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Form 4 Mathematics Paper 1 Exam Revision Questions With Answers Set 2

Four towns are situated in such a way that town Q is 240 km due east of town P. Town R is 100 km due south of town Q and on a bearing of 112° from P. The fourth town S is 225 km on a bearing of 202° from P.
a) Draw a sketch diagram showing that positions of towns P, Q, R, and S.
b) Find the size of angle PQR and angle RPS.
c) Without using scale drawing, calculate to the nearest whole number, the distance of:
i. town R from town P
ii. town S from town R
d) Determine the bearing of P from R

(8m 2s)

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59. A vertical pole 3 metres high casts a shadow 5 metres long on the ground. Calculate to the nearest whole number the angle of elevation of the sun.
60. Six men take 10 days to plant 480 trees. Find how many trees 9 men can plant in 8 days.
61. A group consisting of 60 adults and children hired a bus for sh 18 600 in order to take a trip. To raise the money each adult paid sh 400 and each child sh 250. Find the number of adults and the number of children in the group.
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70. A trader sold an article at sh 3 600 after allowing his customer a 10% discount on the marked price of the article. In so doing he made a profit of 50%. a) Calculate i. the marked price of the article. ii. the price at which the trader had bought the article. b) If the trader had sold the same article without giving a discount, calculate the percentage profit he would have made.
71. Use logarithms to evaluate #73.48 ÷ {(0.7592)^3 × 0.08723} ^(2/5) #
72. Factorize and simplify as far as Possible. #(15x^2+xy-6y^2)/(5x^2-8xy+3y^2 )#
73. Twenty four men working at the rate of 10 hours a day take 18 days to complete a certain job. How long would 30 men working 9 hours a day take to complete the same job?
74. Solve the equation #3/(2x) =7/(5x-1)#
75. a)Using mathematical tables find i) the reciprocal of 2.754. ii) the square of 4.765. b) Hence or otherwise calculate to 3 significant figures the value of #4.7652 + 1/2.754#
76. Solve for x in the equation #25^x+5^(2x) =50#
77. A cylindrical tank of radius 2 m and height 1.5 m initially contains water to a depth of 50 cm. Water is added to the tank at the rate of 62.84 litres per minute for 15 minutes. Find the new height of water in the tank. (Take p = 3.142)
78. The straight line passing through the points A(-1, 2k) and B(k, -1) is parallel to the line whose equation is 2y + 3x = 8. Find the value of k and hence write down the coordinates of A and B.
79. Jerusha invested sh 50 000 at the rate of 10% per annum compound interest for #2 1/2# years. Kemuto invested sh 35 000 at the rate of 15% per annum simple interest for the same period. Whose investment earned more interest and by how much?
80. a) Find the greatest common divisor of the terms #8x^4y^3 and 2x^2y^5 # b) Hence factorize completely the expression #8x^4y^3 - 2x^2y^5#
81. Evaluate #7 1/2 ÷3/5 of 4 1/6 +8 1/3 times1 1/5#
82. The marked price of some goods was sh 480 000. A salesman sold these goods at a discount of #2 1/2 %#. He received sh 18 720 as commission on the sale. At what percentage rate of commission was he paid?
83. The base areas of two cylindrical containers are #135 cm^2# and #240 cm^2# respectively. a) Determine the area scale factor and hence the linear scale factor. b) If the capacity of the smaller container is #540 cm^3#, what is the capacity of the larger container in litres?
84. The longer parallel side of a trapezium is three times as long as the shorter parallel side. The perpendicular distance between the parallel sides is 15 cm. If the area of the trapezium is #180 cm^2#, calculate the length of its longer parallel side.
85. Three towns A, B and C are such that town B is 90 km on a bearing of 150° from town A and town C is 120 km on a bearing of 060° from town B. a) Draw a sketch showing the positions of the three towns. b) Calculate the distance between towns A and C.
86. The diagram below shows a trough which is 4 m long and has a triangular cross-section. All dimensions arc as shown on the diagram a) Calculate I. the cross-sectional area of the trough in square metres. II. the capacity of the trough in litres. b) The trough which is initially one third full of water is filled by a pipe which delivers water at the rate of 0.8 litres per second.
87. Banda and Chuma live in two towns 240 km apart. One day at 9.45 a.m. Banda left his town and drove towards Chuma's town at an average speed of 60 km/h. Chuma left his town at 10.50 a.m. on the same day and drove towards Banda's town at an average speed of 80 km/h. a) Find I. the distance from Banda's town to the place where the two met. II. the time they met
88. During the first year a poultry farmer had four times as many hens as ducks and one third as many turkeys as ducks. In the second year the number of ducks increased by 10%, the number of hens increased by 25% while the number of turkeys decreased by 20%. At the end of the second year the farmer had a total of 955 birds. Calculate to one decimal place the percentage increase in the total number of
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90. At the end of year 2000 a cooperative society realised a gross income of sh 33.5 million. The total expenses incurred by the society during that year was sh 20.75 million. Each year 60% of the net income is paid to members as dividends which is calculated per share. During the year 2001 the society's gross income increased by 30% while its total expenditure decreased by 20%.
91. The diagram below shows a rectangle measuring 15 cm by 12 cm from which two semi-circles each of a diameter 5.6 cm are removed. The figure represents the cross section of a wooden block 10.5 metres long. The wood making the block has a density of 0.8 g/#cm^3#. a) Calculate to one decimal place i. the cross sectional area of the block ii. the mass of the wood in the block in kilograms.
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93. Without using logarithms or calculator, evaluate #root3((0.95 times 5.5 times 10.5)/(0.21 times2.09))#
94. Kamemia uses #1/3#of his farm for planting coffee, #1/4# for planting tea and #2/5#of the remainder for mixed farming. He still has 6 hectares of unused land. Find the size of Kamemia's land.
95. Mwaura is now twice as old as his daughter and four times as old as his son. In eight years time Mwaura's age will be equal to the sum of ages of his daughter and son. Determine Mwaura's present age.
96. The straight line passing through the point (-3, -4) is perpendicular to the line whose equation is 2y + 3x = 11, and intersects the x-axis and the y- axis at P and Q respectively. Determine the equation of the second line and hence write down the coordinates of P and Q.
97. Given the column vectors #p=((1),(2)), q=((-3),(-6)) and r= ((2),(-3))# and that #a=3p- 1/3q + r#, express a as column vector.
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