KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Form 3 Mathematics
The roots of a quadratic equation are x = -3/5 and x = 1. Form the quadratic equation in the form ax2 + bx + c = 0 where a, b and c are integers.
Form 4 Mathematics
The equation of a curve is given as y = 2x3 -9/2 x2 -15x + 3.
(a) Find: (i) the value of y when x = 2; (ii) the equation of the tangent to the curve at x = 2. (b) Determine the turning points of the curve. Form 3 Mathematics
An institution intended to buy a certain number of chairs for Ksh 16 200. The supplier agreed to offer a discount of Ksh 60 per chair which enabled the institution to get 3 more chairs.
Taking x as the originally intended number of chairs, (a) Write an expressions in terms of x for: (i) original price per chair; (ii) price per chair after discount. (b) Determine: (i) the number of chairs the institution originally intended to buy; (ii) price per chair after discount; (iii) the amount of money the institution would have saved per chair if it bought the intended number of chairs at a discount of 15%. Form 4 Mathematics
(b) Mambo bought 3 exercise books and 5 pens for a total of Ksh 165. 1f Mambo had bought 2 exercise books and 4 pens, he would have spent Ksh 45 less. Taking x to represent the price of an exercise book and y to represent the price of a pen:
(i) Form two equations to represent the above information. (ii) Use matrix method to find the price of an exercise book and that of a pen. (iii) A teacher of a class of 36 students bought 2 exercise books and 1 pen for each student. Calculate the total amount of money the teacher paid for the books and pens. Form 1 Mathematics
The comer points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a bearing of 30°. D is 7km from C on a bearing of 300°.
(a) Using a scale of 1cm to represent 1km, draw a diagram to show the positions of A, B, C and D. (b) Use the scale drawing to determine: (i) the bearing of A from D; (ii) the distance BD in kilometres. Form 4 MathematicsForm 2 Mathematics
A solid S is made up of a cylindrical part and a conical part. The height of the solid is 4.5 m.
The common radius of the cylindrical part and the conical part is 0.9 m. The height of the conical part is 1.5 m. (a). Calculate the volume. correct to 1 decimal place, of solid S. (b). Calculate the total surface area of solid S. A square base pillar of side 1.6 m has the same volume as solid S. Determine the height of the pillar, correct to 1 decimal place. Form 2 Mathematics
The masses, in kilograms, of patients who attended a clinic on a certain day were recorded follows.
(a) Starting with the class 35 — 39, make a frequency distribution table for the data.
(b) Calculate: (i) the mean mass; (ii)the median mass (c) On the grid provided below draw a histogram to represent the data Form 2 Mathematics
Two lines L1: 2y — 3x- 6 = 0 and L2: 3y + x — 20 = 0 intersect at a point A.
(a) Find the coordinates of A. (b) A third line L3 is perpendicular to L2 at point A. Find the equation of L3 in the form y = mx + c, Where m and c are constants. (c) Another line L4 is parallel to L1 and passes through (—1,3). Find the x and y intercepts of L4 Form 2 MathematicsThe figure below shows a model of a roof with a rectangular base PQRS PQ = 32 cm and QR = 14 cm. The ridge XY = 12 cm and is centrally placed. The faces PSX and QRY are equilateral triangles M is the midpoint of QR. Calculate (a) (i) the length of YM (ii) The height of Y above the base PQRS (b) The angle between the planes RSXY and PQRS (c) The acute angle between the lines XY and QS Form 3 MathematicsThree quantities P,Q and R are sure that P varies directly as the square of Q and inversely as the square root of R. (a) Given that P = 20 when Q = 5 and R = 9, find P when Q and R = 25 (b) If Q increases by 20% and decreases by 36%, find the percentage increase in P. Form 4 Mathematics
A particle moves in a straight line. It passes though point O at t = O with velocity v= 5m/s. The acceleration a m/s2 of the particle at time t seconds after passing through O is given by a = 6t + 4
(a) Express the velocity v of the particle at time t seconds in terms of t (b) Calculate (i) The velocity of the particle when t = 3 (ii) The distance covered by the particle between t = 2 and t = 4 Form 3 MathematicsTriangle ABC is the image of triangle PQR under the transformation (b) Triangle ABC in part (a) above is to be enlarged scale factor 2 with centre at (11, -6) to map onto A’B’C. Construct and label triangle A’B’C’ on the grid above. (c) By construction find the coordinates of the centre and the angle of rotation which can be used to rotate triangle A’B’C’ onto triangle A” B” C”, shown on the grid above. Form 3 Mathematics
(a) Given that the matrix
Find A-1 the inverse of A (b) Kimtai bought 200 bags of sugar and 300 bags of rice for a total of Kshs. 850,000. Buya bought 90 bags of sugar and 120 bags of rice for a total of Kshs. 360,000. If the price of a bag of sugar is Kshs x and that of rice is Kshs. Y, (i) Form two equations to represent the information above (ii) Use the matrix A-1 to find the prices of one bag of each item. (c) Kali bought 225 bags of sugar and 360 bags of rice. He was given a total discount of Kshs. 33, 300. If the discount on the price of a bag of rice was 2%, calculate the percentage discount on the price of a bag of sugar. Form 1 MathematicsFor electricity posts, A,B,C, and D stand on a level ground such that B is 21 m on a bearing of 0600 from A, C, is 15 m to the south of B and D is 12 m on a bearing of 1400 from A.
Answer
Form 1 Mathematics
A construction company employs technicians and artisans. On a certain day 3 technicians and 2 artisans were hired and paid a total of Ksh 9000. On another day the firm hired 4 technicians and 1 artisan and paid a total of Ksh 9500‘ Calculate the cost of hiring 2 technicians and 5 artisans in a
day. Form 2 Mathematics
A triangle T With vertices A (2,4), B (6,2) and C (4,8) is mapped onto triangle T’ with vertices A'(10,0) , B'(8,—4) and C'(14,—2) by a rotation.
(a) On the grid provided draw triangle T and its image. (b) Determine the centre and angle of rotation that maps T onto T'. Form 4 Mathematics
Use the mid ordinate rule with six strips to find the area bounded by the curve y = x2 + 1, the lines x = -4 , x = 8 and the x-axis.
Form 1 MathematicsForm 3 Mathematics
Murimi and Naliaka had each 840 tree seedlings. Murimi planted equal number of seedlings per row in x rows while Naliaka planted equal number of seedlings in (x + 1) rows.
The number of tree seedlings planted by Murimi in each row were 4 more than those planted by Naliaka in each row. Calculate the number of seedlings Murimi planted in each row. Form 2 MathematicsForm 1 Mathematics
A garden is in the shape of a right angled triangle. The length of the shortest side is l7 m and the area of the garden is 346.8 m2. Calculate the length of the longest side of the garden.
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