Mid Semester Examination FND07CM Computing Mathematics PDF

MID SEMESTER EXAMINATION FND07CM COMPUTING MATHEMATICS 2 Hours 08:30 AM TO 10:30 AM Total Marks: 100 INSTRUCTIONS TO CAND...

MID SEMESTER EXAMINATION FND07CM COMPUTING MATHEMATICS 2 Hours 08:30 AM TO 10:30 AM Total Marks: 100 INSTRUCTIONS TO CANDIDATES 1. This examination paper consists of FIVE (5) pages (including the cover page). 2. Answer all FOUR (4) Questions each question starting from a new page. 3. Write in clear handwriting and number the questions you attempt accordingly on ruled papers. 4. All workings need to be shown. Calculators are allowed. QUESTION 01 (25 marks) a) Simplify: (i) (12 × 8 − 6! ) ÷ (8 + 7) (2 marks) " " % (ii) # × ,$ + " - (3 marks) %! & (iii) %" ÷' (2 marks) b) Convert (show all working): (i) 0.325 𝑡𝑜 𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 (2 marks) (ii) 98.75% 𝑡𝑜 𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 (3 marks) c) Approximate the following: (i) 121.3 × 98.6 (2 marks) (ii) (3.89)" (3 marks) d) Find: (i) 𝑊𝑟𝑖𝑡𝑒 392 𝑎𝑠 𝑎 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑝𝑟𝑖𝑚𝑒 𝑓𝑎𝑐𝑡𝑜𝑟𝑠. (3 marks) (ii) 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝐿𝐶𝑀 𝑎𝑛𝑑 𝐻𝐶𝐹 𝑜𝑓 28, 48 𝑎𝑛𝑑 68. (5 marks) QUESTION 02 (25 marks) a) Simplify to the simplest form: $) (i) 1( ! (1 mark) !) *# " (ii) ,!'- (3 marks) % (iii) 𝐹𝑖𝑛𝑑 𝑥 𝑖𝑛 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛: # = 2+ (3 marks) b) Simplify: (i) √13 ÷ √13 (1 mark) √" (ii) !-√" (2 marks) (iii) 7√54 − √24 (3 marks) c) Simplify the expressions below: (i) 7𝑥 × 2𝑦 ! × (2𝑦)! (3 marks) % (ii) ! (4𝑥 − 6𝑦 + 4𝑥 − 4𝑦 + 8) (3 marks) d) Simplify:.-/-0 (i) 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓. ! -/! -0! 𝑖𝑓 𝑘 = −3, 𝑚 = 1 𝑎𝑛𝑑 𝑛 = 4 (3 marks) 1-% (ii) 𝑀𝑎𝑘𝑒 𝑡 𝑡ℎ𝑒 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑜𝑓 𝑚 = /-$ (3 marks) QUESTION 03 (25 marks) a) Solve for x: (i) −7 = −8𝑥 − 12𝑥 (2 marks) (ii) 8(𝑥 + 5) + 2 = 4.8𝑥 + 4 (3 marks) b) Work out the simultaneous equations below: (i) 3𝑥 + 2𝑦 = 7 4𝑥 − 3𝑦 = 15 (4 marks) (ii) 𝑇ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑡𝑤𝑜 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑖𝑠 14 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑠 2. 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠. (3 marks) c) (i) 𝐸𝑥𝑝𝑎𝑛𝑑 (𝑥 + 8)(𝑥 − 2) (2 marks) (ii) 𝑆𝑜𝑙𝑣𝑒 6𝑥 ! − 17𝑥 + 12 = 0 (4 marks) d) Solve: (i) 2𝑚 + 13 ≥ 8 (3 marks) +-# !+-" (ii) " + #