-
Mr. Owino spends a quarter of his salary on school fees. He spends two-thirds of the remainder on food and a fifth of what is left on transport. He saves the balance. In a certain month he saved Sh.3400. What is his salary?
Date posted:
August 16, 2019
-
Tsuma bought some rice at sh 30 per kg.He packed two- fifths of the rice in 2kg packets which he sold at shs. 85 per packet. He packed the other three- fifths in 3 kg packets and sold thee at shs. 120 per packet. He sold all the rice in this way and made a profit of sh. 4400.
a) Determine the amount of rice bought.
b) Calculate to one decimal place.
i) The percentage profit he made.
ii) The percentage profit she would have made if he had sold all the rice in 2kg packet.
Date posted:
August 15, 2019
-
Use tables of reciprocal only to work out
Date posted:
August 15, 2019
-
Under an enlargement centre ( 2,1) the image of P ( 1,-1) is P` ( 4,5). Determine the scale factor of the enlargement
Date posted:
August 15, 2019
-
The sum of the digits in three digit number is nine. The tens ten is digits half the sum of the other two and the hundreds digit is half the units digit. Find the number.
Date posted:
August 15, 2019
-
Find the equation of a line perpendicular to 2x +4Y = 8, which crosses the line at its y –Intercept.
Date posted:
August 15, 2019
-
If x: y = 4:7 and y :z = 5:3 find the ratio x:y: z
Date posted:
August 15, 2019
-
The diagram below (not drawn to scale) shows the position of a harbor H and three islands A,B and C. C is due North of H. The bearing of A from H is 0620 and angle HAB=1280 HA=54km and AB=31km.
a) Calculate the distance HB
b) Find the bearing of B from A
c) Given that the bearing of A from C is 1330, calculate AC
d) A light ship L is positioned due North of H and equidistant from A and H.
Calculate HL.
Date posted:
August 15, 2019
-
Four towns P, Q, R and S are such that town Q is 120km due east of town P. Town R is 160km due north of town Q, town S is on a bearing of 3300 from P and on a bearing of 3000 from R.
a) Using ruler and compasses only, show the relative positions of towns P,Q,R and S. Take a scale of 1cm rep 50km.
b) Determine
i) The distance SP in km
ii) The bearing of S from Q
iii) How far north, S is, from line QP produced.
Date posted:
August 15, 2019
-
A flag post 12m long is fixed on top of a tower. From a point on horizontal ground, the angles of elevation of the top and bottom of the flag post are 460 and 330 respectively.
Calculate
a) The horizontal distance from the point on the ground to the base of the tower.
b) The total height of the tower and the flag.
c) The shortest distances from the point on the ground to
i) The top of the flag post.
ii) The top of the tower.
Date posted:
August 15, 2019
-
The figure below shows a portable Kennel.
a) Calculate
i) The total surface area of the walls and the floor.
ii) The total area of the roof.
b) The cost of roofing is Ksh 500 per square meter and that of making walls and floor is Ksh 600 per m2.Find the cost of making the Kennel.
c) Find the cost of roofing another Kennel whose dimensions are 50% more than those of the given Kennel
d) Calculate the volume of air inside the Kennel in cm3.
Date posted:
August 15, 2019
-
A poultry farmer has twenty times as many hens as turkeys and three quarters as many ducks as turkeys.
a) If there are t, turkeys, write down a simplified expression in terms of t for the total number of birds on the farm.
b) Given that he has 72 ducks, calculate as a percentage the sum of turkeys and ducks to the number of hens on the farm.
Date posted:
August 15, 2019
-
The figure below shows an arc ACE of a circle with centre O and radius 6cm. If BC=CD=4cm, calculate the area of the shaded region if DE=AB =1.53cm.
Date posted:
August 15, 2019
-
The coordinates of the points P and Q are (1, -2) and (4, 10) respectively. A point T divides the line PQ in the ratio 2:1
a) Determine the coordinates of T
b) Find the equation of the line perpendicular to PQ and passing through T.
Date posted:
August 15, 2019
-
A sales man earns a basic wage of Ksh 1,500 per week. In addition , he is paid commission per week as follows:
Commission
For sales up to Ksh 50,000 0%
For sales above Ksh 50,000
i) For the first Ksh 25,000 2%
ii) For the next Ksh 25,000 2 ½ %
iii) For any amount above Ksh100,000 5%
During that week, he sold goods worth Ksh 115,000.What was his total pay for that week?
Date posted:
August 15, 2019
-
A cylinder of radius 14cm contains water. A metal solid hemisphere of radius 6.8cm is submerged into the water in the cylinder. Find the change in height of the water in the cylinder.
Date posted:
August 15, 2019
-
Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially Simiyu had five stones less than Nasike, how many stones did each have?
Date posted:
August 15, 2019
-
Evaluate without using calculator or mathematical tables leaving your answer as a simplified fraction.
Date posted:
August 15, 2019
-
Three business partners Omoit, Achola and Amoit contributed Ksh. 100,000, Ksh.80,000 and ksh.50,000 respectively to start a business. After one year the business realized a profit which they shared in the ratio of their contributions.
(a) If Amoit’s share of profit was Kshs.20, 000, how much was the total amount of profit?
(b) At the beginning of the second year, Amoit boosted his shares by Ksh. 10,000. If the business profit increased by 20% at the end of the second year. Calculate;
(i) Omoit’s share of the profit.
(ii) The difference between Omoit’s and Achola’s share of the profit.
Date posted:
August 15, 2019
-
1600cm3 of fresh water of density 1g/cm3 are mixed with 1400cm3 of sea water of density 1.25g/cm3. Determine the density of the mixture.
Date posted:
August 15, 2019
-
The G.C.D of two numbers is 36 and their L.C.M. is 1260. If one of the numbers is 252,find the other number.
Date posted:
August 15, 2019
-
Solve the inequalities and represnt the solution on number line. 3x – 9 < 5x + 3≤ 2x – 6
Date posted:
August 15, 2019
-
Okisai is three times as old as his son now. If ten years ago the sun of their ages was 44. How Old was Okisai when his son was born ?
Date posted:
August 15, 2019
-
Atyang bought 3 blouses and 2 skirts for a total of Ksh.500. Awino bought 4 blouses and 5 skirts for a total of Ksh.900. Find the cost of 1 blouse and 3 skirts.
Date posted:
August 15, 2019
-
Nairobi and Eldoret are each 250km from Nakuru. At 8.15a.m, a lorry leaves Nakuru for Nairobi.
At 9.30am, a car leaves Eldoret for Nairobi via Nakuru at a speed of 100km/h. Both vehicles arrived
Nairobi at the same time.
(a) Calculate their time of arrival in Nairobi.
(b) Find the cars speed relative to that of the lorry.
(c) How far apart are the vehicles at 12.45pm.
Date posted:
August 15, 2019
-
If the expression 25y² - 70y + (16 + K) is a perfect square; where K is a constant;find the value of K.
Date posted:
August 15, 2019
-
Use the quadratic formula to solve the equation 2x² - 9x + 3 = 0 giving your answer to 4 significant figures.
Date posted:
August 15, 2019
-
The diagram below represents a model of a pillar. The radii of the top and the base are 7cm and 3.5cm respectively. The height of the cylindrical part is 10cm while the height of the whole pillar is 15cm.
(a) Calculate the volume of the model in cm³.
(b) Calculate the mass of the material used to construct the pillar given that the actual height of the
whole pillar is 60m and the density of the material used is 0.832g/cm³. (Give your answer in tones).
Date posted:
August 15, 2019
-
The capacity of two similar rectangular tanks are 1,000,000 litres and 512,000 litres respectively.
(a) Determine the length of the larger tank if the smaller one is 240cm long.
(b) Calculate the surface area of the smaller tank if the larger tank’s surface area is 1875m².
(c) Estimate the mass of the smaller tank if the mass of the larger one is 800kg.
Date posted:
August 15, 2019
-
The figure below shows a triangle ABC which is right-angled at C. CB = 8cm and AC = 6cm. Find the length of CD given that CD is perpendicular to AB.
Date posted:
August 15, 2019