Igcse Maths Ce S Report P1f And 2f Nov 05 Final

IGCSE MATHEMATICS 4400, NOVEMBER 2005 CHIEF EXAMINER’S REPORTS Paper 1F General Comments Approximately 600 candidates (200 Foundation and 400 Higher) found all four papers accessible and the vast majority of candidates at both tiers took the opportunity to show what they knew. Hardly any candidates were entered at an inappropriate tier. The standard of this paper proved to be appropriate and most of the questions in the first half of the paper were very well answered. The only exception to this was Question 6(d) (Probability explanation). Although the questions on the second half were more demanding, most of them had a reasonable success rate. Full marks on Question 15 (Construction) and Question 17 (Angle with reasons) were, however, rare. In general, candidates’ answers were well presented and clearly explained. A substantial number of candidates scored marks well above the grade C threshold. For them, sitting this exam was certainly a positive educational experience but this must be weighed against the grade C ceiling. Question 1 Occasionally, the fraction in part (a)(i) was left as 106 but, otherwise, the question served its purpose as a straightforward start to the paper. Question 2 Most candidates were able to mark a pair of parallel lines but many, in the second part, marked another pair of parallel lines instead of perpendicular ones. In the third part, the most common error was to mark an obtuse angle, instead of a reflex angle, and sometimes the letter “R” was positioned so that it was not clear which angle was the intended answer. In the final part, a few candidates produced complicated calculations, usually leading to the wrong answer, but the majority, as intended, simply used a square counting method and obtained the correct area. Question 3 This question was well answered, many candidates gaining full marks. A minority thought 40 was the number Jan thought of but, if marks were lost, it was usually in either part (b)(ii), with 1 being given as a multiple of 5 or 5 itself omitted, or in part (b)(iv), with 1 being given as a prime number. Question 4 The first three parts were almost always correct. The fourth part was also well answered, the most common error being failure to simplify the ratio 35 : 14. Question 5 Almost all candidates performed the first step, 10 ÷ 1.26 = 7.93… correctly and most went on to scored full marks. Question 6 Parts (a) and (c) were well answered but, in part (b), G was often wrongly positioned, usually at 0.9. Completely correct explanations in part (d) were rare. Examples of answers gaining full marks were “There would have to be 1½ green beads and you can’t have half beads” and “The number of beads must be a multiple of 10”.

Question 7 Knowledge of geometry varied widely. In part (b), many gave “The sides are not equal” as their explanation and, in part (d), 28 (4 x 7) was the most popular wrong answer. There were many errors in the other parts but none appeared regularly. Question 8 Incorrect answers were rare. Question 9 Many candidates either converted litres to m 3 or realised division was required but only a minority did both correctly. P

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Question 10 The majority found the value of x, algebraic methods and trial methods being equally popular. Question 11 Most found the mode correctly. Finding the median proved more difficult and, although many candidates were successful, a substantial minority, who knew that the median was something to do with the middle value, either found the median of the numbers 0, 1, 2, 3, 4, 5 or of the frequencies. The third part (mean) was well answered, the most common error being the evaluation of 0 x 1 as 1. The final part proved difficult and 96 (575 ÷ 6) appeared regularly. Question 12 The majority of candidates scored well on the first three parts, generally using trial methods in parts (b) and (c). Most achieved some success in part (d) but N = L + W × h ÷ 6 , which gained 2 marks out of 3, appeared as often as the correct formula. Question 13 Both parts had a fair success rate but 0.17037… (2.6 – 9.8 ÷ 2.7 + 1.2) was a popular wrong answer to part (a) and it was not unusual to see a correct calculator value rounded to 0.09 or 0.1 in part (b). Question 14 The quality of answers varied widely, many not realising that the graph was a straight line. Some of the candidates who appreciated this made an inappropriate choice of scale on the y-axis, which resulted in their graph going off the grid at x = -1. Question 15 This question proved difficult but a substantial minority constructed the kite accurately. Some misinterpreted the information given, misunderstanding the term “shorter diagonal”, while others did not appreciate the meaning of “construct” and ignored the instruction to “show all construction lines”. A drawing within the tolerance but with no visible construction scored 1 mark out of 4. The same mark was awarded for a drawing within the tolerance to which an assortment of spurious or irrelevant arcs had been added. A preliminary sketch is often helpful in questions of this type.

Question 16 This was well answered, although 26% of 85 (22.1) was sometimes calculated but not subtracted from 85. Question 17 Only a small minority gained full marks. If marks were lost, it was usually for inadequate reasons, especially giving just “parallel lines” as the reason that angle ACD is 18°. “Alternate angles” was required. “Z angles” was also accepted but will not be in future. A few candidates wrote mini essays, which should be discouraged. Working with concise reasons alongside the related line in the working is much easier to follow. Question 18 The calculation was often performed accurately, although occasional sign errors led to answers of -22.8. Some candidates did not appreciate that uv was a product. Question 19 The candidates who attempted this question with some success, as many did, often achieved it using informal, intuitive methods involving proportion. Premature approximation regularly led to the loss of accuracy marks. Question 20 The responses to this transformation question were very mixed, only a minority scoring full marks. Wrongly positioned images were quite common in both parts. In part (a), the rotation was sometimes clockwise and, in part (b), many images were larger than the original triangle. Question 21 This was a demanding question but the equation was solved correctly by a significant number of candidates, trial methods being employed as often as algebraic methods and with comparable success. Some candidates who used algebra progressed as far as 5x = 2 but gave the solution as x = 2½ .

Paper 2F General Comments All candidates were able to display their understanding in at least some aspects of this paper and low marks were rare. Presentation was good on the whole. Some candidates, however, lost marks by omission of working. The algebraic questions were less well answered than others. A significant number of candidates unnecessarily used percentages instead of fractions in several contexts. Question 1 (a) Many candidates gave 1023. (b) Tens or tenths were common answers. 0.03 was seen but did not score the mark. (c) Common incorrect answers were 3, 3.46 and 4. (d) Some candidates gave the square root. (e) Answers to part (i) included 27, 29 and 30. A few candidates incorrectly gave 28.00. (f) (f) 102 was often given. (g) Common incorrect answers were 1.71, 25 and 625. Question 2 This question was answered correctly by almost all candidates. Question 3 (a) Some candidates gave an incorrect order, but showed no working, thus losing the possibility of scoring 1 mark. Some candidates converted each quantity to a fraction with a numerator of 1. These generally did not achieve the correct answer. (b) This was well answered. Question 4 (a) Most candidates answered this correctly. Those who did not do so failed to use the “30” given in the question. (b) Most candidates gave 11 – 2 = 9. Some found a mean. (c) Many candidates showed little understanding of the proportion calculation required. Some gave a correct calculation for 5 mobile phones rather than 2, presumably using the frequency of 2, rather than “2 mobile phones”. Question 5 This question was well answered, although a few candidates either found the total in part (a) or found only the interest in part (b). In part (a), some candidates divided by 4. A significant number of candidates attempted the “one step” method which did not give just the interest as required. In part (b), it was frequently incorrectly carried out, with division by 1.12. Question 6 Some candidates gave imperial units in one or both parts. Many candidates gave only units. In part (b), answers included 2g and 2 kg. Question 7 (a) This part was well answered. A few candidates gave the position to term rule although all that was required was the term to term rule. (b) Parts (i) and (ii) were well answered. In part (iii), some candidates attempted (and usually failed) to write out 100 terms. Others “scaled up” the 10 th term and obtained 38 x 10 = 380. A few showed some understanding by calculating 11 + 100 x 3. P

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Question 8 (a) This part was generally well answered. Some candidates omitted the draws. (b) Some candidates thought there were 18 possibilities altogether rather than 9. Question 9 (a) This was very well answered. (b) A few gave less obvious correct answers such as (-3, 4) and (-2, 2), but many candidates gave incorrect answers such as (1, 1), (2, 1) or (4, 1). (c) The midpoint was not understood by a large number of candidates. Some found the midpoint by eye, rather than by calculation, giving answers such as (0.1, 2.5). Question 10 (a) Most candidates gave some version of “equilateral”, although some gave “isosceles”. (b) Most candidates drew a trapezium correctly. (c) Many also gave a correct answer here, although some drew an isosceles triangle. Question 11 (a) Common incorrect answers were 1 and 3. (b) X was often marked at Q or elsewhere on the line x = 3 or at (1, 1) or (0, 0). (c) Many candidates appeared to know which line was required but gave answers such as 3x + 7y or y = 3x or x = 3, y = 7. Question 12 (a) Most candidates answered all three parts correctly. The most common error was to assume that z = 90°. (b) Most candidates answered both parts correctly. In part (ii), some explained their calculation without quoting reasons such as the angle sum of a triangle. Many candidates found e to be 130°, and gave as their reason “angles on a straight line add up to 180°”. Question 13 A few candidates confused ∪ with ∩ . (a) Many candidates answered this part correctly, although some gave extra numbers such as 9 or 10 or 17. Some gave a long list of numbers, ignoring the limits. (b) Some candidates failed to understand the intersection notation. Many gave one or two numbers that were not included in their lists of members. A few probably understood the notation, but gave the answer “0” which did not score the mark. (c) This was generally well answered although a few wrote “yes” and then correctly explained why 11 is not a member of B. Presumably they understood ∈ to mean ∉ . Some candidates stated “No”, but gave an inadequate reason, such as “11 is a member of A.” Question 14 Both parts were well answered by many candidates. A few multiplied instead of dividing. In both parts candidates who scaled each individual part of the ratio separately were generally less successful than those who dealt with the total. Question 15 This question was often well answered. However, many candidates showed a poor grasp of algebra, including a lack of appreciation of the difference between x 2 and 2x. In part (a), some candidates clearly did not understand the term “factorise”. They tried to subtract or they factorised the two terms separately. P

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Question 16 (a) A few candidates misread the scale, giving 22 and 82. Others gave, e.g. 23 and 24. (b) The answer “at his destination” was occasionally seen, but gained no mark. (c) Some candidates confused distance and speed, giving the answer 40 to 60. Many gave answers such as “0 to 40 and 60 to 120”. (d) Many candidates did not convert to hours. Some misread the graph, giving 6/20 or 4.4/20. Some multiplied instead of dividing. Many thought that 20 minutes = 0.3 hours, which is slightly better than those who used 0.2 hours. (e) A few candidates attempted a distance/speed calculation. Some gave answers with no discernible reasoning behind them, for example, 67 minutes or 168 minutes. Question 17 (a) Common incorrect answers were 140°, 40° and 50°. (b) Some candidates attempted a perpendicular bisector, but many either did not attempt a construction or drew only one pair of arcs. Many others drew lines or arcs which bore no relation to the perpendicular bisector. (c) Few candidates answered this correctly. Common answers were 60° and 240°. A few candidates attempted to draw the position of C and measure the bearing. Usually the result was incorrect. Question 18 (a) Many candidates seemed unfamiliar with the relevant vocabulary, describing “slides” and “rotation downward”. Many gave a rotation and a “move” of some kind, gaining no marks. Some candidates gave a partially correct answer, omitting the centre and/or the sense. Others omitted the word “rotation”, thinking that this could be implied by giving the angle. Some lost the mark for “rotation” by using the term “turn” instead. (b) This part was well answered. The most commonly incorrectly answered sub-part was (iv). This suggests that the term “congruent” was unfamiliar to some candidates. A few candidates also gave the wrong answer to (ii) or (iii). Question 19 Many candidates answered both parts correctly. In some cases, candidates felt the need to convert to fractions or percentages, thus opening up the possibility of unnecessary errors. (a) A few candidates added 0.25 + 0.25 + 0.1 and obtained 0.59. (b) Some added correctly and then either subtracted from 1 or divided by 2. Others added 0.25 + 0.25. A few multiplied. A small number ignored the given probabilities and just counted outcomes: 2/4 = 0.5.

MATHEMATICS 4400 PAPERS 1F & 2F NOVEMBER 2005, GRADE BOUNDARIES Foundation Tier Grade

C

D

E

F

G

Lowest mark for award of grade

70

54

39

24

9

Note: Grade boundaries may vary from year to year and from subject to subject, depending on the demands of the question paper.