All Questions
The table below show income tax rate for the year 2019.
|
Taxable Income (Kshs. per month) |
Tax rate (Kshs per Kshs. 20) |
|
1 – 12,000 |
2 |
|
12,001 – 22,500 |
3 |
|
22,501 – 33,000 |
4 |
|
33, 000 – 43,500 |
5 |
|
43,501 – 54,000 |
6 |
|
54,001 and over |
7 |
Emerick earns a basic salary of Kshs. 38,780. He is entitled to the following allowances per month: house allowance – Kshs. 10,000, medical allowance – Kshs. 3,850 and a non-taxable transport allowance of Kshs. 5,200. He is entitled to a personal tax relief of Kshs. 1,054 monthly.
Calculate:
(a) Emerick’s monthly taxable income. (2 marks)
(b) Emerick’s monthly Pay As You Earn. (5 marks)
(c) His net monthly salary given that the following deductions are made from his monthly pay: NHIF – Kshs. 3,000, Bank loan – Kshs. 7,568, WCPS – Kshs. 780. (3 marks)
The table below shows the heights of tree seedlings measured in a tree nursery.
(a) Complete the table below. (2 marks)
|
Height |
f |
x |
d=x-5.45 |
|
3.0 – 3.9 |
3 |
|
|
|
4.0 – 4.9 |
5 |
|
|
|
5.0 – 5.9 |
7 |
|
|
|
6.0 – 6.9 |
8 |
|
|
|
7.0 – 7.9 |
5 |
|
|
|
8.0 – 8.9 |
2 |
|
|
(b) Use the table to calculate the standard deviation correct to decimal places. (4 marks)
(c) i) On the grid provided, draw an ogive to represent the information above. (2 marks)
ii) Use the ogive to find the range of height between the 20th and the 80th percentile. (2 marks)
Solve for x in the equation (3 marks)
Use logarithms only to evaluate, correct to 4 decimal places (4 marks)
Calculate the percentage error in the perimeter of a circle of radius 3.5 cm. (3 marks)
The figure below shows a ranch ABCD drawn to a scale of 1: 100,000. A security light tower is to be installed in the ranch such that it meets the following conditions:
- It is nearer to A than it is to B
- It is at least 200 metres from the point C
- It is further from the line CD than it is to A
Shade the possible region in the ranch where the tower would be installed to meet the above conditions. (4 marks)
The probability of Kisumu Day High School to win a hockey match is 7/8. If it losses in hockey, then it has a probability of winning in soccer as 3/4. Otherwise, the probability of winning the soccer match is 2/3. Calculate the probability of the school winning either of the two games. (3 marks)
The table below show the number of days (d ) and heights of tree seedlings (h ) in a tree nursery
|
Number of days (d) |
1 |
2 |
3 |
4 |
5 |
|
Height (h cm) |
3.7 |
6.0 |
7.5 |
8.3 |
8.8 |
(a) On the grid provided, draw a graph to represent the information in the table given. (2 marks)
(b) Use the graph to determine the rate of change of height (h
) with the number of days at d=3 (2 marks)
An airport R is 4320 nautical miles to the north of another airport T (450S, 1080E). find the position of T (3 marks)
The equation of a trigonometric function is 
. The function has a period of 7200.
(a) Identify the phase angle of the function (1 mark)
(b) Determine the value of a (1 mark)