General comments In this paper, candidates need to show all the necessary working and maintain the notation in which the question has been asked.

Transcription

1 MATHEMATICS (4024/11) REPORT General comments In this paper, candidates need to show all the necessary working and maintain the notation in which the question has been asked. For example = 0.7 does not earn marks as the two are not equal. Candidates should avoid unnecessary rounding off their answers as it results in loss of marks. Candidates often use pencil on the working and after obtaining the answer, erase everything leaving the answers without working. This also results in loss of marks in cases where marks are awarded for the working, i.e. where the question earns more than one mark. To obtain maximum possible marks, candidates should avoid writing two or more answers on the answer space of which one is not correct as the worst option is the one that is considered. Candidates should be discouraged to use rough papers as majority of them wrote answers without workings. Candidates should pay attention to specific instructions per question. For instance, where candidates were asked to express the answer in terms of, they used its value. Generally, the majority of candidates seemed to have a problem with manipulation of directed numbers as most of the questions which required the use of directed numbers were not well. General performance Generally, performance was below average as most candidates scored below 40 marks which is 50%.

2 Performance on individual questions Que s. no. 1. Evaluate 2-1 Question Expected answer Performance Common errors and misconceptions This was fairly done Common errors are 1 and 1 which resulted from subtracting whole numbers separately and then fraction part. Evaluate (2 3) 9 Common error was incorrect use of arithmetic rules. 2. Evaluate , The common error was incorrect placing of the decimal point. Arrange these values in order of size, starting with the smallest 22%,, , 22%, The common error was to put the numbers in reverse order where was placed as the smallest value. 3. Express the ratio 30 minutes to 2 hours in its lowest terms. Give your answer in the form m:n, where m and n are integers 2:9 Common errors were 1:4.5 and 30:150 where candidates take simplify to mean 1:x. Find the simplest interest on $200 for 4 years at 0.6% per year $4.80 or in cents done Errors in this questions included $480 and $0.480 brought by incorrect manipulation of decimal fractions. 4. Find two solutions of the inequality 3x 4 11 Two numbers between 2 and 2 Common errors were and 2 where candidates did not realize that the equality sign excluded the boundary

3 number. Candidates also changed the inequality sign to an equal sign and ended up solving an equation. 5. The length of a side of a square is given as d cm, correct to the nearest 10 cm. Find an expression in terms of d for: the upper bound of the perimeter of the square, the lower bound of the area of the square 4d + 20 Generally these questions were not well answered Common errors were d or d + 5 brought by inappropriate application of limits of accuracy Error included - 0.5, - 5 and - 25 obtained by inappropriate expansion of brackets (d 6. Evaluate Find (5 ) (2.4 ). Give your answer in standard form Both part questions were unsatisfactorily done Errors included 131 and 136 where 5 was evaluated as 1 or 6. 9 was also common which was obtained by adding 5, 3, 1 and the indices 0, 1, 2 Errors included 1.2, 1.2 and 1.2 where answers were obtained by incorrect addition of directed numbers and majority failed to write the number in standard form. 7. By making suitable approximations, estimate the value of 20 Fairly Common errors were to write 4 instead of 40 in the working and 2 in the answer space instead of 20. Significant figures were the main source of errors in this question.

4 8. Giving each answer as a fraction in its lowest terms, evaluate Common error was = 4 resulting from ( ) done was also common Common error was resulting from lack of understanding of negative index. 9. A television priced at $500 is sold for $400. Find the percentage discount. Tax on the original price of a radio is charged at 20% of the original price. After tax was included, a customer paid $60 for the radio. Calculate the tax charged. 20% $10 Unsatisfactorily Majority of candidates who attempted this question divided 400 by 500 and got the answer as 80% Common error was $12 which was obtained by calculating 20% if $ was also common which was obtained by subtracting 12 from In the diagram, the triangle ABC is equilateral. Ref. to question paper. C is east of B Find the bearing of B from A 210 done Common errors were 150 and 300 which were obtained by calculating the angle from A to B in an anticlockwise direction and subtracting 60 from 360 respectively. Find the bearing of A from C A boat sails around a course represented by minutes 30 which was obtained in the same manner as above Popular answer was 84 minutes

5 triangle ABC. It started at 13:38 and finished at 14:21. How many minutes did it take? which was obtained by calculating time in units of 100 instead of A model of a car is made to a scale of The height of the actual car is 1.5m Find the height, in centimeters of the model 3.75 or 3 done 150 cm and 1500 cm were common answers obtained by either multiplying 1.5 m by 100 or Those who managed to get correct figures were unable to place the decimal point correctly. The luggage capacity of the model is 5 millilitres. Find the luggage capacity, in litres, of the actual car. 320 Unsatisfactory performance 0.2, 200 and were common. There was little recognition that the scale given in question was to be used in this question. Candidates, who recognized that they had to use the scale, did not convert length scale to volume scale. 12. The lengths of the leaves of a plant were measured; the results are shown in the table. Length 1 x 3 3 x 4 4 x 5 5 x 7 7 x 10 (x cm) Freq Freq. density Complete the table to show the frequency densities One leaf is chosen at random All of 4, 5, 6, 6, 4 Unsatisfactory Common error was to give cumulative frequency instead of frequency density Popular answer was obtained by

6 Find the estimate of the probability that this leaf is more than 6 cm long. performance adding frequency 12 as it is to f(x) = Find f(4) - Common error in this question was to leave out the (-ve) sign in front of the fraction or to express the answer as a decimal and then round it off to Find (x) Candidates attempted to find the inverse using flow diagram and this was problematic. This resulted in numerous incorrect answers. 14. Express, in set notation, the subset shaded in the diagram. Ref. to question paper = {a, b, c, d, e, f, g, h} P = {a, b, c} Q = {b, c, d, e, f} (A B) C or (A C) (B C) In attempting this question, some candidates did not insert the brackets hence obtained incorrect answers. Generally this concept seemed not to be well understood. (i) (ii) Find n(p Q) List the members of the subset P Q 6 d, e, f done Error was to list elements of P Q instead of giving the number. Common error was inclusion of a in the set. 15. This figure has rotational symmetry of order 3. Ref. to question paper. How many lines of symmetry does the figure have? 0 Common error was 3 and candidates treated the shape/figure as a solid

7 Find x. Find y Error was 53 Common error was 127 obtained by subtracting 53 from An ordinary die is thrown 15 times. These are the numbers thrown (i) (ii) Find the mode Find the median x 5 3 Common error was to give the largest number which is 6 as the answer (mode) Error was 1; candidates did not arrange the numbers in order before determining the median. The mean of these three numbers is -5. Find x. x = 13 Different errors were made due to incorrect manipulation of directed numbers and also due to improper manipulation of equation involving fractions. 17. The diagram shows the points A (1, 4), B (3, 12) and C (15, 4). The equation of the line through B and C is 2x + 3y = 42. Ref. to question paper The region inside triangle ABC is defined by three inequalities. One of these is 2x + 3y = 42 Write down the other two inequalities y 4 y 4x Errors were 2x + 3y 42; 2x + 3y 42 and the inclusion of

8 How many points, with coordinates (10, k), where k is an integer, lie inside the triangle ABC? 18. The diagram shows a hexagon. Ref. to question paper. Find x. 19. [Volume of a cone = h] Cone 1 has radius 2x cm and height 7x cm. Cone 2 has radius x cm and height 4x cm. Find an expression, in terms of and x, for the difference in volume of the two cones. Give your answer in its simplest form. 3 done 76 8 equal sign in the inequalities. Candidates did not write the expression in terms of instead they substituted the value of. Those who managed to write the expression in terms of were not able to simplify (2xcm correctly. Common errors were and 4x. 20. Two bags contain beads. The first bag contains 2 white, 2 red and 3 black beads The second bag contains 3 white and 2 black beads. One bead is taken, at random, from each bag The tree diagram is shown Ref. to question paper. Find the probability Both beads are white, Error was obtained by adding and instead of multiplying them. Both beads are red, 0 Errors were and simplified) (which was not

9 Exactly one bead is black Common error was which simplified to obtained by adding all the probabilities where the second bead was black. 21. In the diagram (Ref. to question paper), = 2p + q, = 2p q and D is the midpoint of CE. (i) (ii) Express, in its simplest form, in terms of p and/or q,. 4q 2p 5q For both (i) and (ii), majority of candidates did not simplify their expressions. Common errors included (2p q) and 4q 2p Given that = kp, express in terms of k, p and q. Given that AE is parallel to BC, find k. kp + 5q 10 Candidates did not realize that if two vectors are parallel, one is the scalar multiple of the other, hence had difficulty in finding the value of k.

10 22. In the diagram (Ref. to question paper), the circle, centres P and Q, intersect at B and E. ABC and APE are straight lines. BD is parallel to AE. B A = 36 and B C = 122 Find B E Find E D Error was 36 obtained by taking triangle ABE as isosceles Find B C 61 (d) Find D Q 25 done Error was 29 obtained by considering line BD to bisect angle EBQ. 23. The diagram is the speed-time graph of part of a train s journey. (Ref. to question paper) The train slows down uniformly from a speed of u m/s to a speed of 6 m/s in 10 seconds. During the next 20 seconds it travels at a constant speed of 6 m/s/ It then slows down uniformly to a stop after a further 30 seconds. Calculate the retardation from t = 30 to t = 60. Calculate the speed of the train when t = 40. The distance travelled by train is from t = 0 to t = 10 is 85 m. Find u. (-), or (-) Common error was 0.5 obtained by equating to 0.5 Majority of candidates divided 85 by 10 and obtained 8.5 as the answer. They did not recognize that the distance was given by the area underneath the graph.

11 24. The first and second terms of a sequence are 15 and 11 respectively. The nth term of the sequence is 10 + An + Show that A + B = 5 and 4A + B = 2 Solve the simultaneous equations Hence find the third term of the sequence A + B = 5 correctly obtained from 15 = 10 + A + B 4A + B = 2 correctly obtained from 11 = A + Both A = -1 and B = 6 9 done Instead of proving the given statements, majority of candidates solved the equations and proved by substituting these values. They did not realize that they had to substitute 1 for the first term and 2 for the second term. done Common error was 7 which obtained using arithmetic sequence formula. 25. The diagram shows triangle A and B and the point (0, 4). (Ref. to question paper). Describe fully the single transformation that maps triangle A onto triangle B. Triangle A is mapped onto triangle C by an enlargement centre P, scale factor -. On the diagram, draw triangle C. Find the value of Reflection along x = -1 Triangle with vertices (0, 6), (-1, 5), (-2, 5) 4 done done Majority of candidates were able to identify reflection and could realize where the mirror line was but had a problem in writing its equation. Majority of candidates did not answer this question. Common error found by squaring 26. A = ( ) Common error was to give top right hand element as 9 instead of 3. Candidates were unable to

12 Find ( Find A A ) - 2A Write down, as a 2 2 matrix, the answer to 3 A ( ) ( ) ( ) done done manipulate directed numbers correctly -3 (-6). Common error was to square the entries in matrix A Most candidates did not realize that A gives an identity matrix and tried to multiply all the three matrices.