KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 2 MathematicsThe area of a rhombus is 60cm2. Given that one of its diagonals is 15 cm long, calculate the perimeter of the rhombus
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Form 1 MathematicsForm 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 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.
Form 2 Mathematics
A line L is perpendicular to the line 2⁄3x + 5⁄7 y = 1 . Given that L passes through (4,11), find:
(a) gradient of L1 (b) equation of L in the form y = mx + c, where m and c are constants. Form 1 Mathematics
Given that the exterior angle of a regular hexagon is x. find the size of each interior angle of the hexagon.
Form 2 MathematicsForm 1 Mathematics
A trader bought maize for Ksh 20 per kilogram and beans for Ksh 60 per kilogram. She mixed the maize and beans and sold the mixture at Ksh 48 per kilogram. If she made a 60% profit,
determine the ratio maize to beans per kilogram in the mixture. |
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