el EXAMINATION NOs THE MALAWI NATIONAL EXAMINATIONS BOARD 2021 MALAWI SCHOOL CERTIFICATE OF EDUCATION EXAMINATION MATHEMATICS Subject Number: M131/I Time Allowed: 2 hours Wednesday, 3 November 8:00 - 10:00 am PAPER I (100 marks) Question] Tick if Do not write in Instructions Number | answered | these columns 1. This paper contains 14 printed pages. 1 Please check. 2 | 3 | 2. Answer all the 20 questions in this paper. a 3. The maximum number of marks for each 5 d answer is indicated against each question. § 4. Write your answers in the spaces provided 8 z on the question paper. 9 s i 5. Scientific calculators may be used. iI 6. ‘The graph paper and the blank answer sheet | — at the end of the question paper can be used if required. Do not tear them off. oo eee =a 15 7. All working must be clearly shown. 16 a 17 8. Write your Examination Number at the top |~ 18 | of each page of your question paper in the 7 1 spaces provided. a 4 a 9. In the table provided on this page, tiek against the question number you have answered, a © 2021 MANEB Turn overEXAMINATION NO. ee 2021 Page 2 of 14 MI3iii 1, Simplify 2115 ~ 102s, giving the answer in base 10. (4 marks) ¥ a Factorise completely 2m?n + 9mn—Sn (4 marks) Continued/...EXAMINATION NO,; 2021 Page 3 of 14 : Tie wT 2 = ca 3. Given that f(s) = +2, calculate the value of x when fox) =7 (S marks) 4, Without using a calculator, simplify , giving the answer with a rational denominator. (5 marks) Continued/oat 2021 5. 6. EXAMINATION NO.: Solve the equation 2x? ~ 4x3 =0, decimal places. Make d subject of the formula $= 5 Ra+@-nal, —_ Page 4 of 14 MI3iq giving the answer correct to two (6 marks) (4 marks) Continued/.EXAMINATION NO. 2021 Page 5 of 14 MI31/1 7. Figure 1 shows two chords AB and DC ofa circle ABCD with centre O. Figure 1 | Given that DC = 8 cm and ON = 3 cm, OM = 2 cm calculate the length of AB, leaving the answer in surd form. (6 marks) Continued: 8EXAMINATION NO.: 2021 Page 6 of 14 MI31/1 8. A water bill for a certain family was K4 942.64. If the bill includes Value Added Tax (VAT) of 20%, service fee of K285.94 and meter rental charge, calculate the meter rental charge. (4 marks) 9. The Table below shows income tax rates in Malawi. Income per month (K) Rate(%) __| pirstaeets 100 000 | 0 (free) Next 2.900 000 | 30 [Excess (over) 3.000 000 | 35 If an employee receives K3 885 000 per month, calculate the income tax paid per month. (5 marks Continued/...EXAMINATION NO.: 2021 Page 7 of 14 Misi ‘ 45 8: A/3i 10. Given that 2M- = , find matrix M. (; ul } (i 1 } wre (4 marks) 11. Figure 2 shows a right angled triangle PQR in which RP = 10 cm and PQ = 4 cm. R Q, ey Ton P Figure 2 Calculate the value of angle QRP, giving the answer correct to the nearest degree. (4 marks) Continued’...EXAMINATION NO.: 2021 Page 8 of 14 Main 12, Figure 3 shows a circle PQRS in which PT an c d RT are tangents at P and R respectively. Figure 3 Given that angle PTR = 68° and TRQ = 35°, calculate the value of angle QPT. (6 marks) Continued’.EXAMINATION NO: 2021 Page 9 of 14 MI31/1 13, Figure 4 shows an image triangle A'B'C! of triangle ABC under enlargement. cd 10) Figure 4 If triangle A'B'C! was drawn using the scale factor of 2 and centre (0,0), using the same axes, draw triangle ABC in Figure 4, (5 marks) Continued’... orEXAMINATION NO.: 2021 Page 10 of 14 14, The quantity x varies directly as y* and inversely as w. When x= 32, y=8 and w=4. Find x when y=10and w= 25. (6 marks} Continued:EXAMINATION N 2021 Page 11 of 14 MI3I/ 15. Calculate the size of an exterior angle of a regular octagon (6 marks) 16. Figure 5 is an equilateral triangle PQS in which PR bisects angle SPQ. Pp R Q Figure 5 Show that triangle PRQ is congruent to triangle PRS. (4 marks) Continued/..EXAMINATION NO. 2021 Page 12 of 14 MIN 17. Calculate the distance between x and y intercepts of the graph of the equation y= fe +8. (4 marks) 18. A farmer mixed 25 kg of manure costing K150 per kg with 5 kg fertilizer costing K480 per kg. If the mixture was sold at K250 pet kg, calculate the profit made per kg. (6 marks) Continued’...2021 EXAMINATION NO.:, Page 13 of 14 MISA 19. Figure 6 is a square based pyramid ABCDE in which DC = pie pyrami in which DC = 12 em E B an —€ Figure 6 ITEM is a slant height of triangle BCE, calculate the total surface area of the pyramid, giving the answer correct to the nearest whole number: (7 marks) ContinuedEXAMINATION NO.:. Page 14 of 14 MI3I/I 2021 20. Figure 7 shows unshaded region R represented by four inequalities. tHe Hf atte oe LTTE STI POSTE TTT Nb Ht hi 4 isc le Hay aH | Figure 7 Write down the four inequalities. (6 marks) END OF QUESTION PAPER NB: This paper contains 14 printed pages.