MATHEMATICS (309/1) REPORT The 2013 Mathematics (309/1) paper was of average standard. The paper covered a wide range of the syllabus. It was neither gender bias nor culture bias. It did not have language barrier based on the region or location of the candidates. In 2012 eight (08) candidates obtained all the marks [scored 80] whereas in 2013 only three (03) candidates scored the total. On the other hand there were quite a number of zeros [00] in 2012 whereas there were only four (04) lowest scores of [01] in 2013, showing that indeed the paper was simpler. It was expected that most candidates would perform well on this paper. However, the actual performance of the candidates, after marking, went far below expectations. One cannot say whom to blame; Perhaps teachers did not reach to the depth of the syllabus or learners are now adopting a carefree culture, but what is evident is that there is a decrease in quality of performance, year after year. It is suggested that either ECoL as the national body committed to standards and responsible for examinations or any other relevant stakeholder should intervene, by limitlessly holding clinics for teachers to equip them with the requirements of the Lesotho syllabus as far as assessment is concerned. Errors in the questions Besides the reported poor performance of the candidates there were a number of mistakes observed on the assessment tool itself outlined as follows: Question 9 The figure was twisted during scanning and hence does not seem to have a line of symmetry. Question 16 (b) The index 2 was wrongly written i.e. P = was written as P= I2R while in
Question18 (a) (ii) the equation + 7x + 12 was presented as x2 + 7x + 12 Question 16 The diagram was misleading: The sizes of the angels drawn did not correspond to their numeric values thus: An angel of 10 o looked greater than the angel q = 110º, as reflected in the diagram In this case, candidates were tempted to transposing them. Question 26 The graph was wrongly drawn. The y-intercept on the graph did not agree with the equation of line. Generally It is worth mentioning that measures were put in place to accommodate these new ideas (errors) into the marking memo and mark each question according to the learners interpretations. It is again important to note that inasmuch as omission of units in the answers is not considered a serious offence (except in a case where the question was testing the units)wrong or irrelevant units nullify everything and give the wrong answer, meaning loss of marks. Performance analysis question by question. Question 1 Work out: (a) 4 + 3 Expected response: or 7 Common errors: 7 or 7 Misconceptions: students would add numerators and denominators without looking for the LCM. General performance: it was well done.
(b) Expected answer: or 3 Common errors:,, Misconceptions: students would still add numerators and denominators. General performance: well performed. Four basic operations should be emphasized. Question 2 Round off 3.2061 to 2 decimal places. Expected response: 3.21 Common errors: 3.200, 3.201 Misconceptions: candidates confused decimal places with significant figures. General performance: it was average. Question 3 Work out (a) 3.5 + 2.6 Expected response: 6.1 General performance: it was well done; most candidates got the question correct. (b) 1.2 0.3 Expected response: 0.36 Common errors: 3.6, 00.036, 00.36 Misconceptions: they were not able to identify where the decimal point should be placed. General performance: average.
Question 4 Find the product of -6 and +2 Expected response: -12 Common errors: 12, -4, 8 Misconceptions: candidates would add instead of multiplying General performance: average. More emphasis on the terminology: product, sum, difference and quotient. Question 5 Write the next two terms in the sequence 3, 4, 6, 9, and 13. Expected response: 18, 24. Common errors: 17, 29. Misconceptions: candidates were not able to find the correct rule for the sequence. General performance: good. Question 6 Work out (a) -27 +3 Expected response: -9. Common errors: 9, -8 Misconceptions: candidates ignored the negative sign. General performance: average. (b) -7 - -3 Expected answer: -4. Common errors: 4, -10
Misconceptions: same as in 6. (a) General performance: good. Question 7 Express (a) (i) 3120 in standard form Expected answer: 3.12 Common errors: 3120 or 3.12 = or 3.12 Misconceptions: did not remember the form a and for those who used it, they did not understand that 1 a 9 should be considered in order to get the correct answer: where a is a positive integer and n, an integer. General performance: good. (ii)24 as the product of its prime factors. Expected answer: 3 or 2 2 2 3 Common errors: 2 2 3, 0, 1, 2 General performance: fairly done. More emphasis on the terminology: product, sum, difference and quotient. (b) Simplify n Expected answer: mn Common errors:, m = 1.5 General performance: poorly done.
Question 8 Shade the region A B in the Venn diagram. A B Expected answer: A B Common errors: A B Misconceptions: candidates shaded B 1 (unwanted region). General performance: average. More emphasis should be made on the use of set symbols and set notation.
Question 9 For the given diagram (a) Find the number of lines of symmetry. Expected answer: 1 Misconception: learners looked at this as just a circle not a figure. Some saw a circle with some irregularity on the circumference. General performance: well done. (b) What is its order of rotational symmetry? Expected answer: 1 Misconception: as in (a) above. General performance: well done.
Question 10 (a) What is the type of angle marked in the diagram? Expected answer: obtuse Common errors: acute, reflex. Misconception: candidates were not able to identify the marked angle, only wanted to choose an angle opposite to the marked angle. General performance: average. (b) Measure and write the size of the marked angle. Expected answer: ± Common errors: 150º, 140º. General performance: fairly done. More emphasis should be made on the use of protractor. Question 11 Arrange the following fractions in order of size starting with the smallest.,,, Expected answer:,, Common errors:,, Misconceptions: candidates arranged only the numerators; they did not look at the LCM. General performance: average.
Teachers should strongly emphasis ordering. Question 12 Calculate the bearing of b from D in the diagram. N N B 120 D Expected answer: 300 Common errors: 60, 240 Misconception: candidates were unable to identify the wanted angle, they would subtract 120 from 360. General performance: very poorly done. Teachers should put more emphasis on the calculations of bearing. Question 13 List all integers which satisfy the inequality. -1 2 Expected answer: 0, 1, 2 Common errors: -1, 0, 1, 2 or 1, 2 Misconception: candidates confused the use of and signs.
General performance: very poorly done. Teachers should put more emphasis on the inclusive and exclusive inequalities. Question 14 (a) In a class of 50 students, the ratio of girls to boys is 2:3. Calculate the number of girls. Expected answer: 20 girls Common errors: 30, 25 Misconception: candidates would calculate number of boys or rather divide 50 by 2. General performance: fairly done. (b) Mpho s salary is increased from M1500 to M1800. Calculate the percentage increase. Expected answer: 20% Common errors: 30%, 83% Misconception: candidates would simply divide 1500 by 1800 then multiply without calculating the increase. General performance: very poorly done.
Question 15 Describe the transformation that maps triangle ABC onto triangle A B C. C Q B A B C A R S P Expected answer: reflection in line PQ Common errors: rotation on y=0 or rotation on line P or Q. Misconceptions: candidates considered the point P or Q instead of line PQ or QP. General performance: very poorly done. Question 16 (a) Solve the equation + 1 = 7 Expected response: x = 18 Common errors: 7, 20 Misconception: candidates would multiply x and 7 by 3 leaving 1, then subtract. General performance: not good. Teachers should put more emphasis onequationsolving.
(b) (i) Make R the subject of the formula. P = I 2 R Expected answer: R= Common errors:r =, R =, R = General performance: not well done. Teachers should strongly emphasize the basic operation and solution on equations. (ii) Given that I = and R = 10, find the value of P in the formular. P = I 2 R Expected answer: 10 Common errors: 20, 150 Misconceptions: candidates would simply multiply 2 by R, ignoring the value of I. General performance: very poorly done. Question 17 Find values of angles marked p and q in the diagram. 10 p 120 q Expected answer: p = 60 and q = 110 Common errors: p = 110 or p = 70 or p = 100 and q = 60
General performance: not well done. Question 18 (a) Factorize completely (i) 2ax+ 3a Expected answer: a (2x + 3) Common errors: 2a (x + 3a) General performance: fairly done. (ii) + 7x + 12 Expected answer: 3 (3x + 4) (b) Remove the brackets and simplify (x + 1) (x 2) Expected answer: - x 2 Common errors: x + 1 x 2 General performance: very poorly done. More emphasis on algebraic manipulation and directed numbers. (c) Given that f (x) = 3x 1, find f (2) Expected answer: 5 Common errors: 6, 6 2 1 General performance: not well done. More emphasis should be laid on functions and mappings.
Question 19 Calculate the time from 8:45 a.m.to 10:35 a.m. Expected answer: 1hr 50mins Common errors: 1:50, 1:50hrs Misconception: candidates confused time duration with time. More emphasis should be on time calculations. Question 20 PQR is a right angled triangle. PQ = 12cm and QR = 5cm. Q 12cm P 5cm R (a) Calculate the length of PR Expected answer: 13cm Common errors: Misconceptions: candidates would subtract 25 from 144 to get 119, and then take the square root. General performance: poorly done. More emphasis on Pythagoras theorem, squares and square roots.
(b) Given that ( ) ( ) ( ) 24.6 65.4 22.6 Find the angle QPR Expected answer: 22.6 Common errors: 24.6, 65.4 Misconception: candidates considered cos, sin and tan ratios as equivalent ratios. General performance: very poorly done. Teachers should strongly put more emphasis on trigonometric ratios (SOH CAH TOA). Question 21 A regular polygon has as exterior angle of 72 (a) How many sides does it have? Expected answer: 5 sides Common errors: 72 sides, 8 sides, 6 sides Misconceptions: candidates just picked up a side of any of regular polygons or the size of exterior angle. More emphasis on polygons both regular and irregular polygons.
(b) Calculate the sum of its interior angles. Expected answer: 540 Common errors: 12600, 1080 720 Misconceptions: wrong multiplication General performance: both 21 (a) and 21 (b) were not well done. Same as in 21 (a). Question 22 Given that A =( ), B = ( ) and C = (0 1) Find (a) B - A Expected answer: ( ) Common errors: ( ) ( ) ( ) Misconception: candidates would consider the negative sign as non-existing. General performance: very poorly done. Teachers should put more emphasis on the matrix operation and four basic operations. (b) CA Expected answer: (2-1) Common errors: ( ) or (2 1) or ( ) or ( ) Misconception: candidates were unable to identify the order of the matrix. General performance: not well done.
More emphasis should be made on the matrix multiplication. Question 23 The masses of five boys are 51kg, 52kg, 47kg, 52kg, and 53kg. Find (a) the modal mass Expected answer: 52kg Common errors: 53kg, 51kg Misconceptions: candidates were unable to differentiate mode from median. General performance: average (b) the median mass Expected answer: 52kg Common errors: 53kg, 51kg Misconceptions: same as in (a) General performance: same as in (a) More emphasis should be made on statistics. (c) Calculate the mean mass of the boys. Expected answer: 51kg Common errors: 52kg, 53kg Misconceptions: same as in (a) General performance: same as in (a)
(d) A boy is chosen at random. What is the probability that his mass is 52kg? Expected answer: Common errors: Misconceptions: candidates would add the total of mass and pick up 52kg. General performance: not well done Teachers should strongly emphasis concepts o statistics. Question 24 Tsoto walks 4km in 30 minutes to school. Calculate his average speed in kilometers per hour. Expected answer: 8 km/h Common errors: 7.5 km/h Misconceptions: students would divide distance by time without converting time into hours. Then they would round off to get their 8 km/h. General performance: very poorly done; most students did not get the question correct. Teachers should put more emphasis on conversion of units.
Question 25 Use = 3.14 for this question. (a) The diagram shows the sector of a circle A O 50cm B Calculate (i) the arc AB Expected answer: 78.5 Misconceptions: candidates were not able to see from a diagram that this is a quarter of a circle, they also considered as instead of 3.14. General performance: not well done. (ii) the perimeter of the sector Expected answer: 178.5 cm Common errors: 100 Misconceptions: candidates just added 50cm to another 50cm. General performance: not well done. (iii) the area of the sector Expected answer: 1962.5 Common errors: 19.62, 1962 Misconceptions: candidates considered diameter as 50cm instead of 100cm.
General performance: very poorly done. Teachers should advise students to read instructions carefully. Candidates should not just use as 3.14 or but should follow the instructions. (b) Calculate the volume of the cylinder. 10cm 20cm Expected answer: 6280 Common errors: 62.80, 6280.52 Misconceptions: misuse of ; some candidates did not use. General performance: very bad For the whole question more emphasis should be made on mensuration.
Question 26 The diagram shows the graphs of straight lines y x = -1 and 2x + 3y = 4 y - axis 5 4 3 2x + 3y = 4 y x = -1 2 1 0 1 2 3 4 5 6 x- axis (a) Use the graph to find the solution of the simultaneous equations y x = -1 and 2x + 3y + 4. Expected answer: x = 3 and y = 2 Common errors: x = 2 or x = -2 and y = 3 Misconceptions: candidates were unable to identify the intersection, which is the solution of the two lines. General performance: average (b) Find the gradient of the line 2x + 3y = 4 Expected answer: Common errors:, 1, 2 or 3 Misconceptions: candidates ignored the negative sign, or they just picked up any value from the equation. General performance: very poor.
More emphasis on the solution of equations. Question 27 By construction, bisect the angle DEF in the diagram D EF Expected answer: A line that cuts the angle DEF into two equal angles Common errors: no arcs seen Misconceptions: candidates used the protractor instead of bisecting the angle. General performance: very poor. Teachers should train the learners on construction. Question 28 Find the mapping for the following set of ordered pairs; (0, 0), (1, 5), (2, 10), (3, 15) Expected answer: x 5x Common errors: 5 or 5 Misconceptions: candidates were unable to identify that outputs are in the form of the sequence.
Question 29 A point V has coordinates (2, 1). (a) Find the coordinates of V under the translation vector ( ). Expected answer: (6, 4) Common errors: ( ), 6 or 4 Misconception: candidates were not able to differentiate between a column vector and a coordinate. They ignored the brackets for coordinate system. General performance: not well done. (b) Find the length of V V. Expected answer: 5 units Common errors: 8.1, 5cm, (6, 4), 6, 4 etc. Misconceptions: candidates were not able to differentiate part (a) and part (b). General performance: average Teachers should put more emphasis on vectors.