# CLS MAY. 2023 1.1 MATHEMATICS EXAM (1) (1)

.docx
School
Florida International University **We aren't endorsed by this school
Course
ACCOUNT 01
Subject
Mathematics
Date
Nov 3, 2023
Pages
4
CLS MAY 2023 Duration: 3 Hours REGIONAL CENTRE TRAINING INSTITUTE (RCTI) Certificate in Land Survey STAGE 1 TERM 1 EXAMINATION MAY 2023 SERIES Mathematics Duration: 3 Hours INSTRUCTIONS 1. Attempt <ALL FIVE> 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 Centre'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 MS. LYDIA MR. SIMON
CLS MAY 2023 QUESTION ONE (20 Marks) a) Solve the equation 2 2 x + 1 = 5 ( 3 x ) 1 (8 Marks) b) Convert i ¿ 101 10 to binary number ii ¿ 75 10 to base 2 (6 Marks c) Simplify the following expressions i) x 5 y 2 2 x 3 xy 8 x 3 y 2 y x 3 (2 Marks) d) Solve for x given that x 3 5 = 4 x 2 2 ( 4 Marks ) QUESTION TWO (20 MARKS) a) Solve without using a calculator i) log32 log 4 + log 3 log256 (3 Marks) ii) log 75 + log 2 log3 (3 Marks) b) Solve the equations i) log x + log ( x 1 ) = log ( x 2 + x 1 ) (4 Marks) ii) Log(x-1) +log(x+1) = 2log(x+2) (6 Marks) c) Given that log2=0.3010 and log3 =0.4771 Simplify i) log 54 ii) log 1.5 (4 Marks) QUESTION THREE MS. LYDIA MR. SIMON
CLS MAY 2023 a) Given that a x 2 + bx + c = 9 , show that x = b 2 4 ac 2 a . Hence solve the equation t 2 + t 5 = 0 (11 Marks) b) Use factorization to solve the quadratic equation 5 r 2 3 r + 2 = 0 (4 Marks) c) Use the complete square method to solve the equations 3 x 2 + 4 x 7 = 0 (5 Marks) QUESTION FOUR a) Solve the following simultaneous equation by substitution method 10 x + y = 35 4 x 7 y =− 27 (4 Marks) b) Use the elimination method to solve the system of linear equation 7 x + y + 5 z = 27 4 x + 3 y + 5 z = 21 6 x + y + 2 z = 9 (8 Marks) c) Make x the subject of the formu la i) a x + b = k ii) T = 2 π x k iii) log a x + log a b = n iv) 2 x + 3 ( 1 x ) = 5 x 9 (8 Marks) QUESTION FIVE (a) The first term of an arithmetic progression is 4 and the last term is 20. The sum of the terms of 252. Calculate the: (i) Number of terms; (ii) Common difference; (iii) 10 th term. (8 marks) (b) The average of the 1st and 4th terms of a geometric progression is 140. Given that the First term is 64, determine the Common ratio; (i) Tenth term; MS. LYDIA MR. SIMON
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