KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Form 3 Mathematics
The radius of a spherical ball is measured as 7 cm, correct to the nearest centimeter. Determine, to 2 decimal places, the percentage error in calculating
the surface area of the ball.
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Form 3 Mathematics
The sides of a triangle were measured and recorded as 8 cm, 10 cm and 15 cm. Calculate the percentage error in perimeter, correct to 2 decimal places.
Form 3 Mathematics
a) Expand (a – b)6
b) Use the first three term of the expansion in a (a) to find the approximate value of (1.98)6 Form 1 MathematicsForm 2 Mathematics
The vertices of a triangle are A(1,2), B(3,5) and C(4,1). The coordinates of C' the image of C under a translation vector T, are (6-2).
(a) Determine the translation vector T. (b) Find the coordinates of A' and B' under translation vector T. Form 3 Mathematics
The ages in years of five boys are 7, 8, 9, 10 and 11 while those of five girls are 4, 5, 6, 7 and 8. A boy and a girl are picked at random and the sum of their ages is recorded.
(a) Draw a probability space to show all the possible outcomes. (b) Find the probability that the sum of their ages is at least 17 years. Form 2 MathematicsForm 2 Mathematics
(a) Solve the inequalities 2x — 5 > - 11 and 3 + 2x ≤ 13, giving the answer as a combined inequality.
(b) List the integral values of x that satisfy the combined inequality in (a) above. Form 1 Mathematics
Three grades A, B, and C of rice were mixed in the ratio 3:4:5. The cost per kg of each of the grades A, B and C were Ksh 120, Ksh 90 and Ksh 60 respectively.
Calculate: (a) The cost of one kg of the mixture; (b) The selling price of 5 kg of the mixture given that the mixture was sold at 8% profit, Form 2 Mathematics
The frequency table below shows the daily wages paid to casual workers by a certain company.
(a) Draw a histogram to represent the above information.
(b) (i) State the class in which the median wage lies. (ii) Draw a vertical line, in the histogram, showing where the median wage lies. (c) Using the histogram, determine the number of workers who earn sh 450 or less per day. Form 3 MathematicsForm 4 Mathematics
The displacement, s metres, of a moving particle after,t seconds is given by, s =2t 3- 5t2 + 4t + 2. .
Determine: (a) the velocity of the particle when t = 3 seconds; (b) the value o f t when the particle is momentarily at rest; (c) the displacement when the particle is momentarily at rest; (d) the acceleration of the particle when t = 3 seconds. Form 4 Mathematics
(a) Using the trapezium rule with seven ordinates, estimate the area of the region bounded by the curve y = -x2 +,6x+ 1, the lines x = 0, y = 0 and x = 6.
(b) Calculate: (i) the area of the region in (a) above by integration; (iii) the percentage error of the estimated area to the actual area of the region,correct to two decimal places. Form 2 Mathematics
In a triangle ABC, BC =8 cm, AC= 12 cm and angle ABC = 120°.
(a) Calculate the length of AB, correct to one decimal place. (b) If BC is the base of the triangle, calculate, correct to one decimal place: (i) the perpendicular height of the triangle; (ii) the area of the triangle; (iii) the size of angle ACB. Form 4 Mathematics
Find the value of p.
(b) A saleswoman earned a fixed salary of Ksh x and a commission of Ksh y for each item sold. In a certain month she sold 30 items and earned a total of Ksh 50 000. The following month she sold 40 items and earned a total of Ksh 56 000. (i) Form two equations in x and y. (ii) Solve the equations in (i) above using matrix method. (iii) In the third month she earned Ksh 68 000. Find the number of items sold. Form 2 Mathematics
Makau made a journey of 700 km partly by train and partly by bus. He started his journey at 8.00 a.m. by train which travelled at 50 km/h. After alighting from the
train, he took a lunch break of 30 minutes. He then continued his journey by bus which travelled at 75 km/h. The whole journey took 11 1/2 hours. (a) Determine: (i) the distance travelled by bus; (ii) the time Makau started travelling by bus. (b) The bus developed a puncture after travelling 187 1/2 km. It took 15 minutes to replace the wheel. Find the time taken to complete the remaining part of the journey Form 2 Mathematics
A solid consists of a cone and a hemisphere. The common diameter of the cone and the hemisphere is 12 cm and the slanting height of the cone is 10 cm.
(a) Calculate correct to two decimal places: (i) the surface area of the solid; (ii) the volume of the solid (b) If the density of the material used to make the solid is 1.3 g/cm3, calculate its mass in kilograms. Form 2 Mathematics
A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm, if the volume of the smaller cone is 160 cm3, find the
volume of the frustum Form 1 Mathematics
Three police posts X, Y and Z are such that Y is 50 km on a bearing of 060° from X while Z is 70 km from Y and on a bearing of 300° from X.
(a) Using a suitable scale, draw a diagram to represent the above situation. (b) Determine the distance, in km, of Z from X. Form 1 Mathematics
(a) Express 10500 in terms of its prime factors.
(b) Determine the smallest positive number P such that 10500P is a perfect cube. |
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