KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 MathematicsA minor sector of a circle of radius 28cm includes an angle of 1350 at the center. a) (i) convert 1350 into radians. Hence of otherwise find the area of the sector. ii) Find the length of the minor arc. b) The sector is folded to form a right circular cone. Calculate the : i) Radius of the cone ii) Height of the cone. (Take the value of Ð to be 22/7) (8mks)
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Form 4 MathematicsA triangle T whose vertices are A (2,3) B(5,3) and C (4,1) is mapped onto triangle T1 whose vertices are A1 (-4,3) B1 (-1,3) and C1 (x,y) by a transformation Find the: (i) Matrix M of the transformation (ii) Coordinates of C1 b) Triangle T2 is the image of triangle T1 under a reflection in the line y = x. Find a single matrix that maps T and T2 (8mks) Form 1 Mathematics
In this question use a ruler and a pair of compasses
Line PQ drawn below is part of a triangle PQR. Construct the triangle PQR in which
a) < QPR = 300 and line PR = 8cm b) On the same diagram construct triangle PRS such that points S and Q are no the opposite sides of PR<PS = PS and QS = 8cm c) A point T is on the a line passing through R and parallel to QS.If <QTS =900, locate possible positions of T and label them T1 and T2, Measure the length of T1T2. Form 2 Mathematics
The figure below represents a right prism whose triangular faces are isosceles. The base and height of each triangular face are 12cm and 8cm respectively. The length of the prism is 20cm.
Calculate the:
Form 1 MathematicsForm 1 MathematicsForm 3 Mathematics
The average rate of depreciation in value of a water pump is 9% per annum. After three complete years its like value was sh 150,700. Find its value at the start of the three – year period.
Form 2 Mathematics
Solve the following inequalities and represent the solutions on a single number line:
3 – 2x < 5 4 – 3x ≥ -8 Form 1 Mathematics
A Kenyan tourist left Germany for Kenya through Switzerland. While in Switzerland he bought a watch worth 52 Deutsche Marks. Find the value of the watch in:
(a) Swiss Francs. (b) Kenya Shillings Use the exchange rates below: 1 Swiss Franc = 1.28 Deutsche Marks. 1 Swiss Franc = 45.21 Kenya Shillings Form 3 Mathematics
The position vectors of points X and Y are
x = 2i + j – 3k and y = 3i + 2j -2k respectively. Find xy; Form 4 Mathematics
The diagram on the grid below represents as extract of a survey map showing two adjacent plots belonging to Kazungu and Ndoe.
The two dispute the common boundary with each claiming boundary along different smooth curves coordinates ( x, y) and (x, y2) in the table below, represents points on the boundaries as claimed by Kazungu Ndoe respectively.
(a) On the grid provided above draw and label the boundaries as claimed by Kazungu and Ndoe
Form 4 Mathematics
(b) In a certain week a businessman bought 36 bicycles and 32 radios for total of Kshs 227 280. In the following week, he bought 28 bicycles and 24 radios for a total of Kshs 174 960
Using matrix method, find the price of each bicycle and each radio that he bought (c) In the third week, the price of each bicycle was reduced by 10% while the price of each radio was raised by 10%. The businessman bought as many bicycles and as many radios as he had bought in the first two weeks. Find by matrix method, the total cost of the bicycles and radios that the businessman bought in the third week. Form 1 Mathematics
Two cylindrical containers are similar. The larger one has internal cross- section area of 45cm2 and can hold 0.945 litres of liquid when full. The smaller container has internal cross- section area of 20cm2
(a) Calculate the capacity of the smaller container (b) The larger container is filled with juice to a height of 13 cm. Juice is then drawn from is and emptied into the smaller container until the depths of the juice in both containers are equal. Calculate the depths of juice in each container. (c) On fifth of the juice in the larger container in part (b) above is further drawn and emptied into the smaller container. Find the difference in the depths of the juice in the two containers. Form 3 Mathematics
In the figure below, OQ = q and OR = r. Point X divides OQ in the ratio 1: 2 and Y divides OR in the ratio 3: 4 lines XR and YQ intersect at E.
(a) Express in terms of q and r
(i) XR (ii) YQ (b) If XE = m XR and YE = n YQ, express OE in terms of: (i) r, q and m (ii) r, q and n (c) Using the results in (b) above, find the values of m and n. Form 1 Mathematics
A retailer planned to buy some computers form a wholesaler for a total of Kshs 1,800,000. Before the retailer could buy the computers the price per unit was reduced by Kshs 4,000. This reduction in price enabled the retailer to buy five more computers using the same amount of money as originally planned.
(a) Determine the number of computers the retailer bought (b) Two of the computers purchased got damaged while in store, the rest were sold and the retailer made a 15% profit Calculate the profit made by the retailer on each computer sold Form 3 Mathematics
A frequency distribution of marks obtained by 120 candidates is to be represented in a histogram. The table below shows the grouped marks. Frequencies for all the groups and also the area and height of the rectangle for the group 30 – 60 marks.
(a) (i) Complete the table
(ii) On the grid provided below, draw the histogram (b) (i) State the group in which the median mark lies (ii) A vertical line drawn through the median mark divides the total area of the histogram into two equal parts Using this information or otherwise, estimate the median mark Form 2 Mathematics
In the diagram below PA represents an electricity post of height 9.6 m. BB and RC represents two storey buildings of heights 15.4 m and 33.4 m respectively.
The angle of depression of A from B is 5.50 While the angle of elevation of C from B is 30.50 and BC = 35m.
(a) Calculate, to the nearest metre, the distance AB
(b) By scale drawing find, (i) The distance AC in metres (ii) Angle BCA and hence determine the angle of depression of A from C Form 1 Mathematics
Three business partners: Asha Nangila and Cherop contributed Kshs 60,000, Kshs 85,000 and Kshs 105 000 respectively. They agreed to put 25% of the profit back into business each year. Thay also agreed to put aside 40% of the remaining profit to cater for taxes and insurance. The rest of the profit would then be shared among the partners in the ration of their contributions. At the end of the first year, the business realized a gross profit of Kshs 225 000
(a) Calculate the amount of money Cherop received more than Asha at the end of the first year (b) Nangila further invested Kshs 25,000 into the business at the beginning of the second year. Given that the gross profit at the end of the second year increased in the ratio 10: 9, calculate Nangila's share of the profit at the end of the second year. ​Related Questions and Answers on Commercial Arithmetic I
Form 3 Mathematics
A rally car traveled for 2 hours 40 minutes at an average speed of 120 km/h. The car consumes an average of 1 litre of fuel for every 4 kilometers.
A litre of the fuel costs Kshs 59 Calculate the amount of money spent on fuel Form 1 Mathematics
Points L and M are equidistant from another point K. The bearing of L from K is 3300.
The bearing of M from K is 2200.Calculate the bearing of M from L Form 3 MathematicsForm 1 Mathematics
The sum of two numbers x and y is 40. write down an expression, in terms of x, for the sum of the squares of the two numbers.
Hence determine the minimum value of x2 + y2 Form 1 Mathematics
(a) Draw a regular pentagon of side 4 cm
(b) On the diagram drawn, construct a circle which touches all the sides of the pentagon |
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