KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 Mathematics
(a) Expand and simp1ify (2 —x)5. (b) Use the first 4 terms of the expansion in part
(a) above to find the approximate value of (1.8)5 to 2 decimal places.
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Form 4 Mathematics
A particle starts from O and moves in a straight line so that its velocity V ms-1 after time t seconds is given by V = 3t-t2. The distance of the particle from O at time t seconds is s metres.
(a) Express s in terms of t and c where c is a constant. (b) Calculate the time taken before the particle returns to 0. Form 1 Mathematics
A trader sells a bag of beans for shs. 2100 and that of maize at shs. 1200. He mixed beans and maize in the ratio 3:2. Find how much the trader should sell a bag of the mixture to realize the same profit.
Form 3 MathematicsForm 3 Mathematics
A bag contains 2 white balls and 3 black balls. A second bag contains 3 white balls and 2 black balls. The balls are identical except for the colours, b
Two balls are drawn at random, one after the other from the first bag and placed in the second bag. Calculate the probability that the 2 balls are both white. Form 4 MathematicsForm 1 Mathematics
When Ksh 40 000 was invested in a certain bank for 5 years it earned a simple interest of Ksh 3 800.
Find the amount that must have been invested in the same bank at the same rate for 7 - years to earn a simple interest of Ksh 3 420. Form 1 Mathematics
Five people can build 3 huts in 21 days. Find the number of people, working at the same rate that will build 6 similar huts in 15 days.
Form 1 Mathematics
The length of a flower garden is 2 m less than twice its width. The area of the garden is 60 m2.
Calculate its length. Form 1 Mathematics
A tea dealer mixes two brands of tea, x and y, to obtain 35 kg of the mixture worth Ksh 62 per kg. 1f brand x is valued at Ksh 68 per kg and brandy at Ksh 53 per kg, calculate the ratio, in its simplest form, in which the brands x and y are mixed.
Form 3 MathematicsForm 3 Mathematics
The length and width of a rectangle measured to the nearest millimeter are 7.5 cm and 5.2 cm respectively.
Find, to four significant figures, the percentage error in the area of the rectangle. 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. Form 2 Mathematics
A carpenter constructed a closed wooden box with internal measurements 1.5 metres long, 0.8 metres wide and 0.4 metres high. The wood used in constructing the box was 1.0 cm thick and had a density of 0.6 gcm3.
(a) Determine the: (i) volume, in cm3, of the wood used in constructing the box; (ii) mass of the box, in kilograms, correct to 1 decimal place. (b) Identical cylindrical tins of diameter 10 cm, height 20cm with a mass of 120 g each were packed in the box. Calculate the: (i) maximum number of tins that were packed; (ii) total mass of the box with the tins. Form 1 Mathematics
A saleswoman is paid a commission of 2% on goods sold worth over Ksh 100 000. She is also paid a monthly salary of Ksh 12 000. In a certain month, she sold 360 handbags at Ksh 500 each.
(a) Calculate the saleswoman’s earnings that month. (b) The following month, the saleswoman’s monthly salary was increased by 10%. Her total earnings that month were Ksh 17 600. Calculate: (i) the total amount of money received from the sales of handbags that month; (ii) the number of handbags sold that month. Form 2 MathematicsForm 3 MathematicsForm 2 Mathematics
A cylindrical solid whose radius and height are equal has a surface area of 154 cm2. Calculate its diameter, correct to 2 decimal places. (Take π = 3.142)
Form 3 Mathematics
Given that 3θ is an acute angle and sin 3θ = Cos 2θ°, find the value of θ.
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