KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 2 Mathematics
A minor arc of a circle subtends an angle of 105 at the centre of the circle. If the radius of the circle is 8.4 cm, find the length of the major arc (Take π= 22/7).
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Form 3 Mathematics
Given that x is an acute angle and cos x = 2/5 √5 find, without using mathematical tables or a calculator, tan (90-x).
Form 2 Mathematics
A students obtained the following marks in four tests during a school term: 60%, 75%, 48% and 66%. The tests were weighted as follows: 2,1, 4 and 3 respectively.
Calculate the students weighed mean mark of the tests Form 2 Mathematics
Two trains T1 and T2 traveling in the opposite directions, on parallel tracks are just beginning to pass one another. Train T1 is 72 m long and traveling at 108 km/h. T2 is 78 m long and is traveling at 72 km/h.
Form 3 Mathematics
Find the number of terms of the series 2 + 6 + 10 + 14 + 18 + ……….. that will give a sum of 800.
Form 1 Mathematics
The marked price of a car in a dealer’s shop was Kshs 400,000. Wekesa bought the car at 8% discount. The dealer still made a profit of 15%.
Calculate the amount of money the dealer had paid for the car. Form 2 Mathematics
A bus travelling at an average speed of 63 km / h left a station at 8:15 am. A car later left the same station at 9.00 am and caught up with the bus at 10.45 am.
Find the average speed of the car. Form 3 Mathematics
Give that OA =2i a + 3 j and OB = 3i -2j, find the magnitude of AB to one decimal place
Form 1 MathematicsForm 1 Mathematics
The external length, width and height of an open rectangular container are 41 cm and 15.5 cm respectively. The thickness of the materials making the container is
5mm. if the container has 8 lit res of water, calculate the internal height above the water level. Form 2 Mathematics
A man who can swim at 5km/h in still water swims towards the east to cross a river. If the river flows from north to south at the rate of 3km/h
a) Calculate: i) The resultant speed ii) The drift b) If the width of the river is 30m, find the time taken, in seconds, for the man to cross the river. Form 2 Mathematics
A triangular plot ABC is such that the length of the side AB is two thirds that of BC. The ratio of the lengths AB:AC = 4:9 and the angle at B is obtuse.
a) The length of the side BC
b)
i) The area of the plot
iii) The size of ∠ABC Form 3 Mathematics
In the figure below, K M and N are points on the circumference of a circle centre O.
The points K, O, M and p are on a straight line. PN is a tangent to the circle at N.Angle KOL = 1300 and angle MKN = 400
Find the values of the following angles, stating the reasons in each case:
a) ∠MLN
b) ∠OLN c) ∠LNP d) ∠MPN Form 3 Mathematics
If A,B and C are the points P and Q are p and q respectively is another point with position vector r = 3q - ½p. Express in terms of p and q.
i) PR
ii) RQ hence show that P,Q and R are collinear. iii) Determine the ratio PQ:QR. Form 3 Mathematics
The simultaneous equations below, are satisfied when x = 1 and y = p
-3x + 4y = 5 qx2 – 5xy + y2 = 0
a) Find the values of P and Q.
b) Using the value of Q obtained in (a) above, find the other values of x and y which also satisfy the given simultaneous equations. Form 2 Mathematics
The figure below represents a model of a solid structure in the shape of a frustum of a cone with hemispherical top. The diameter of the hemispherical part is 70cm and is equal to the diameter of the top of the frustum. The frustum has a base diameter of 28cm and slant height of 60cm.
Calculate
Form 4 MathematicsForm 4 Mathematics
The marks scored by 40 students in a mathematics test were as shown in the table below.
a) Find the lower class boundary of the modal class
b) Using an assumed mean of 64, calculate the mean mark c i) On the grid provided, draw the cumulative frequency curve for the data ii)Use the graph to estimate the semi-interquartile range Form 4 Mathematics
A particle was moving along a straight line. The acceleration of the particle after t seconds was given by (9 -3t) ms-2. The initial velocity of the particle was 7 ms-1.
Find: a) the velocity (v) of the particle at any given time (t); b) The maximum velocity of the particle; c)the distance covered by the particle by the time it attained maximum velocity Form 3 Mathematics
A quantity P varies partly as the square of m and partly as n. When P = 3.8, m = 2 and n = When P = -0.2, m = 3 and n = 2.
(a) Find: (i) the equation that connects P, m and n; (ii) the value of P when m = 10 and n = 4. (b) Express m in terms of P and n. (c) If P and n are each increased by 10%, find the percentage increase in m correct to 2 decimal places. |
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