-approved
More informationPossible 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 informationMathematics 2004 TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION. Name: Teacher: S T R A T H F I E L D G I R L S H I G H S C H O O L.
Name: Teacher: S T R A T H F I E L D G I R L S H I G H S C H O O L 004 TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions All questions may be attempted. All questions are of
More informationM12/5/MATSD/SP1/ENG/TZ2/XX MATHEMATICAL STUDIES STANDARD LEVEL PAPER 1. Candidate session number 0 0. Thursday 3 May 2012 (afternoon)
22127405 MATHEMATICAL STUDIES STANDARD LEVEL PAPER 1 Thursday 3 May 2012 (afternoon) 1 hour 30 minutes Candidate session number 0 0 Examination code 2 2 1 2 7 4 0 5 INSTRUCTIONS TO CANDIDATES Write your
More informationMATHEMATICS (Project Maths Phase 2)
PRE-JUNIOR CERTIFICATE EXAMINATION, 2012 MARKING SCHEME MATHEMATICS (Project Maths Phase 2) HIGHER LEVEL Page 1 of 44 PAPER 1 Page 2 of 44 Question 1 Part (a) Part (b) Part (c) Scale 10C Scale 5A Scale
More informationPure 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 informationPage Points Score Total: 100
Math 1130 Spring 2019 Sample Midterm 3c 4/11/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 10 pages (including this cover page) and 10 problems. Check to see if
More informationMathematics (Project Maths Phase 3)
2014. M330 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2014 Mathematics (Project Maths Phase 3) Paper 2 Higher Level Monday 9 June Morning 9:30 12:00 300
More informationMATHEMATICS: PAPER I. 1. This question paper consists of 8 pages and an Information Sheet of 2 pages (i ii). Please check that your paper is complete.
GRADE 1 STANDARDISATION PROJECT SEPTEMBER 014 MATHEMATICS: PAPER I Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 8 pages and an Information
More informationGATUNDU FORM 4 EVALUATION EXAM 121/1 MATHEMATICS PAPER I JULY/AUGUST 2015 TIME: 2 ½ HOURS
GATUNDU FORM 4 EVALUATION EXAM 121/1 MATHEMATICS PAPER I JULY/AUGUST 2015 TIME: 2 ½ HOURS SECTION I ANSWER ALL QUESTIONS 1. Without using Logarithms tables or a calculator evaluate. 384.16 x 0.0625 96.04
More informationMathematics Extension 1
NSW Education Standards Authority 08 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time hours Write using black pen Calculators approved
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 informationMathematics. Total marks 100. Section I Pages marks Attempt Questions 1 10 Allow about 15 minutes for this section
0 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time 3 hours Write using black or blue pen Black pen is preferred Board-approved calculators may
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 information2016 Mathematics. Advanced Higher. Finalised Marking Instructions
National Qualifications 06 06 Mathematics Advanced Higher Finalised ing Instructions Scottish Qualifications Authority 06 The information in this publication may be reproduced to support SQA qualifications
More informationMockTime.com. (b) (c) (d)
373 NDA Mathematics Practice Set 1. If A, B and C are any three arbitrary events then which one of the following expressions shows that both A and B occur but not C? 2. Which one of the following is an
More informationFURTHER MATHEMATICS. Written examination 2 (Analysis task) Wednesday 3 November 2004
Victorian Certificate of Education 2004 SUPERVISOR TO ATTACH PROCESSING LABEL HERE FURTHER MATHEMATICS Written examination 2 (Analysis task) Core Wednesday 3 November 2004 Reading time: 11.45 am to 12.00
More informationGRADE 12 SEPTEMBER 2012 MATHEMATICS P1
Province of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE 12 SEPTEMBER 2012 MATHEMATICS P1 MARKS: 150 TIME: 3 hours *MATHE1* This question paper consists of 8 pages, 3 diagram sheets and
More informationThe Purpose of Hypothesis Testing
Section 8 1A:! An Introduction to Hypothesis Testing The Purpose of Hypothesis Testing See s Candy states that a box of it s candy weighs 16 oz. They do not mean that every single box weights exactly 16
More information, 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 information2. Find the midpoint of the segment that joins the points (5, 1) and (3, 5). 6. Find an equation of the line with slope 7 that passes through (4, 1).
Math 129: Pre-Calculus Spring 2018 Practice Problems for Final Exam Name (Print): 1. Find the distance between the points (6, 2) and ( 4, 5). 2. Find the midpoint of the segment that joins the points (5,
More informationUNIVERSITY OF LONDON GENERAL CERTIFICATE OF EDUCATION
UNIVERSITY OF LONDON GENERAL CERTIFICATE OF EDUCATION Ordinary Level SUMMER, 1957 P U R E M A T H E M A T I C S (a) ARITHMETIC AND TRIGONOMETRY TUESDAY, June 18. Morning, 9.0 to 11.0 All necessary working
More informationNational Quali cations
H 2018 X747/76/11 National Quali cations Mathematics Paper 1 (Non-Calculator) THURSDAY, 3 MAY 9:00 AM 10:10 AM Total marks 60 Attempt ALL questions. You may NOT use a calculator. Full credit will be given
More informationTRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION 2017 MATHEMATICS
Name: Class: TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION 2017 MATHEMATICS General Instructions: Total Marks 100 Reading Time: 5 minutes. Section I: 10 marks Working Time: 3 hours. Attempt Question 1 10.
More informationEnd of year revision
IB Questionbank Mathematical Studies 3rd edition End of year revision 163 min 169 marks 1. A woman deposits $100 into her son s savings account on his first birthday. On his second birthday she deposits
More information4x 2-5x+3. 7x-1 HOMEWORK 1-1
HOMEWORK 1-1 As it is always the case that correct answers without sufficient mathematical justification may not receive full credit, make sure that you show all your work. Please circle, draw a box around,
More information3 Inequalities Absolute Values Inequalities and Intervals... 5
Contents 1 Real Numbers, Exponents, and Radicals 3 1.1 Rationalizing the Denominator................................... 3 1.2 Factoring Polynomials........................................ 3 1.3 Algebraic
More information(MATH 1203, 1204, 1204R)
College Algebra (MATH 1203, 1204, 1204R) Departmental Review Problems For all questions that ask for an approximate answer, round to two decimal places (unless otherwise specified). The most closely related
More informationMATHEMATICS PRELIMINARY EXAMINATION PAPER 1
MATHEMATICS PRELIMINARY EXAMINATION PAPER 1 GRADE 1 LEARNING OUTCOMES: LO 1 LO MARKS: 150 TIME: 3 hours ASSESSMENT STANDARDS: AS 1,, 3, 4,5, 6 AS 1,, 3, 4, 5, 6, 7, 8 LEARNER S NAME: CLASS: INSTRUCTIONS
More informationNATIONAL SENIOR CERTIFICATE GRADE 11
NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICS P1 NOVEMBER 01 MARKS: 150 TIME: hours This question paper consists of 8 pages. Copyright reserved Mathematics/P1 DBE/November 01 INSTRUCTIONS AND INFORMATION
More informationMA Practice Questions for the Final Exam 07/10 .! 2! 7. 18! 7.! 30! 12 " 2! 3. A x y B x y C x xy x y D.! 2x! 5 y E.
MA 00 Practice Questions for the Final Eam 07/0 ) Simplify:! y " [! (y " )].!! 7. 8! 7.! 0! "! A y B y C y y D.!! y E. None of these ) Which number is irrational? A.! B..4848... C. 7 D.. E.! ) The slope
More informationMathematics Higher Level
J.18/0 Pre-Junior Certificate Examination, 016 Mathematics Higher Level Marking Scheme Paper 1 Pg. Paper Pg. 36 Page 1 of 56 Name/version: Printed: Whom: exams Checked: Pre-Junior Certificate Examination,
More informationMathematical studies Standard level Paper 1
N17/5/MATSD/SP1/ENG/TZ0/XX Mathematical studies Standard level Paper 1 Monday 13 November 2017 (afternoon) Candidate session number 1 hour 30 minutes Instructions to candidates y Write your session number
More informationCoimisiún na Scrúduithe Stáit State Examinations Commission. Leaving Certificate Marking Scheme. Mathematics. Higher Level
Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate 016 Marking Scheme Mathematics Higher Level Note to teachers and students on the use of published marking schemes Marking
More informationThursday 25 May 2017 Morning
Oxford Cambridge and RSA H Thursday 25 May 2017 Morning GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) *4401106953* Candidates answer on the Question Paper. OCR supplied materials: None Other materials
More informationMathematics (Project Maths Phase 2)
2013. M230 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2013 Mathematics (Project Maths Phase 2) Paper 2 Higher Level Monday 10 June Morning 9:30 12:00 300
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 informationMAT 111 Final Exam Fall 2013 Name: If solving graphically, sketch a graph and label the solution.
MAT 111 Final Exam Fall 2013 Name: Show all work on test to receive credit. Draw a box around your answer. If solving algebraically, show all steps. If solving graphically, sketch a graph and label the
More informationSTRATHFIELD GIRLS HIGH SCHOOL TRIAL HIGHER SCHOOL CERTIFICATE MATHEMATICS. Time allowed Three hours (Plus 5 minutes reading time)
STRATHFIELD GIRLS HIGH SCHOOL TRIAL HIGHER SCHOOL CERTIFICATE 00 MATHEMATICS Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of
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 informationin terms of p, q and r.
Logarithms and Exponents 1. Let ln a = p, ln b = q. Write the following expressions in terms of p and q. ln a 3 b ln a b 2. Let log 10 P = x, log 10 Q = y and log 10 R = z. Express P log 10 QR 3 2 in terms
More informationMATHEMATICS: PAPER I. 1. This question paper consists of 8 pages and an Information Sheet of 2 pages (i ii). Please check that your paper is complete.
NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 014 MATHEMATICS: PAPER I Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 8 pages and an Information
More informationTRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION Three Hours (plus five minutes reading time) Total marks - 100
Student Number: TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION 016 Year 1 MATHEMATICS Time Allowed: Teacher Responsible: Three Hours (plus five minutes reading time) Mitchell Parrish General Instructions
More informationGeneral Mathematics 2001 HIGHER SCHOOL CERTIFICATE EXAMINATION. General Instructions Reading time 5 minutes. Total marks 100
00 HIGHER SCHOOL CERTIFICATE EXAMINATION General Mathematics General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Calculators may be used A formulae sheet is provided
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 informationFree Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom
Free Response Questions 1969-010 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions
More informationf exist? Why or why not? Non-AP Calculus Summer Assignment 1. Use the graph at the right to answer the questions below. a. Find f (0).
1. Use the graph at the right to answer the questions below. 4 1 0 - - -1 0 1 4 5 6 7 8 9 10 11-1 - a. Find f (0). b. On what intervals is f( x) increasing? c. Find x so that f( x). d. Find the zeros of
More information11 th Philippine Mathematical Olympiad Questions, Answers, and Hints
view.php3 (JPEG Image, 840x888 pixels) - Scaled (71%) https://mail.ateneo.net/horde/imp/view.php3?mailbox=inbox&inde... 1 of 1 11/5/2008 5:02 PM 11 th Philippine Mathematical Olympiad Questions, Answers,
More informationKENYA NATIONAL EXAMINATION COUNCIL REVISION MOCK EXAMS 2016 TOP NATIONAL SCHOOLS
KENYA NATIONAL EXAMINATION COUNCIL REVISION MOCK EXAMS 2016 TOP NATIONAL SCHOOLS ALLIANCE BOYS HIGH ELDORET MATHEMATICS PAPER 2 SCHOOLS NET KENYA Osiligi House, Opposite KCB, Ground Floor Off Magadi Road,
More informationFURTHER MATHEMATICS Units 3 & 4 - Written Examination 2
THIS BOX IS FOR ILLUSTRATIVE PURPOSES ONLY 2016 Examination Package - Trial Examination 4 of 5 Figures STUDENT NUMBER Letter Words FURTHER MATHEMATICS Units 3 & 4 - Written Examination 2 (TSSM s 2014 trial
More informationMANLY SELECTIVE CAMPUS
NORTHERN BECHES SECONDRY COLLEGE MNLY SELECTIVE CMPUS General Instructions HIGHER SCHOOL CERTIFICTE Reading time 5 minutes Working time 3hours Write using black or blue pen Write your Student Number at
More informationMathematics: Paper 1 Grade 11
Mathematics: Paper 1 Grade 11 November Examination 2016 Read the following instructions carefully before answering the questions. Time: 3 hours Marks: 150 1. This question paper consists of 8 questions.
More informationTime: 1 hour 30 minutes
Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C Silver Level S3 Time: 1 hour 30 minutes Materials required for examination Mathematical Formulae (Green) Items included with question papers Nil
More informationMark. Total. 1 (i) 1 hour = 3600 seconds. (ii) 0.1 kilogram = 100 grams. 1 kilometre 8. = millimetres. (iii) (iv) 5 minutes =
WKING s 1 (i) 1 hour = 3600 seconds 3600 4 (ii) 0.1 kilogram = 100 grams 100 (iii) 1 kilometre 8 = 125 000 millimetres 125000 (iv) 5 minutes = 1 / 12 hour. 1 / 12 or equivalent; e.g. 5 / 60. For answer
More informationPhysicsAndMathsTutor.com
PhysicsAndMathsTutor.com June 005 1 AsequenceS has terms u 1, u, u,... defined by for n 1. u n = n 1, (i) Write down the values of u 1, u and u, and state what type of sequence S is. [] (ii) Evaluate 100
More informationNABTEB Past Questions and Answers - Uploaded online
NATIONAL BUSINESS AND TECHNICAL EXAMINATIONS BOARD MAY/JUNE 006 NBC/NTC EXAMINATION MATHEMATICS 0.085 0.67 1(a) Evaluate, 3.36 leaving your answer in standard form. If the angles of a polygon are given
More informationThirty-third Annual Columbus State Invitational Mathematics Tournament. Instructions
Thirty-third Annual Columbus State Invitational Mathematics Tournament Sponsored by Columbus State University Department of Mathematics March rd, 007 ************************* ANSWER KEY The Mathematics
More informationState Examinations Commission. Coimisiún na Scrúduithe Stáit. Leaving Certificate Marking Scheme. Mathematics.
Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate 2018 Marking Scheme Mathematics Ordinary Level Note to teachers and students on the use of published marking schemes Marking
More information2017 Canadian Team Mathematics Contest
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 017 Canadian Team Mathematics Contest April 017 Solutions 017 University of Waterloo 017 CTMC Solutions Page Individual Problems
More informationCollege Algebra and College Algebra with Review Final Review
The final exam comprises 30 questions. Each of the 20 multiple choice questions is worth 3 points and each of the 10 open-ended questions is worth 4 points. Instructions for the Actual Final Exam: Work
More informationGATUNDU SOUTH SUB-COUNTY KCSE REVISION MOCK EXAMS 2015
GATUNDU SOUTH SUB-COUNTY KCSE REVISION MOCK EXAMS 2015 MATHEMATICS PAPER 2 SCHOOLS NET KENYA Osiligi House, Opposite KCB, Ground Floor Off Magadi Road, Ongata Rongai Tel: 0711 88 22 27 E-mail:infosnkenya@gmail.com
More informationMath Makeup Exam - 3/14/2018
Math 22 - Makeup Exam - 3/4/28 Name: Section: The following rules apply: This is a closed-book exam. You may not use any books or notes on this exam. For free response questions, you must show all work.
More informationJUNIOR CERTIFICATE EXAMINATION
JUNIOR CERTIFICATE EXAMINATION 01 MARKING SCHEME MATHEMATICS ORDINARY LEVEL PAPER 1 Page 1 GENERAL GUIDELINES FOR EXAMINERS 1. Penalties of three types are applied to candidates work as follows: Blunders
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Wednesday, August 13, :30 to 11:30 a.m.
MATHEMATICS B The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Wednesday, August 13, 2008 8:30 to 11:30 a.m., only Print Your Name: Print Your School s Name: Print
More informationALGEBRA II WITH TRIGONOMETRY EXAM
First Round : March 7, 00 Second Round: April, 00 at The University of Alabama ALGEBRA II WITH TRIGONOMETRY EXAM Construction of this test directed by Congxiao Liu, Alabama A&M University and Alzaki Fadl
More informationThursday 26 May 2016 Morning
Oxford Cambridge and RSA H Thursday 26 May 2016 Morning GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) * 5 9 8 5 4 1 9 7 8 4 * Candidates answer on the Question Paper. OCR supplied materials: None Other
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II. Thursday, August 16, :30 to 3:30 p.m., only.
ALGEBRA II The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II Thursday, August 16, 2018 12:30 to 3:30 p.m., only Student Name: School Name: The possession or use of any
More informationSupervising Examiner s/ Invigilator s initial: Total Marks : 100
Index No: 0 1 0 1 4 Alternative No. Supervising Examiner s/ Invigilator s initial: Mathematics READ THE FOLLOWING DIRECTIONS CAREFULLY: Writing Time: 3 hours Total Marks : 100 1. Do not write for the first
More information1. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y 3x
MATH 94 Final Exam Review. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y x b) y x 4 c) y x 4. Determine whether or not each of the following
More informationUnit 1 & 2 Maths Methods (CAS) Exam
Name: Teacher: Unit 1 & 2 Maths Methods (CAS) Exam 2 2017 Monday November 20 (1.00pm - 3.15pm) Reading time: 15 Minutes Writing time: 120 Minutes Instruction to candidates: Students are permitted to bring
More information2017 HSC Mathematics Extension 1 Marking Guidelines
07 HSC Mathematics Extension Marking Guidelines Section I Multiple-choice Answer Key Question Answer A B 3 B 4 C 5 D 6 D 7 A 8 C 9 C 0 B NESA 07 HSC Mathematics Extension Marking Guidelines Section II
More informationIYGB. 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 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 informationThe Grade Descriptors below are used to assess work and student progress in Mathematics from Year 7 to
Jersey College for Girls Assessment criteria for KS3 and KS4 Mathematics In Mathematics, students are required to become familiar, confident and competent with a range of content and procedures described
More informationMarkscheme May 2016 Mathematical studies Standard level Paper 1
M16/5/MATSD/SP1/ENG/TZ/XX/M Markscheme May 016 Mathematical studies Standard level Paper 1 4 pages M16/5/MATSD/SP1/ENG/TZ/XX/M This markscheme is the property of the International Baccalaureate and must
More information2018 Mathematics. Advanced Higher. Finalised Marking Instructions
National Qualifications 08 08 Mathematics Advanced Higher Finalised Marking Instructions Scottish Qualifications Authority 08 The information in this publication may be reproduced to support SQA qualifications
More informationAP Calculus Free-Response Questions 1969-present AB
AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions
More informationSTEP III, cosh x sinh 2 x dx u 4 du. 16 (2x + 1)2 x 2 (x 4) f (x) = x 4
STEP III, 24 2 Section A: Pure Mathematics Show that and find a ( ) ( ) sinh x 2 cosh 2 x dx = 2 cosh a 2 2 ln + 2 + 2 cosh a + 2 2 ln 2 a cosh x + 2 sinh 2 x dx. Hence show that ( ) cosh x sinh x + 2
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 information