KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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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.
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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 2 MathematicsForm 3 MathematicsThe diagram below represents a cuboid ABCDEFGH in which FG= 4.5 cm, GH = 8cm and HC = 6 cm Calculate: (a) The length of FC ( 2 marks) (b) (i) the size of the angle between the lines FC and FH ( 2 marks) (ii) The size of the angle between the lines AB and FH ( 2 marks) (c) The size of the angle between the planes ABHE and the plane FGHE (2mks) Form 3 Mathematics(a) complete the table below, giving your values correct to 2 decimal places ( 2 marks) (b) On the grid provided, using the same scale and axes, draw the graphs of y = sin x0 and y = 1 – cos x0 ≤ x ≤ 1800 Take the scale: 2 cm for 300 on the x- axis 2 cm for I unit on the y- axis (c) Use the graph in (b) above to (i) Solve equation 2 sin xo + cos x0 = 1 ( 1 mark) (ii) Determine the range of values x for which 2 sin xo > 1 – cos x0 ( 1 mark) Form 1 MathematicsA boat at point x is 200 m to the south of point Y. The boat sails X to another point Z. Point Z is 200m on a bearing of 3100 from X, Y and Z are on the same horizontal plane. (a) Calculate the bearing and the distance of Z from Y ( 3 marks) (b) W is the point on the path of the boat nearest to Y. Calculate the distance WY ( 2 marks) (c) A vertical tower stands at point Y. The angle of point X from the top of the tower is 60 calculate the angle of elevation of the top of the tower from W (3 marks) 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 MathematicsForm 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 2 Mathematics
A triangle ABC with Vertices A (-2,2),B (1,4)and C (-1,4) is mapped on to triangle A'B'C' by a reflection in the line y=x+1.
(a) On the grid provided draw (i) triangle ABC (ii) the line y = x + 1; (iii) triangle A'B'C'. (b) Triangle A"B"C" is the image of triangle A'B'C' under a negative quarter turn (0,0). On the same grid, draw triangle A"B"C". (c) State the type of congruence between triangles: (i) ABC and A’B’C’; (ii) A’B’C’ and A”B”C” Form 2 Mathematics
(a) A line, L1, posies through tho points (3,3) and (5,7). Find the equation of L1, in the form y = mx+c where m and c arc constonti.
(b) Another line L2 is perpendicular to L1, and passes through (-2, 3). Find: (i) the equation of L2; (ii) the x-intercept of L2. (c) Determine the point of intersection of L1, and L2. Form 2 Mathematics
A bus plies between two towns P and R via town Q daily. On each day it departs from P at 8.15 a.m. and stops for 40 minutes at Q before proceeding to R.
On a certain day, the bus took 5 hours 40 minutes to travel from P to Q and 3 hours 15 minutes to travel from Q to R. Find, in 24 hour clock system, the time the bus arrived at R. Form 2 Mathematics
A trader bought two types of bulbs A and B at Ksh 60 and Ksh 56 respectively. She bought a total of 50 bulbs of both types ct a total of Ksh 2872.
Determine the number of type A bulbs that she bought. Form 2 Mathematics
Solve the inequality 2x - 1 ≤ 3x + 4 < 7 - x.
​Related Questions and Answers on Linear InequalitiesForm 1 Mathematics
Using a ruler and a pair of compass only, construct a rhombus PQRS such that PQ = 6cm and SPQ = 75°.
Measure the length of PR. Form 1 Mathematics
A tourist converted 5820 US dollars into Kenya Shillings at the rate of Ksh 102.10 per dollar. While in Kenya, he spent Ksh450 000 and converted the balance into dollars at the rate of Ksh 103.00 per dollar.
Calculate the amount of money, to the nearest dollar, that remained. Form 3 Mathematics
Given that sin 2x = cos (3x — 10°), find tan x, correct to 4 significant figures.
Form 1 Mathematics
A retailer bought a bag of tea leaves. If the retailer were to repack the tea leaves into smaller
packets of either 40 g, 250g or 350 g, determine the least mass, in grams, of the tea leaves in the bag. Form 1 Mathematics
Three villages A, B and C rife Such that B is 53 km on a bearing of 295° from A and C is 75 km east of B.
(a) Using a scale of 1 cm to represent 10 km, draw a diagram to show the relative positions of villages A, B and C. (b) Determine the distance, in km, of C from A. 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 |
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