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Form 4 Mathematics Paper 1 Exam Revision Questions With Answers Set 3
Solve for x in the equation #27^((x-1)) ×9^x=81^x#
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1.
A trader marked a pair of shoes at sh 1 400. He sold the pair of shoes at a discount of 10% and still made a profit of 25% on the cost price. Determine how much the trader had paid for the pair of shoes.
2.
Solve the equation #2/(3x)-1/4=5/(12x)#
3.
In a mixed secondary school there are 60 more boys than girls. Half of the boys and #2/3# of the girls are boarders. If there are 240 boarders, find the total number of students in the school.
4.
A lorry travelled between towns A and B, a distance of 280 km. For the first 150 km the lorry travelled at an average speed of 50 km/h and for the remaining part of the journey at an average speed of 65 km/h. Calculate the average speed for the whole journey.
5.
Jamal imported 50 wrist watches from Germany at a cost of 1 450 Euros. He then spent 20% of the total cost of the watches in transporting them to Kenya. He finally sold the watches in Kenya at a profit of 30%. Given that 1 Euro = Ksh 88.95, calculate to the nearest Kenya shilling the selling price of each watch.
6.
The figure above shows a triangle PQR in which PR = 5 cm and angle PRQ = 60°. PS is perpendicular to QR and QS : SR= 3: 1. Calculate to one decimal place the length of PQ.
7.
Given that log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990. Find, without using mathematical tables or a calculator, the value of log 4 320.
8.
The radius of a cylinder is increased by 30% while its height decreased by 20%. The capacity of the old cylinder is #500cm^3#. Determine the capacity of the new cylinder.
9.
A lorry travels from Nairobi to Lodwar and back. From Nairobi to Lodwar the average speed of the lorry is 70 km/h and from Lodwar to Nairobi, the lorry average speed is 20 km/h slower and takes 4 hours longer than on the journey from Nairobi to Lodwar. a) Find the distance between Nairobi and Lodwar. b) Diesel consumption is 0.32 litres per kilometre on the journey from Nairobi to Lodwar.
10.
The base area of a cylindrical Container is #72cm^2#. The Container is enlarged so that the new container is similar to the old container and has a base area of #128 cm^2#. a) Find in its simplest terms the area scale factor of the enlargement i. the linear scale factor ii. the volume scale factor. b) The radius of the new container is 20 cm.
11.
Simplify without using, a calculator #(2/3 of4 1/2+1)/(3 3/4-1 1/4×1 3/5)#
12.
Factorize completely #12x^2 — 27#
13.
Determine all the integral values of x which satisfy the inequalities 2x — 5 < 4 — x = x + 8
14.
A straight line AB passes through the points A(5, 8) and B(-1, -4). a) Find the equation of line AB in the form y = mx + c. b) Hence calculate to one decimal place the size of the acute angle line AB makes with the x-axis.
15.
A certain type of steel is made by mixing carbon, phosphorous and iron is the ratio 1 : 2 : 5. A piece of the steel contains 3.6 kg of phosphorous. Determine the total mass of carbon and iron in that piece of steel.
16.
Solve the following simultaneous equation by substitution method. 4x + 3 = 5 5x - y = 11
17.
The figure below shows a right angled triangle ABC. The dimensions of the triangle in centimeters are given in terms of x. Determine a) the value of x. b) the perimeter of the triangle.
18.
Three businesswomen, Amina, Ndinda and Kagendo contributed sh 25 000, sh 45 000 and sh 60 000 respectively to start a business. The profits made each month was shared in the ratio of their contributions. During a certain year Kagendo received sh 16 380 more than Amina got. Determine Ndinda's share of the profits during that month.
19.
The diagram below shows a sector of a circle of radius 15 cm subtending an angle of 240° at the centre of the circle. The sector represents the net of the curved surface of a solid cone. a) Calculate i. in terms of n the area of the sector. ii. the base radius of the cone. b) Determine the total surface area of the cone.
20.
A bathroom measuring 2.5 m long, 2.0 m wide and 3.0 m high is to be renovated by covering all the four walls and the floor with tiles. The room has one door measuring 2 m high and 90 cm wide and a high end window on the opposite wall measuring 1.5 m long and 40 cm wide. The walls are to be covered with tiles to a height of 1.2 m. The remaining part of the walls (except the door and window) and the
21.
The diagram alongside shows a solid frustrum whose top radius is 35 cm and bottom radius 42 cm. The height of the frustrum is 50 cm as shown. a)Calculate i) the curved surface area of the frustrum ii) the area of the top surface iii) the area of the bottom surface. iv) to 3 significant figures, the total surface area of the frustrum in square metres.
22.
Moraa is now three times as old as her daughter. Five years ago her age was 10 years more than her daughters age will be 5 years from now. Determine Moraa's present age.
23.
Ole Lokoliani uses #1/6# of his land for planting maize,#1/12#. for beans and #4/9# of the remainder for grazing. He still has 15 hectares of fallow land. Find the size of his land.
24.
Solve for x in the equation #27^((x-1)) ×9^x=81^x#
25.
The table below shows the deviations of a given set of numbers from an assumed mean and their respective frequencies. (a) Complete the table (b) Given that the assumed mean is 24, calculate the actual mean of the distribution.
26.
The curved surface area of a cylindrical container is #1 980 cm^2#. If the radius of the container is 21 cm, calculate to one decimal place, the capacity of the container in litres. #(Take pi =22/7)#
27.
A group of 300 adults and children organised a trip to Mombasa. Each adult paid sh 400 while each child paid half as much. In this way the group raised a total of sh 74 000 for the trip.
28.
A regular polygon of side 15 cm has an interior angle of 144°. The polygon represents a metal disc which is 2.5 mm thick and is made of a metal whose density is 9.6 g/#cm^3.# a) Determine the number of sides of the polygon. b) Calculate to one decimal place i. the surface area of the disc ii. the volume of metal in the disc. iii. the mass of the disc in kilograms
29.
A picture measuring 18 cm by 14 cm is placed inside a frame leaving a margin of uniform width all around the picture. The width of the margin is y centimetre and the area of the frame is #320 cm^2#. The margin is covered with velvet material at a cost of sh 8.50 per square centimetre. a) Draw a sketch of the frame, the picture and the margin. b) Determine i. the value of y.
30.
The figure above shows two circles with the centres A and B and of radii 7.2 cm and 10cm respectively. Centers A and B are 12 cm apart and AP:PB = 1:2. Calculate to 4 significant places the a) size of angle CAD b) size of angle CBD c) area of the shaded region. #(Take pi =3.142)#
31.
In the figure above vector OA = a and OB = b. P is the midpoint of OA and Q divides OB in the ratio 2:1. a) Express the following vectors in terms of a and b i. BP ii. AQ b) Lines BP and AQ intersect at R such that BR = mBP and AR = nAQ. Where m and n are constants. Express OR in two different ways in terms of a.b, m and n. Hence find the values of m and n. c) Determine the ratio AR:RQ and h
32.
Use logarithms to evaluate. #53.89 div[(0.09254)^2 times 12.85]^(2/5)#
33.
Twenty four men working at the rate of 10 hours a day take 16 days to complete a job. How long would 40 men working at the rate of 8 hours a day take to complete the same job?
34.
Solve the equation #(x + 3 )/3 - (x-5 )/2 = (3x - 8 )/4#
35.
Solve for y in the equation #16^y + 4^(2y) = 8 #
36.
A rectangular tank has a base measuring 2.7 m by 2 m. This tank contains water to a height of 25 cm. Water is pumped into the tank continuously from 1.35 p.m. to 2.25 p.m. at the rate of 1.08 litres per second. Find the new height of water in the tank.
37.
The figure below shows a circle centre 0 and radius 8 cm. Sector OPQ subtends an angle of 135° at the centre of the circle. Calculate to 2 decimal places the area of the shaded region.
38.
a)Use mathematical tables to find i) the square of 4.978. ii) the recipricol of 31.65. b) Hence evaluate to 4 significant figures the value of #4.978^2 - (1 )/(31.65 )#
39.
The sum of the ages of three sisters Akinyi, Moraa and Nafula is 44 years. Moraa is twice as old as Akinyi and three times as old as Nafula. Find their ages.
40.
Two similar cylindrical containers are such that the base area of the smaller container is #4/25# the base area of the larger container. The capacity of the smaller container is #880 cm^3#. Calculate the capacity of the larger container in litres.
41.
Four skirts and 3 blouses cost sh 3 550 while 5 skirts and 6 blouses cost sh 5 000. What is the cost of each item?
42.
Evaluate #(8 2/5-3 2/3÷1 5/6)/(1 1/5+1 1/3×1 1/2)#
43.
The line whose equation is 4y - 3x = 12 and the x-axis meet at a point such that the acute angle between them is ß°. Calculate the size of this angle in degrees correct to 2 decimal places.
44.
The base radius of a cylinder is increased by 20% while its height is decreased by 15% . Calculate the percentage increase in the volume of the cylinder.
45.
The angle of elevation of the top of a building from a point A is 18.5°. The angle of elevation of the top of the building from another point B is 50.6°. If point B is 20m from the base of the building, calculate to one decimal place (a) the height of the building. (b) the distance between A and B.
46.
Three boats are anchored in the harbour such that boat Q is 150 m on a bearing of 050° from boat P. Boat R is 200 m on a bearing of 140° from boat Q (a) Draw a sketch showing the positions of boats P, Q and R. (b) Calculate (i) the size of angle PQR (ii) the distance PR.
47.
Kalome spent sh 31 500 to buy a number of skirts and blouses from a wholesaler at sh 600 per skirt and sh 300 per blouse. Awiti bought the Sallie number of skirts and blouses from another wholesaler where she paid 10% less per skirt and 20% more per blouse. Awiti spent sh 900 less than Kalome. (a) Determine the number of skirts and blouses each trader bought. (b)Kalome sold all his clothes at a
48.
(a) Solve the following inequalities and represent the solutions on a number line. i) #1/4 x-1/3=1/2 x+2/3# #3/5 x-1/2=1/4 x+1/5# ii)# x-4<8-3x# #4x-2<7x+1# (b) The diagram below shows a region R bounded by four lines #l_1, l_2, l_3 and l_4#. Write down the four inequalities which are satisfied simultaneously by region R.
49.
The graph below is the velocity-time graph of a vehicle in linear motion. Study the graph and use it to answer the questions below. (a) Determine the acceleration between (i) P and Q (ii) Q and R (iii) R and S (iv) S and T.
50.
A sector of a circle of radius 40 cm subtends an angle of 126° at the centre of the circle. #(Take pi=22/7)# (a) Calculate i) the area of the sector ii) the length of the arc. (b) The sector is folded to form an inverted right cone. Calculate (i) the base radius of the cone (ii) to one decimal place the vertical height of the cone. (c) Calculate the capacity of the cone in litres.
51.
Four boats P, Q, R and S are anchored on a bay such that boat Q is 180 m on a bearing of 075° from P. Boat R is 240 m on a bearing of 165° from Q. Boat S is 185 m to the south of P and due west of R. (a) Draw a sketch diagram to show the positions of P, Q, R and S. (b) Without using scale drawing, calculate (i) the distance PR. (ii) to 3 significant figures the bearing of P from R.
52.
The diagram above shows a wooden structure which has a rectangular block and a cylindrical block. The rectangular block measures 100 cm by 50 cm by 40 cm and has a circular hole of radius 10 cm drilled right through it. The cylindrical block has a radius of 20 cm and height 25 cm. (a) Taking pi= 3.142, calculate (i) the volume of wood used to make the rectangular block (ii) the volume of wood
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