School

Florida International University **We aren't endorsed by this school

Course

PSY 350

Subject

Finance

Date

Nov 3, 2023

Pages

4

Uploaded by gitausimon062 on coursehero.com

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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