# CLS SEPT 2022

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CLS SEPT 2021 REGIONAL CENTRE TRAINING INSTITUTE (RCTI) Certificate in land Survey STAGE 2 TERM 1 EXAMINATION July 2023 SERIES MATHEMATICS Duration: 3 Hours INSTRUCTIONS 1. Attempt ALL questions 2. Every Questions Carries 20 Marks 3. Show ALL your workings 4. Only a silent, Non- Programmable calculator may be used in this examination 5. Mobile phones are not allowed in the examination room 6. No reading or external writing materials are allowed into the examination room 7. No communication is allowed except with the express permission of the Invigilator 8. Observe all Center's examination rules and regulations Candidates should check the question paper to ascertain that all pages are printed as indicated and that no questions are missing Mr. Imathiu Mr. Karit
QUESTION ONE 20 MARKS (a) Mr Marwa is employed as a grounds man in a technical institution. He earns ksh. 12,000 per month and he is entitled to a house allowance of ksh 2,250. He is married man. During the month of July he worked overtime and was paid ksh 3,000 as overtime allowance. Calculate the tax for the month of July if he is entitled to a family relief of Kes.2,640 per year. Monthly Income slab ksh Rates % 0 - 2640 2641 - 5280 5281 - 7920 7921 - 10560 10561 - 13200 13201 - above 10 15 20 25 35 40 (15 marks) b) Solve the Simultaneous equations (i) 4 log 2 m + 3log 2 n = 32 (ii) 3 log 2 m 2log 2 n = 7 (5 marks) QUESTION TWO 20 MARKS (a) Given that θ is an acute angle and sin θ = 4 5 determine without using tables: (i) Cos θ (ii) Tan θ (iii) Cosec θ (iv) Sec θ (6 Marks) (b) Prove the trigonometric identity i) Cosθ 1 Sinθ + Cosθ 1 + Sinθ = 2 Secθ (4 Marks) ii) 2cos θ 1 Sinθ + Cosθ Sinθ + 1 = 3 Secθ + tanθ (5 Marks) iii) 1 tan 2 θ 1 + tan 2 θ = 1 2sin 2 θ ( 5 Marks )
QUESTION THREE 20 Marks a) A ladder 5 m long, leaning against a vertical wall makes an angle of 65 0 with the ground. (i) How high on the wall does the ladder reach? (ii) How far is the foot of the ladder from the wall? (iii) What angle does the ladder make with the wall? (8 mks) b) Given the matrices A = [ 3 2 5 6 ] B = [ 2 2 4 1 ] Find (i) 3A + 2B (ii) A T B T (iii) ( BA ) 1 (iv) 3 A T B T (12 mks) QUESTION FOUR 20 Marks (a) Sunshine Traders had the following records in their accounts for the year and then to 30th June 2002. Kes. Stock as at 01/07/2021 40,000 Stock as at 30/06/2022 60,000 Purchase 260,000 Carriage Inwards 10,000 Capital 200,000 Gross Profit mark up 40% Expenses as a percentage of Gross profit 40% Required a) Average Stock b) Rate of stock turn over c) Gross Profit Margin d) Return on Capital Invested
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