KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Demystifying Gross Tax and Gross Salary in Relation to Income TaxThe Difference Between Gross Tax and Gross Salary in Relation to Income Tax Gross tax and gross salary are two terms that are often associated with income tax calculations. Understanding the difference between these two terms is important in order to grasp the concept of income tax more effectively.
Taxable income is derived from the gross salary by subtracting any allowable deductions, exemptions, or tax credits that the individual is eligible for. These deductions and exemptions may include items such as business expenses, contributions to retirement plans, educational expenses, or certain personal deductions. The difference between gross tax and gross salary can be understood as follows: Gross salary is the total income earned by an individual, whereas gross tax is the total amount of tax liability based on that income before any deductions or exemptions are taken into account. It is important to note that after calculating the gross tax, the final tax liability is determined by applying any applicable tax credits or deductions. The resulting amount is the net tax, which represents the actual amount of tax owed by the individual. In conclusion, the difference between gross tax and gross salary lies in the fact that gross salary refers to the total income earned before any deductions, while gross tax refers to the total tax liability before any deductions or exemptions are applied. Understanding these terms helps in comprehending the calculation and impact of income tax on an individual's earnings. Related Questions
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QUESTION 1 | KCSE 2022 | SEQUENCES AND SERIES | PAPER 2 | FORM 3 LEVEL An investor took a loan from a bank that charged interest. the loan and the interest accrued were repaid in monthly instalments. The investor repaid Ksh. 1500 in the first month and in each subsequent month the instalments were reducing by Ksh. 50 until the loan was fully repaid. Determine the maximum amount that may be paid for that loan. [3 marks]
QUESTION 24 | KCSE 2022 | MATRICES AND TRANSFORMATIONS | PAPER 1 | FORM 4 LEVELTriangle ABC and A'B'C' are drawn on the grid provided.
(a) Describe fully a single transformation that mapped triangle ABC onto triangle A'B'C'. (2 marks) (b) On the same grid, draw: (i) triangle A"B"C" the image of triangle A'B'C' under a rotation of +90° about Ο (0, 0). (2 marks) (ii) triangle A"B"C", the image of triangle A"B"C" under a reflection in the line y = -x. (2 marks) (c) Draw the line of symmetry of triangle A'B'C' and hence determine its equation in the form y = mx +c, where m and c are constants. (4 marks) QUESTION 23 | KCSE 2022 | DIFFERENTIATION | PAPER 1 | FORM 4 LEVELA supermarket sold 530 packets of milk daily when the price was Ksh 50 per packet.
Whenever the price per packet was increased by Ksh 4, the number of packets sold daily decreased by 20. If n represents the number of times the price was increased: (a) write an expression in terms of n for: (i) the price of a packet of milk after the price was increased. (1 mark) (ii) the number of packets of milk sold after the price was increased. (1 mark) (iii) the total sales, in simplified expanded form, after the price of a packet of milk was increased. (2 marks) (b) Determine: (i) the number of times the price was increased to attain maximum sales. (3 marks) (ii) the price of a packet of milk for maximum sales. (1 mark) (iii) the maximum sales. (2 marks) The diagram below is a sketch of two curves y = 2x² + 1 and y = x² + 1 drawn on the same grid.13/11/2023 QUESTION 22 | KCSE 2022 | AREA APPROXIMATION | PAPER 1 | FORM 4 LEVELThe diagram below is a sketch of two curves y = 2x² + 1 and y = x² + 1 drawn on the same grid.
QUESTION 21 | KCSE 2022 | STATISTICS II | PAPER 1 | FORM 3 LEVELThe amount of money, in Kenya shillings, spent on airtime by a group of 30 people in a period of an hour was recorded as shown below.
(a) Complete the frequency distribution table below. QUESTION 20 | KCSE 2022 | GEOMETRICAL CONSTRUCTIONS | PAPER 1 | FORM 1 LEVEL In the figure below, line AB = 10 cm and is part of a trapezium ABCD. Point X is such that angle BAX = 45°.
QUESTION 19 | KCSE 2022 | EQUATIONS OF A STRAIGHT LINE | PAPER 1 | FORM 2 LEVELA triangle ABC is right angled at point A. The vertices of the triangle are A(1, -2), B(5, 4) and C(m, n).
The equation of line BC is 5y - x = 15.
A shot put is spherical and has mass of 7.26kg. It is made of a metal with a density of 6.93 g/cm³13/11/2023 QUESTION 18 | KCSE 2022 | DENSITY | PAPER 1 | FORM 1 LEVELA shot put is spherical and has mass of 7.26kg. It is made of a metal with a density of 6.93 g/cm³. (Take PIE = 22/7).
A contractor hired Wema and Tatu to transport 144 tonnes of stones to building sites A and B.13/11/2023 QUESTION 17 | KCSE 2022 | COMMERCIAL ARITHMETIC I | PAPER 1 | FORM 3 LEVELA contractor hired Wema and Tatu to transport 144 tonnes of stones to building sites A and B.
To transport 48 tonnes of stones for a distance of 28 km, the contractor paid Ksh 24000.
QUESTION 16 | KCSE 2022 | COMMON SOLIDS | PAPER 1 | FORM 1 LEVEL The base, ABCDEF, of a right pyramid is a regular hexagon of side 2.5 cm. Point V is the vertex of the pyramid and the length of the slanting edges is 4 cm.
Draw a labelled net of the pyramid. (3 marks) QUESTION 15 | KCSE 2022 | STATISTICS I | PAPER 1 | FORM 2 LEVELThe table below shows the mean marks in a mathematics test of two classes. Calculate, correct to 2 decimal places, the mean mark of the classes.
QUESTION 14 | KCSE 2022 | Volume & Capacity of Solids | PAPER 1 | FORM 2 LEVELThe capacities of two similar containers are 54ml and 250 ml respectively. The difference in the heights of the two containers is 4cm.
Calculate the height of the larger container. (3 marks) QUESTION 12 | KCSE 2022 | TRIGONOMETRY | PAPER 1 | FORM 2 LEVELAn electric post erected vertically is 20m from point P on the same level ground. The angle of elevation of the top, T, of the post from P is 30°. Given that S is the mid point of the post, calculate, correct to 1 decimal place, the angle of elevation of S from P. (3 marks)
QUESTION 11 | KCSE 2022 | Commercial Arithmetic I | PAPER 1 | FORM 1 LEVELA Kenyan bank bought and sold United Arab Emirates (UAE) dirhams on two different dates as shown below. A Kenyan tourist who travelled to UAE on 1st August 2021 converted Ksh 130050 to UAE dirhams.
During her stay in UAE, she spent 3520 UAE dirhams. She arrived back to Kenya on 16th August 2021. On the same day she converted the remaining amount of money to Kenya shillings at the same bank. Calculate the amount of money in Kenya shillings that she received from the bank. (3 marks) QUESTION 7 | KCSE 2022 | TIME | PAPER 1 | FORM 1 LEVELA watch loses 8 seconds every hour. It was set to read the correct time at 1100 h on Sunday.
Determine the time, in a 12-hour system, the watch will show on the following Thursday when the correct time is 0500 h. (3 marks) QUESTION 9 | KCSE 2022 | bearings | PAPER 2 | FORM 1 LEVELPort L is 120 km on a bearing of S30°W from port K. A ship left port K at 1000 h and sailed at a speed of 40 km/h along the bearing of S60°E.
Using scale drawing, determine the bearing of the ship from port L at 1400 h. (4 marks) QUESTION 9 | KCSE 2022 | Bearings | PAPER 1 | FORM 1 LEVELPort L is 120 km on a bearing of S30°W from port K. A ship left port K at 1000 h and sailed at a speed of 40 km/h along the bearing of S60°E. Using scale drawing, determine the bearing of the ship from port L at 1400 h. (4 marks)QUESTION 10 | KCSE 2022 | Matrices & Transformations | PAPER 1 | FORM 4 LEVEL The image of P(-2, 5) under a translation T is P'(2, 2). Q'(9,-5) is the image of Q under the same translation T. Determine the coordinates of Q. (3 marks)QUESTION 8 | KCSE 2022 | RELATIVE SPEED | PAPER 1 | FORM 3 LEVELA lorry left town A for town B and maintained an average speed of 50 km/h. A car left town A for town B 42 minutes later and maintained an average speed of 80 km/h. At the time the car in town B, the lorry haf 25 km to cover to town B. Determine the distance between town A and B (3 marks)QUESTION 6 | KCSE 2022 | AREA OF QUADLIRATERALS | PAPER 1 | FORM 2 LEVELIn a quadrilateral ABCD, AD = CD = 6 cm and BA = BC = 12 cm. Angle ADC = 300 degrees. Calculate, correct to 2 decimal places, the area of the quadrilateral ABCD.QUESTION 5 | KCSE 2022 | QUADRATIC EQUATIONS | PAPER 1 | FORM 3 LEVELSimplify: [18ax - (3a-4x)(3a + 4x)] / (3a-8x) (3 marks)QUESTION 4 | KCSE 2022 | LCM | PAPER 1 | FORM 1 LEVELKipkoech and Tanui began a 5000m race together at the starting line. Kipkoech and Tanui took 72 seconds respectively to run a 400 m lap. The two athletes were together again after some time. Determine the number of laps that Tanui had to run to complete the race after they were 72 seconds and 80 at the starting line together. (3 marks)QUESTION 3 | KCSE 2022 | INDICES & LOGARITHMS | PAPER 1 | FORM 2 LEVELSolve for x in the equation: 5^(2x-1) - 25^x = 500 |
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