KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
The shortest distance between two points A (40°N, 20°W) and B (0°S, 20°W) on the surface of y the earth is 8008km. Given that the radius of the earth is 6370km,
determine the position of B. (Take n = 22/7 ).
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Form 4 MathematicsForm 4 MathematicsForm 4 Mathematics
Determine the amplitude and period of the function, y = 2 cos (3x — 45)°.
Form 4 Mathematics
a) Complete the table below, giving your values correct to 2 decimal places.
Form 4 Mathematics
The line PQ below is 8cm long and L is its midpoint
Form 4 Mathematics
Form 4 Mathematics
Omondi makes two types of shoes: A and B. He takes 3 hours to make one pair of type A and 4 hours to make one pair of type B. He works for a maximum of 120 hours to x pairs of type A and Y pairs of type B.It costs him sh 400 to make a pair of type A and sh 150 to make a pair of type B.
His total cost does not exceed sh 9000. He must make 8 pairs of type A and more than 12 pairs of type B. Form 4 Mathematics
A ship leaves port p for port R though port Q.Q is 200 km on a bearing of 2200 from P.R is 420 km on the bearing of 1400 from from Q.
Form 4 Mathematics
The equation of acurve is given by y = x3 – 4x2 – 3x
(a) Find the value of y when x = -1 (b) Determine the stationary points of the curve (c) Find the equation of the normal to the curve at x = 1 Form 4 Mathematics
(a) Complete the table below for the function y = x2 – 3x + 6 in range -2 ≤ x ≤ 8
(b) Use the trapezium rule with strips to estimate the area bounded by the curve,y = x2 – 3x + 6, the lines x = -2, x = 8, and x - axis
(c) Use the mid-ordinate rule with 5 strips to estimate the area bounded by the curve,y = x2 – 3x + 6, the lines x = -2, x = 8, and x –axis (d) By integration, determine the actual area bounded by the curve y = x2 – 3x + 6, the lines x = -2, x = 8, and x –axis Form 4 Mathematics
A mixed school can accommodate a maximum of 440 students. The number of girls must be at least 120 while the number of boys must exceed 150. Taking x to represent the number of boys and y the number of girls, write down all he inequalities representing the information above.
Form 4 Mathematics
The table below shows marks scored by 42 students in a test.
a) Starting with the mark of 25 and using equal class intervals of 10, make a frequency distribution table.
b) On the grid provided , draw the ogive for the data c) Using the graph in (b) above , estimate: (i) The median mark (ii) The upper quartile mark Form 4 Mathematics
The equation of a curve is given by y = 5x − 1/2 x2
(a) On the grid provided, draw the curve of y = 5x − 1/2 x2 for 0 ≤ x ≤ 6 (b) By integration, find the area bounded by the curve, the line x =6 and the x-axis. (c) (i) On the same grid as in,(a).draw the line y = 2x. (ii) Determine the area bounded by the curve and the line y = 2 x. Form 4 Mathematics
Two towns A and B lie on the same latitude in the northern hemisphere. When its 8am at A, the time at B is 11.00am.
Form 4 MathematicsThe diagram below is a sketch of the curve y =x2 + 5.
Form 4 Mathematics
(a) Complete the table below, giving the values correct to 1 decimal place.
b) On the grid provided, using the same scale and axes, draw the graphs of y = 2 sin (χ+20)0 and y = √3 cos χ for 00 ≤ χ ≤ 2400.
c) Use the graphs drawn in (b) above to determine: i) the value of χ for which 2sin (χ + 20) = √3 cos χ; ii)the difference in the amplitudes of y =2sin(χ + 20) and y =√3 cos χ. Form 4 Mathematics
The figure ABCDEF below represents a roof of a house. AB=DC=12 m, BC = AD = 6m, AE = BF = CF= DE = 5m and EF = 8m
(a) Calculate, correct to 2 decimal places, the perpendicular distance of EF from the plane ABCD.
(b) calculate the angle between : (I) the planes ADE and ABCD (II) The line AE and the plane ABCD, correct to 1 decimal place; (III) The planes ABFE and DEFE, correct to 1 decimal place. Form 4 MathematicsForm 4 Mathematics
The position of two towns are (20 S,300 E) and 20S, 37.4 0E) calculate , to the nearest km, the shortest distance between the two towns.(take the radius ofthe earth to be 6370 km)
Form 4 Mathematics
A point P moves inside a sector of a circle, centre O, and chord AB such that 2cm < OP ≤ 3cm and angle APB = 65 Draw the locus of P
Form 4 MathematicsForm 4 MathematicsThe velocity Vms-1 of particle in motion is given by V =3t2 – t +4, where t is time in seconds. Calculate the distance traveled by the particle between the time t=1 second and t=5 seconds. Form 4 Mathematics
The displacement, s metres, of a moving particle from a point O, after t seconds is given by, s = t3 – 5t2 + 3t + 10
a) Find s when t =2. b) Determine: i. The velocity of the particle when t = 5 seconds; ii. The value of t when the particle is momentarily at rest. c) Find the time, when the velocity of the particles is maximum. Form 4 Mathematics
A trader bought 2 cows and 9 goats for a total of Ksh 98, 200. If she had bought 3 cows and 4 goats she would have spent Ksh 2,200 less.
a) Form two equations to represent the above information. b) Use matrix method to determine the cost of a cow and that of a goat. c) The trader later sold the animals she had bought making a profit of 30% per cow and 40% per goat. i. Calculate the total amount of money she received. ii. Determine, correct to 4 significant figures, the percentage profit the trader made from the sale of the animals |
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