KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
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Form 4 Mathematics
The acceleration of a body moving along a straight line is (4 - t) m/s2 and its velocity is v m/s after t seconds.
(a) (i) If the initial velocity of the body is 3 m/s, express the velocity v in terms of t. (ii) Find the velocity of the body after 2 seconds. (b) Calculate: (i) the time taken to attain maximum velocity; (ii) the distance covered by the body to attain the maximum velocity. Form 4 Mathematics
A tourist took 1 h 20 minutes to travel by an aircraft from town T(3°S, 35°E) to town U(9°N, 35°E). (Take the radius of the earth to be 6370km and π =22/7
(a) Find the average speed of the aircraft. (b) After staying at town U for 30 minutes, the tourist took a second aircraft to town V(9°N, 5°E). The average speed of the second aircraft was 90% that of the first aircraft. Determine the time, to the nearest minute, the aircraft took to travel from U to V (c) When the journey started at town T, the local time was 0700h. Find the local time at V when the tourist arrived. Form 4 MathematicsForm 4 MathematicsForm 4 MathematicsForm 4 Mathematics
The equation of a curve is y = 2x3 + 3x2.
(a) Find: (i) the x - intercept of the curve; (ii) the y - intercept of the curve. (b) (i) Determine the stationery points of the curve. (ii) For each point in (b) (i) above, determine whether it is a maximum or a minimum. (c) Sketch the curve. Form 4 Mathematics
The displacement s metre of a particle moving along straight line after t seconds is given by. S = 3t + 3/2 t2 – 2t3
Form 4 MathematicsForm 4 Mathematics
A building contractor has two lorries, P and Q, used to transport at least 42 tonnes of sand to a building site. Lorry P carries 4 tonnes of sand per trip while lorry Q
carries 6 tonnes of sand per trip. Lorry P uses 2 litres of fuel per trip while lorry Q uses 4 litres of fuel per trip. The two lorries are to use less than 32 litres of fuel. The number of trips made by lorry P should be less than 3 times the number of trips made by lorry Q. Lorry P should make more than 4 trips. (a) Taking x to represent the number of trips made by lorry P and y to represent the number of trips made by lorry Q, write the inequalities that represent the above information. (b) On the grid provided, draw the inequalities and shade the unwanted regions. (c) Use the graph drawn in (b) above to determine the number of trips made by lorry P and by lorry Q to deliver the greatest amount of sand. Form 4 MathematicsForm 4 Mathematics
The table below shows the values of x and corresponding values of y for a given curve.
a) Use the trapezium rule with seven ordinates and the values in the table only to estimate the area enclosed by the curve, x – axis and the line x = П/2 to four decimal places. (Take П = 3.142) b) The exact value of the area enclosed by the curve is known to be 0.8940.Find the percentage error made when the trapezium rule is used. Give the answer correct to two decimal places. Form 4 MathematicsForm 4 MathematicsForm 4 Mathematics
A point M (60°N, 18°E) is on the surface of the earth. Another point N is situated at a distance of 630 nautical miles east of M.
Find: (a) the longitude difference between M and N; (b) The position of N. Form 4 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 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 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 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 x-axis and 4cm fort unit on the y-axis.
(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 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 = 3t-t2. 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. |
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