KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 1 Mathematics
A two digit number is such that, the sum of its digits is 13. When the digits are interchanged, the original number is increased by 9. Find the original number.
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Form 1 Mathematics
The lengths of three wires were 30m, 36 m and 84m. Pieces of wire of equal length were cut from the three wires. Calculate the least number of pieces obtained.
Form 1 MathematicsForm 2 Mathematics
The base of a right pyramid is a rectangle of length 80 cm and width 60 cm. Each slant edge of the pyramid is 130 cm. Calculate the volume of the pyramid.
Form 3 Mathematics(a) (i) Complete the table below for the function y = x3 + x2 – 2x (2 marks) (ii On the grid provided, draw the graph of y = x3 + x2 – 2x for the values of x in the interval – 3 ≤ x ≤ 2.5 (2 marks) (iii) State the range of negative values of x for which y is also negative (1 mk) (b) Find the coordinates of two points on the curve other than (0,0) at which x- coordinate and y- coordinate are equal (3 marks) Form 2 MathematicsA boat which travels at 5 km/h in still water is set to cross a river which flows from the north at 6km/h. The boat is set on a course of x0 with the north. (a) Given that cos x0 = 3/5 , calculate (i) The resultant speed of the boat ( 2 marks) (ii) The angle which the track makes with the north ( 2 marks) (b) If the boat is to sail on a bearing of 1350, calculate the bearing of possible course on which it can be set ( 4 marks) Form 4 MathematicsForm 4 MathematicsThe gradient of a curve at point (x,y) is 4x – 3. the curve has a minimum value of – 1/8 (a) Find (i) The value of x at the minimum point ( 1 mark) (ii) The equation of the curve ( 4 marks) (b) P is a point on the curve in part (a) (ii) above. If the gradient of the curve at P is -7, find the coordinates of P ( 3 marks) Form 4 MathematicsThe table below gives some of the values of x for the function y = ½ x 2 + 2x + 1 in the interval 0≤ x ≤ 6. (a) Use the values in the table to draw the graph of the function ( 2 marks) (b) (i) Using the graph and the mid – ordinate rule with six (6) strips, estimate the area bounded by the curve, the x- axis, the y- axis and the line = 6 (ii) If the exact area of the region described in (b) (i) above is 78cm2, calculate the percentage error made when the mid – ordinate rule is used. Give the answer correct to two decimal places ( 2 marks) Form 2 MathematicsThe distance between towns M and N is 280 km. A car and a lorry travel from M to N. The average speed of the lorry is 20 km/h less than that of the car. The lorry takes 1 h 10 min more than the car to travel from M and N. (a) If the speed of the lorry is x km/h, find x ( 5 marks) Form 4 Mathematics
The acceleration, a ms-2, of a particle is given by a =25 – 9t2, where t in seconds after the particle passes fixed point O.If the particle passes O, with velocity of 4 ms-1, find:
(a) An expression of velocity V, in terms of t ( 2 marks)
(b) The velocity of the particle when t = 2 seconds ( 2 marks) Form 3 MathematicsA bank either pays simple interest as 5% p.a or compound interest 5% p.a on deposits. Nekesa deposited Kshs P in the bank for two years on simple interest terms. If she had deposited the same amount for two years on compound interest terms, she would have earned Kshs 210 more. Calculate without using Mathematics Tables, the values of P ( 4 marks) Form 2 MathematicsForm 3 MathematicsPoint T is the midpoint of a straight line AB. Given the position vectors of A and T are i-j + k and 2i+ 1 ½ k respectively, find the position vector of B in terms of i, j \ and k. ( 3 marks) Form 2 MathematicsA cylindrical piece of wood of radius 4.2 cm and length 150 cm is cut length into two equal pieces. Calculate the surface area of one piece (Take ∏ as 22/7 (4mks) Form 2 Mathematics
In this question Mathematical Tables should not be used
The base and perpendicular height of a triangle measured to the nearest centimetres are 6 cm and 4 cm respectively. Find (a) The absolute error in calculating the area of the triangle (b) The percentage error in the area, giving the answer to 1 decimal place (2mks) Form 2 Mathematics
The length of a room is 3 m shorter than three times its width. The height of the room is a quarter of its length. The area of the floor is 60 m2.
(a) Calculate the dimensions of the room. (b) The floor of the room was tiled leaving a border of width y m, all round. If the area of the border was 1.69m2, find: (i) the width of the border; (ii) the dimensions of the floor area covered by tiles. Form 3 Mathematics
(a) The 5th term of an AP is 82 and the 12th term is 103.
Find: (i) the first term and the common difference; (ii) the sum of the first 21 terms. (b) A staircase was built such that each subsequent stair has a uniform difference in height. The height of the 6th stair from the horizontal floor was 85 cm and the height of the 10th stair was 145 cm. Calculate the height of the 1st stair and the uniform difference in height of the stairs. Form 4 Mathematics
A trader stocks two brands of rice A and B. The rice is packed in packets of the same size. The trader intends to order fresh supplies but his store can accommodate a maximum of 500 packets. He orders at least twice as many packets of A as of B.
He requires at least 50 packets of B and more than 250 packets of A. If he orders x packets of A and y packets of B, (a) Write the inequalities in terms of x and y which satisfy the above information. (b) On the grid provided represent the inequalities in part (a) above (c) The trader makes a profit of Ksh 12 on a packet of type A rice and Ksh 8 on a packet of type B rice. Determine the maximum profit the trader can make. Form 3 Mathematics
Three quantities X, Y and Z are such that X varies directly as the square root ofY and inversely as the fourth root of Z. When X = 64, Y = 16 and Z = 625.
(a) Determine the equation connecting X, Y and Z. (b) Find the value of Z when Y = 36 and X = 160. (c) Find the percentage change in X when Y is increased by 44%. Form 4 Mathematics
The figure below represents a cuboid ABCDEFGH in which AB = 16 cm, BC = 12 cm and CF = 6 cm.
(a) Name the projection of the line BE on the plane ABCD.
Calculate correct to 1 decimal place: (i) the size of the angle between AD and BF; (ii) the angle between line BE and the plane ABCD; (iii) the angle between planes HBCE and BCFG. (c) Point N is the midpoint of EF. Calculate the length BN, correct to 1 decimal place. |
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