KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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.
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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 3 MathematicsForm 3 MathematicsForm 1 Mathematics
The hire purchase (H.P) price of a public address system was Kshs 276000. A deposit of Kshs 60000 was paid followed by 18 equal monthly installments.
The cash price of the public address system was 10% less than the H.P price. (a) Calculate (i) The monthly installments (ii) The cash price (b) A customer decided to buy the system in cash and was allowed a 5% discount on the cash price. He took a bank loan to buy the system in cash. The bank charged compound interest on the loan at the rate of 20% p.a. The loan was repaid in 2 years. Calculate the amount repaid to the bank by the end of the second year (c) Express as a percentage of the Hire Purchase price, the difference between the amount repaid to the bank and the Hire Purchase price 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 3 MathematicsForm 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 1 Mathematics
Two taps A and B can each fill an empty tank in 3 hours and 2 hours respectively. A drainage tap R can empty the full tank in 6 hours; taps A and R are opened for 5 hours then closed.
(a) Determine the fraction of the tank is still empty (b) Find how long it would take to fill the remaining fraction of the tank if all the three taps are opened Form 3 Mathematics
Two machines, M and N produce 60% and 40% respectively of the total number of items manufactured in a factory. It is observed that 5% of the items produces
by machine M are defective while 3% of the items produced by machine N are defective. If an item is selected at random from the factory, find the probability that it is defective Form 2 Mathematics
The position vectors of points F, G, and H are f, g, and h respectively. Point H divides FG in the ratio 4:-1. Express h in terms of f and g
Form 3 Mathematics
(a) expand (1 − ?)5
(b) Use the expansion in (a) up to the term in x3 to approximate the value of (0.98)5 Form 3 Mathematics
The equation of a circle is given by x2 +4x +y2 -2y – 4 = 0. Determine the centre and radius of the circle
Form 1 MathematicsForm 3 Mathematics
A quadratic curve passes through the points (-2, 0) and (1, 0). Find the equation of the curve in the form y = ax2 +bx +c, where a, b and c are constants
Form 3 Mathematics
The sum of n terms of the sequence; 3, 9, 15, 21, … is 7500. Determine the value of n
Form 4 MathematicsForm 2 Mathematics
A rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m is three – quarters full of milk.
Form 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 2 MathematicsThree points O, A and B are on the same horizontal ground. Point A is 80 metres to the north of O. Point B is located 70 metres on a bearing of 0600 from A. A vertical mast stands at point B. The angle of elevation of the top of the mast from o is 200. Calculate: a) The distance of B from O. (2mks) b) The height of the mast in metres (2mks) |
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