KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
Find the value of p.
(b) A saleswoman earned a fixed salary of Ksh x and a commission of Ksh y for each item sold. In a certain month she sold 30 items and earned a total of Ksh 50 000. The following month she sold 40 items and earned a total of Ksh 56 000. (i) Form two equations in x and y. (ii) Solve the equations in (i) above using matrix method. (iii) In the third month she earned Ksh 68 000. Find the number of items sold.
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Form 2 Mathematics
Makau made a journey of 700 km partly by train and partly by bus. He started his journey at 8.00 a.m. by train which travelled at 50 km/h. After alighting from the
train, he took a lunch break of 30 minutes. He then continued his journey by bus which travelled at 75 km/h. The whole journey took 11 1/2 hours. (a) Determine: (i) the distance travelled by bus; (ii) the time Makau started travelling by bus. (b) The bus developed a puncture after travelling 187 1/2 km. It took 15 minutes to replace the wheel. Find the time taken to complete the remaining part of the journey Form 2 Mathematics
A solid consists of a cone and a hemisphere. The common diameter of the cone and the hemisphere is 12 cm and the slanting height of the cone is 10 cm.
(a) Calculate correct to two decimal places: (i) the surface area of the solid; (ii) the volume of the solid (b) If the density of the material used to make the solid is 1.3 g/cm3, calculate its mass in kilograms. Form 2 Mathematics
A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm, if the volume of the smaller cone is 160 cm3, find the
volume of the frustum Form 1 Mathematics
Three police posts X, Y and Z are such that Y is 50 km on a bearing of 060° from X while Z is 70 km from Y and on a bearing of 300° from X.
(a) Using a suitable scale, draw a diagram to represent the above situation. (b) Determine the distance, in km, of Z from X. Form 1 Mathematics
(a) Express 10500 in terms of its prime factors.
(b) Determine the smallest positive number P such that 10500P is a perfect cube. Form 1 Mathematics
In January, Mambo donated 1/6th of his salary to a children's home while Simba donated 1/5th of his salary to the same children's home. Their total donation for
January was Ksh. 14 820. In February, Mambo donated 1/8th of his salary to the children's home while Simba donated 1/12th of his salary to the children's home. Their total donation for February was Ksh 8 675. Calculate Mambo 's monthly salary. Form 2 Mathematics
Three vertices of a parallelogram PQRS are P(-l, 2), Q(8, -5) and R (5,0).
(a) On the grid provided below draw the parallegram PQRS. (b) Determine the length of the diagonal QS. Form 1 Mathematics
A customer paid Ksh. 5 880 for a suit after she was allowed a discount of 2% on the selling price. If the discount had not been allowed, the shopkeeper would have
made a profit of 20% on the sale of the suit. Calculate the price at which the shopkeeper bought the suit. Form 2 MathematicsForm 1 Mathematics
Using a ruler and a pair of compases only:
(a) construct a parallelogram PQRS in which PQ = 6 cm, QR = 4 cm and angle SPQ= 75°; (b) determine the perpendicular distance between PQ and SR. Form 2 Mathematics
The external length, width and height of an open rectangular container are 41 cm, 21 cm and 15.5 cm respectively. The thickness of the material making the container is 5 mm. If the container has 8 litres of water, calculate the
internal height above the water level. Form 3 Mathematics
A square room is covered by a number of whole rectangular slabs of sides 60cm by 42 cm. Calculate the least possible area of the room in square rnetres.
Form 2 Mathematics
A motorist took 2 hours to travel from one town to another town and 1 hour 40 minutes to travel back. Calculate the percentage change in the speed of the motorist.
Form 1 Mathematics
The diagonal of a rectangular garden measures 11 1/4 m while its width measures 6 3/4 m.Calculate the perimeter of the garden.
Form 2 Mathematics
A rectangular box open at the top has a square base. The internal side of the base is x cm long and the total internal surface area of the box is 432 cm2.
(a) Express in terms of x: (i) the internal height h, of the box; (ii) the internal volume V, of the box. (b) Find: (i) the value of x for which the volume V is maximum; (ii) the maximum internal volume of the box. Form 2 MathematicsForm 2 Mathematics
In the figure below, ABCD is a square. Points P, Q, R and S are the midpoints of AB, BC, CD and DA respectively.
(a) Describe fully:
(i) a reflection that maps triangle QCE onto triangle SDE; (ii) an enlargement that maps triangle QCE onto triangle SAE; (iii) a rotation that maps triangle QCE onto triangle SED. (b) The triangle ERC is reflected on the line BD. The image of ERC under the reflection is rotated clockwise through an angle of 90° about P. Determine the images of R and C: (i) under the reflection; (ii) after the two successive transformations. Form 2 Mathematics
Motorbike A travels at 10 km/h faster than motorbike B whose speed is x km/h.Motorbike A takes 1 1/2 hours less than motorbike B to cover a 180 km journey.
(a) Write an expression in terms of x for the time taken to cover the 180 km journey by: (i) motorbike A; (ii) motorbike B. (b) Use the expressions in (a) above to determine the speed, in km/h, of motorbike A. (c) For a journey of 48 km, motorbike B starts 10 minutes ahead of motorbike A. Calculate, in minutes, the difference in the time of their arrival at the destination. Form 1 Mathematics
The boundaries PQ, QR, RS and SP of a ranch are straight lines such that: Q is 16 km on a bearing of 040° from P; R is directly south of Q and east of P and S is 12 km on a bearing of 1200 from R.
(a) Using a scale of 1cm to represent 2 km, show the above information in a scale drawing. (b) From the scale drawing determine: (i) the distance, in kilometers, of P from S; (ii) the bearing of P from S. (c) Calculate the area of the ranch PQRS in square kilometres. Form 4 Mathematics
(b) Okello bought 5 Physics books and 6 Mathematics books for a total of Ksh 2 440.
Ali bought 7 Physics books and 9 Mathematics books for a total of Ksh 3 560. (i) Form a matrix equation to represent the above information. (ii) Use matrix method to find the price of a Physics book and that of a Mathematics book. (c) A school bought 36 Physics books and 50 Mathematics books. A discount of 5% was allowed on each Physics book whereas a discount of 8% was allowed on each Mathematics book. Calculate the percentage discount on the cost of all the books bought. |
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