KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Form 4 Mathematics
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Form 4 Mathematics
Find the coordinates of the turning point of the curve y= x²-14x +10
KCSE Mathematics Topical Questions and Answers in PDFForm 1 Topical Questions and Answers for KCSE
Marking Schemes
Form 4 Mathematics
The equation of a curve is y=x3+x2-x-1
(i) Determine the stationary point of the curve (Îi) the nature of the stationary points in (a) (i) above. (b) Determine: (i) the equation of the tangent to the curve at x = 1; (ii) the equation of the normal to the curve at x = 1. Form 4 Mathematics
The shaded region on the graph below shows a piece of land ABCD earmarked for building a sub-county hospital.
(a) Write down the ordinates of curves AB and DC for x = 0, 200, 400, 600, 800, 1000 and 1200.
(b) Use trapezium rule, with 6 strips to estimate the area of the piece of land ABCD, in hectares. (c) Use mid-ordinate rule with 3 strips to estimate the area of the piece of land, in hectares. Form 4 MathematicsA curve is represented by the function y = 1/3 x3 + x2 – 3x + 2 (a) Find dy/dx (1 mark) (b) Determine the values of y at the turning points of the curve y = 1/3 x3 + x2 – 3x + 2 ( 4 marks) Form 4 MathematicsDiet expert makes up a food production for sale by mixing two ingredients N and S. One kilogram of N contains 25 units of protein and 30 units of vitamins. One kilogram of S contains 50 units of protein and 45 units of vitamins. If one bag of the mixture contains x kg of N and y kg of S. (a) Write down all the inequalities, in terms of x and representing the information above ( 2 marks) Form 4 Mathematics
The figure below is a right pyramid VEFGHI with a square base of 8cm and a slant edge of 20cm Points A B C and D lie on the slant edges or the pyramid such that VA = VB = VC = VD = 10 cm and plane ABCD is paralell to the base EFGH.
(a) Find the length of AB.
(b) Calculate to 2 decimal places (i) The length of AC (ii) The perpendicular height of the pyramid VABCD (c) The pyramid VABCD was cut off. Find the volume of the frustum ABCDEFGH correct to 2 decimal places Form 4 Mathematics(a) BCD is a rectangle in which AB = 7.6 cm and AD = 5.2 cm. draw the rectangle and construct the lucus of a point P within the rectangle such that P is equidistant from CB and CD ( 3 marks) (b) Q is a variable point within the rectangle ABCD drawn in (a) above such that 600 ≤ AQB≤ 900 On the same diagram, construct and show the locus of point Q, by leaving unshaded, the region in which point Q lies Form 4 MathematicsTriangles ABC and A”B”C” are drawn on the Cartesian plane provided. Triangle ABC is mapped onto A”B”C” by two successive transformations (a) Find R ( 4 marks) (b) Using the same scale and axes, draw triangles A’B’C’, the image of triangle ABC under transformation R ( 2 marks) (c) Describe fully, the transformation represented by matrix R ( 2 marks) Form 4 MathematicsTwo lines L1 and L2 intersect at a point P. L1 passes through the points (-4,0) and (0,6). Given that L2 has the equation: y = 2x – 2, find, by calculation, the coordinates of P. ( 3 marks) Form 4 Mathematics
A hotel buys beef and mutton daily. The amount of beef bought must be at least 30kg and that of mutton at least 20 kg. The total mass of beef and mutton bought should not exceed 100 kg. The beef is bought at Ksh 360 per kg and the mutton at Ksh 480 per kg.
The amount of money spent on both beef and mutton should not exceed Ksh 43 200 per day. Let x represent the number of kilograms of beef and y the number of kilograms of mutton. (a) Write the inequalities that represent the above information. (b) On the grid provided, draw the inequalities in (a) above. (c) The hotel makes a profit of ksh 50 on each kg of beef and ksh 60 on each kg of mutton. Determine the maximum profit the hotel can make Form 4 Mathematics
The figure below is a model of a watch tower with a square base of side 10 cm. Height PU is 15 cm and slanting edges UV = TV = SV = RV = 13 cm.
Giving the answer correct to two decimal places, calculate:
(a) length MP;
(b) the angle between MU and plane MNPQ; (c) Length of VO; (d) The angle between planes VST and RSTU; Form 4 Mathematics
The table below shows some values of the curves y = 2 cos x and y = 3 sin x.
(a) Complete the table for values of y = 2 cos x and y = 3 sin x, correct to 1 decimal place.
On the grid provided, draw the graphs of y = 2 cos x and y = 3 sin x for 0° ≤ x ≤ 360°, on the same axes.
(c) Use the graph to find the values of x when 2 cos x — 3 sin x = 0 (d) Use the graph to find the values of y when 2 cos x = 3 sin x. Form 4 Mathematics
The table below shows the frequency distribution of heights of 40 plants in a tree nursery.
(a) State the modal class.
(b) Calculate: (i) the mean height of the plants; (ii) the standard deviation of the distribution. (c) Determine the probability that a plant taken at random has a height greater than 40 cm. Form 4 Mathematics
The position of two points C and D on the earth’s surface are (θ°N, l0°E) and (θ°N, 30°E)
respectively. The distance between the two points is 600 nm. Determine the latitude on which C and D lie. Form 4 Mathematics
The mass, in kilograms, of 9 sheep in a pen were: 13, 8, 16, 17, 19, 20, 15, 14 and 11.
Determine the quartile deviation of the data. Form 4 Mathematics
State the amplitude and the phase angle of the curve y = 2 sin ( 3/2 x — 30°)
Form 4 MathematicsForm 4 Mathematics
The equation of a curve is given as y=1/3x3-4x+5
Determine: (a) The value of y when x = 3; (b) The gradient of the curve at x = 3; (c) The turning points of the curve and their nature. Form 4 Mathematics
(a) On the grid provided, draw the graph of y = 4 -1/4x2 for -4 ≤ x ≤ 4
(b) Using trapezium rule, with 8 strips, estimate the area bounded by the curve and the x-axis. (c) Find the area estimated in part (b) above by integration. (d) Calculate the percentage error in estimating the area using trapezium rule. Form 4 Mathematics
The diagram below shows triangle ABC with vertices A(-1, -3), B(1, -1) and C(0,0), and line M.
(a) Draw triangle A'B'C' the image of triangle ABC under a reflection in the line M.
(i) Draw triangle A"B"C"
(ii) Describe fully the transformation represented by matrix T. (iii) Find the area of triangle A’B'C' hence find area of triangle A"B"C". |
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