KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
The figure ABCDEF below represents a roof of a house AB= DC = 12m, BC=AD = 6 m, AE=BF = CF = DE = 5 m 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 DCFE, correct to 1 decimal place.
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Form 2 Mathematics
A school decided to buy at least 32 bags of maize and beans. The number of bags of beans were Lo be at least 6. A bag of maize costs Ksh 2500 and a bag of beans costs Ksh 3 500, The school had Ksh 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information,
Form 4 MathematicsForm 4 Mathematics
(a)On the grid provided, draw a graph of the function y = 1/2 x2 - x + 3 for 0 ≤ x ≤ 6.
b) Calculate the mid ordinates for five strips between x = 1 and x = 6, and hence use the mid- ordinate rule to approximate the area under the curve between x = 1, x = 6 and the x = axis c) Assuming that the area determined by integration to be the actual area, calculate the percentage error in using the mid ordinate rule Form 4 Mathematics
The equation of a curve is y = 2x3 + 3x2.
a)Find i)The x – intercept of the curve ii) they-intercept of the curve b i)Determine the stationary 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 gradient of the tangent to the curve y = ax3 + bx at the point (1,1) is -5 , Calculate the values of a and b.
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 4 Mathematics
The figure below represents a cuboid EFGHJKLM in which EF = 40cm, FG=9cm and GM=30 cm. N is the midpoint of LM.
Calculate correct to 4 significant figures
a)The length of GL: b)The length of FJ c)The angle between EM and the plane EFGH; d)The angle between eh planes EFGH and ENH; e)the angle between the lines EH and GL Form 4 Mathematics
The equation of a curve is given by y= 1 + 3sin x.
(a) Complete the table below for y = 1 + 3 sin x correct to 1 decimal place
(b) (i) On the grid provided, draw the graph of y - 1 + 3 sin x for 0° ≤ x ≤ 360°.
ii) State the amplitude of the curve y = 1 + 3 sin x. c) On the same grid draw the graph of y = tan x for 90° ≤ x ≤ 270°. d) Use the graphs to solve the equation ; 1+3 sin x = tan x for 90° ≤ x ≤ 270°. Form 4 Mathematics
The positions of two points P and Q, on the surface of the earth are P(45 °N, 36°E) and Q(45 °N, 71°E). Calculate the distance, in nautical miles, between P and Q, correct to 1 decimal place.
Form 2 Mathematics
A school decided to buy at least 32 bags of maize and beans. The number of bags of maize were to be more than 20 and the number of bags of beans were to
be at least 6. A bag of maize costs Ksh 2500 and a bag of beans costs Ksh 3500. The school had Ksh 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information. Form 4 MathematicsForm 4 Mathematics
The gradient of the curvey y = 2x3 – 9x2 + px – 1 at x = 4 is 36.
a)Find : i) the value of p; ii)The equation of the tangent to the curve at x = 0.5. b) Find the coordinates of the training points of the curve Form 4 Mathematics
Two shopkeepers, Juma and Wanjiku bought some items from a wholesaler. Juma bought 18 loaves of bread, 40 packets of milk and 5 bars of soap while Wanjiku bought 15 loaves of bread, 30 packets of milk and 6 bars of soap. The prices of a loaf of bread, a packet of milk and a bar of soap were Ksh 45, Ksh 50 and Ksh 150 respectively.
(a) Represent: (i) the number of items bought by Juma and Wanjiku using a 2 x 3 matrix. (ii) the prices of the items bought using a 3 x 1 matrix. (b) Use the matrices in (a) above to determine the total expenditure incurred by each person and hence the difference in their expenditure. c) Juma and wanjiku also bought rice and sugar. Juma bought 36 kgs of rice and 23 kgs of sugar and paid Ksh 8160. Wanjiku bought 50 kg of rice and 32 kg of sugar and paid kshs 11340. Use the matrix method to determine the price of one kilogram of rice and one kilogram of sugar Form 4 MathematicsForm 4 MathematicsForm 4 Mathematics
The velocity V ms, of a moving body at time t seconds is given by V = 5t2 – 12t + 7
Find its acceleration after 2 seconds.
Form 4 Mathematics
Figure ABCD below is a scale drawing representing a square plot of side 80 metres.
On the drawing, construct:
(i) the locus of a point P, such that it is equidistant from AD and BC. (ii) the locus of a point Q such that <AQB = 60°. (i) Mark on the drawing the point Q , the intersection of the locus of Q and line AD. Determine the length of BQ1 in metres. (ii) Calculate, correct to the nearest m2, the area of the region bounded by the locus of P, the locus of Q and the line BQ1
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The dimensions of a rectangular floor of a proposed building are such that!
• the length is greater than the width but at most twice the width; • the sum of the width and the length is, more than 8 metres but less than 20 metres. If'x represents the width and y the length. (a) write inequalities to represent the above information. (b) (i) Represent the inequalities in part (a) above on the grid provided. (ii) Using the integral values of x and y, find the maximum possible area of the floor. Form 4 Mathematics
The gradient of a curve is given by dy/dx = x2 - 4x4- 3. The curve passes through the point (1,0). Find the equation of the curve.
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