0607 CAMBRIDGE INTERNATIONAL MATHEMATICS

Transcription

1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June question paper for the guidance of teachers 7 CAMBRIDGE INTERNATIONAL MATHEMATICS 7/ Paper (Extended), maximum raw mark This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes must be read in conjunction with the question papers and the report on the examination. Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

2 Page Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 7 (a) (i) oe M for oe Implied by. 8 oe (ii). 8 or... 8 ft ft their (i) or their more accurate value seen in (i).7 (b).8 (.8 ) M for [ ] oe implied by figs 8 (c) 5 or.5() 9 or 5 million SC for or.5 9 or 5. million M for.9 oe (M for evidence of 9 (%)) If M, SC for or. 9 or million or SC for or or. 9 or or.8 million (this is by.9) [8] (a) 8.9 (8.9 to 8.9) M for 8tan5 oe i.e. explicit expression (b) (9.7.) www M for.5 8 their (a) oe (75.5 to 75.) M for sin oe (5.9 to 5.) (c).8 (.8.) www M for cos oe A for.. seen [8] (a) (i) 5 (ii) 5.8 (5.8 to 5.8) ft ft ft their (i). Allow as final answer M for 5 + oe (b) (i) Reflection, x = 5 B, B independent lose all marks if extra transformation (ii) Enlargement, (, ) [Factor] B, B, B independent lose all marks if extra transformation [8] (a) 9. M for indication of use of mid-values (implied by figs 9) (b) Curve through (, ), (, 5), (, 88), (8, ) B for 5, 88 and seen P ft for three correct plots ft attempt at cum. frequencies. C for correct shape through at least of their points (c) (i) 7 t < (ii) to 5 Dependent on P M for ( to 7) or ( to ) (iii) their reading off cum freq graph (.5 square accuracy) Must be an integer. SC for their reading off cum freq graph (.5 square accuracy) may be on graph or answer [] University of Cambridge International Examinations

3 Page Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 7 5 (a) (i) 8 (88 to 8) Allow57π as final answer M for 8 7 π ( π, 7.8 to 77. ) M for π 8 ( π, 7 to 7.) (ii).8 (.79 to.8) ft ft their (i).5 oe M for their (i) figs 5 soi by figs 8 or 79 to 8 (b) (i) 7 (7.5 to 7.) www M for (sloping edge) = + 8 or better seen (= 85) (sq root =. ) M for cone = π 8 their ( + 8 ) (soi by. to.9) M for hemisphere = π 8 soi (.9 to.) (ii). ft ft 8.5 their (i) with same rounding requirement SC ft for.9 to.9.. or. [] (a) (i) 8 (ii) 88 (iii) ft ft.5 their (ii) 9 if answer positive B for angle BOD = 7 (may be on diagram) (b) SC for angle DBC = or angle BAC = (may be on diagram) [] 7 (a) 8. (8.57..) M for 7 (7.5 + ) or better x x (b) (i) 9x or 9 x or x 9 M for 7.5 xor (not from x + ) (ii) 8 ft ft ft 7 their coefficient of x where answer to (b)(i) is in simplified form (c) 5 : oe Allow non-reduced e.g. : or 7.5 :.5 isw incorrect cancelling after correct answer M for 7.5 their (b)(ii) and.5 their (b)(ii) [7] University of Cambridge International Examinations

4 Page Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 7 8 (a) (i) for reasonable shape including horizontal inflexion SC for poor quality e.g. cubic (ii),, B, B, B (iii) (.775 or.775 to.77,.8 or.859 ) B, B SC for.77 or.78 and.9 (iv).5 Condone. or. to. or.9 or.9 (v) Rotational, [order] or point symmetry [about] (, ) B (or B for rotational) condone 8 for order B Deduct if line symmetry also given (b) (i) x y = oe 5 (ii) Reasonable line through origin with negative gradient Must cut curve 5 times (iii) ±.85 or ±.85 to.857, B, B [5] 9 Allow non-reduced fractions and decimals or percentages. Do not allow words or ratios. isw any incorrect cancelling or converting (a) 8 oe www M for oe 5 (. to.7) (b) 8 = 5 5 oe www M for + oe (M for either 5 5 product) (c) M for combining valid probabilities e.g. then or 5 (M for first probability tried ) [8] University of Cambridge International Examinations

5 - - 8 Page 5 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 7 (a) (b) y = oe Exponential shape over full domain cutting positive x-axis and negative y-axis SC for partial domain only or slight upturn at left hand side (c) (i).75 f ( x ) B, B Allow in words. Condone <. Allow y or x for f(x) (ii) f(x) > Allow f(x) and allow y or x and/or words (d) log log or log final answer SC for.58 or.58 to.585 may be on diagram or log log or log seen [8] (a) 9 B for seen (b) M for x + = x or better (c) B Curve(s) could be for other equation(s) but must lead to correct solutions. Allow B for curve leading to correct solutions but poor quality. Use of formula, B for ( ) ()( ) or better, seen anywhere p + q p q If form or or better B for r r ± p = ( ), r = () or better Use of completing the square B for a correct completed square then B for correct explicit statement for x..7,.7 cao B B If scored, SC for.7 or.7 to.7 and.7 or.7 to.7 Without working maximum score of (d) x oe final answer M for x = y + or y = x or i.e. a correct first step y = x + (e) x + (x + )( x ) final answer Allow x + x for denominator. M for denominator ( x + )( x ) or x + x M for numerator ( x ) + (x + ) with or without brackets [] University of Cambridge International Examinations

6 Page Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 7 (a) B x = 5 ruled B y = x ruled mm accuracy at (, ) and (, ) B y = x ruled Allow mm accuracy at (, ) and (, ) - - In each case line must be long enough to enclose area in next part (b) Region correct cao Dep on B SC if correct side of three correct boundaries (c) h =, k = cao SC for other point in region such that x + y = [9] (a) Points (5, 8), (55, ) and (5, ) plotted P for correct points (b) Negative correlation cao (c) (i) 7 cao (ii).9 cao (d).x +. or. x +.58 isw if correct answer rounded B for. x + c or kx +. SC for.x + 7 (e). ft ft their linear equation in (d). Allow 7. Allow sf in ft (f) Ruled line from x = to 55, through (their 7, their.9) with mm accuracy and 8 on the vertical axis with small square accuracy B if ruled line through mean point with negative gradient (g) Their integer reading at x = ft Integer only Strict ft their graph if ruled line with negative gradient [] University of Cambridge International Examinations

7 Page 7 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June y=x^5-x^ y=-x/5 University of Cambridge International Examinations