KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Form 3 Mathematics
In the figure below, P, Q, R and S are points on the circle centre O. PRT and USTV are straight lines.
Line USTV is a tangent to the circle at S, ZRST = 50° and LRTV = 150°.
(a) Calculate the size of:
(i) angle ORS; (ii) angle USP; (iii) angle PQR. (b) Given that RT = 7 cm and ST 9 cm, calculate to 3 significant figures: (i) the length of line PR; (ii) the radius of the circle.
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Form 2 Mathematics
In a uniformly accelerated motion the distance, s metres, travelled in time t seconds varies partly as the time and partly as the square of the time. When the time is 2 seconds, the distance travelled is 80 metres and when the time is 3 seconds, the distance travelled is 135 metres.
(a) Express s in terms of t. (b) Find: (i) the distance travelled in 5 seconds; (ii) the time taken to travel a distance of 560 metres. Form 3 Mathematics
The first term of an Arithmetic Progression (A.P.) with six terms is p and its common difference is c. Another AP. with five terms has also its first term asp and a common difference of d. The last terms of the two Arithmetic Progressions are equal.
(a) Express d in terms of c. (b) Given that the 4th term of the second A.P. exceeds the 4th term of the first one by 1, find the values of e and d. (c) Calculate the value of p if the sum of the terms of the first A.P. is 10 more than the sum of the terms of the second A.P. Form 3 Mathematics
A hail can accommodate 600 chairs arranged in rows. Each row has the same number of chairs. The chairs are rearranged such that the number of rows are increased by 5 but the number of chairs per row is decreased by 6.
(a) Find the original number of rows of chairs in the hall. (b) After the rearrangement 450 people were seated in the hail leaving the same number of empty chairs in each row. Calculate the number of empty chairs per row. Form 4 Mathematics
A carpenter takes 4 hours to make a stool and 6 hours to make a chair. It takes the carpenter and at least 144 hours to make x stools and y chairs. The labour cost of making a stool is Ksh 100 and that of a chair is Ksh 200. The total labour cost should not exceed Ksh 4 800. The carpenter must make at least 16 stools and more than 10 chairs.
(a) Write down inequalities to represent the above information. (b) Draw the inequalities in (a) above on the grid provided.
(c) The carpenter makes a profit of Ksh 40 on a stool and Ksh loo on a chair.
Use the graph to determine the maximum profi.t the carpenter can make. Form 4 Mathematics
The positions of three ports A, B and C are (34°N, 16°W), (34°N. 24°E) and (26°S, 16°W) respectively.
(a) Find the distance in nautical miles between: (i) Ports A and B to the nearest nautical miles; (ii) Ports A and C. (b) A ship left Port A on Monday at 1330 h and sailed to Port B at 40 knots. Calculate: (i) the local time at Port B when the ship left Port A; (ii) the day and the time the ship arrived at port B. Form 3 Mathematics
In the figure below OJKL is a parallelogram in which OJ = 3p and OL 2r.
(a) If A ¡s a point on LK such that LA = 1/2 AK and a point B divides the line JK externally in the ratio 3:1, express OB and AJ in terms of p and r.
(b) Line OB intersects AJ at X such that OX = mOB and AX= nAJ. (i) Express OX in terms of p, r and m. (ii) Express OX in terms of p, r and n. (iii) Determine the values of m and n and hence the ratio in which point X divides line AJ. Form 4 Mathematics
(a) Complete the table below, giving the values correct to 2 decimal places.
(b) On the grid provided and using the same axes draw the graphs of y = cos x° and y= sin x°— cos x° for 0° ≤ x ≤ 180°.Use the scale; 1 cm for 20°on the xaxis and 4cm fort unit on the yaxis.
(c) Using the graph in part (b): (i) solve the equation sin x° — cos x° 1.2; (ii) solve the equation cos x°= 1/2 sinx; (iii) determine the value of cos x° in part (c) (ii) above. Form 3 MathematicsForm 1 MathematicsForm 3 Mathematics
(a) Expand and simp1ify (2 —x)^{5}. (b) Use the first 4 terms of the expansion in part
(a) above to find the approximate value of (1.8)^{5} to 2 decimal places. Form 4 Mathematics
A particle starts from O and moves in a straight line so that its velocity V ms^{1} after time t seconds is given by V = 3tt^{2}. The distance of the particle from O at time t seconds is s metres.
(a) Express s in terms of t and c where c is a constant. (b) Calculate the time taken before the particle returns to 0. Form 3 MathematicsForm 3 Mathematics
A bag contains 2 white balls and 3 black balls. A second bag contains 3 white balls and 2 black balls. The balls are identical except for the colours, b
Two balls are drawn at random, one after the other from the first bag and placed in the second bag. Calculate the probability that the 2 balls are both white. Form 4 MathematicsForm 1 Mathematics
When Ksh 40 000 was invested in a certain bank for 5 years it earned a simple interest of Ksh 3 800.
Find the amount that must have been invested in the same bank at the same rate for 7  years to earn a simple interest of Ksh 3 420. Form 1 Mathematics
Five people can build 3 huts in 21 days. Find the number of people, working at the same rate that will build 6 similar huts in 15 days.
Form 1 Mathematics
The length of a flower garden is 2 m less than twice its width. The area of the garden is 60 m^{2}.
Calculate its length. Form 1 Mathematics
A tea dealer mixes two brands of tea, x and y, to obtain 35 kg of the mixture worth Ksh 62 per kg. 1f brand x is valued at Ksh 68 per kg and brandy at Ksh 53 per kg, calculate the ratio, in its simplest form, in which the brands x and y are mixed.
Form 3 MathematicsForm 3 Mathematics
The length and width of a rectangle measured to the nearest millimeter are 7.5 cm and 5.2 cm respectively.
Find, to four significant figures, the percentage error in the area of the rectangle. Form 2 Mathematics
A rectangular box open at the top has a square base. The internal side of the base is x cm long and the total internal surface area of the box is 432 cm^{2}.
(a) Express in terms of x: (i) the internal height h, of the box; (ii) the internal volume V, of the box. (b) Find: (i) the value of x for which the volume V is maximum; (ii) the maximum internal volume of the box. Form 2 Mathematics 
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