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Form 4 Mathematics Paper 1 Solved Questions

Form 4 Mathematics Paper 1 Solved Questions. Answers are available in video format.

Lessons (48)

1. To process tea, green tea leaves are dried and then ground to produce fine tea. In the process the mass of green tea leaves decreases in the ratio 2:15.Determine the mass of green tea which must be processed to produce 1.5 tonnes of fine tea.
2m 0s
2. Expand the following expression and then factorize completely #(2a+b)^2 – (a-2b)^2#
5m 20s
3. a).Find the gradient of the straight line joining the points A(1,-2) and B(4,-6). b).Hence find the equation of the straight line passing through A and perpendicular to AB.
3m 38s
4. Solve for the value of x in the equation below #(6x-4)/3 -(2x-1)/2= (6-5x)/6#
2m 34s
5. A school bought 40 textbooks at a total cost of sh 9500.Some books cost sh 200 each while others cost sh 350 each. Find the number of text books which were bought at sh 200 each.
3m 40s
6. You are given the points A (-2, 4), B(3,1) and C(13,-5).Express AB and AC as the column vectors and hence show that points A,B and C are collinear.
5m 41s
7. A lorry driver travelled the first 130 km at an average speed at 65km/h. For the next 3 hours he travelled at an average speed of 50km/h. Find the average speed for the whole journey.
1m 59s
8. Given that log 3 = 0.4771, log 5 =0.6990 and log 7 =0.8451, find without using logarithm tables or a calculator, the value of a).log 1575 b).log 2205
8m 27s
9. A cylindrical tank of diameter 1.4m and height 1.2m is one-quarter full of water. This water is transferred to an empty rectangular container measuring 1.2 m long and 70cm wide. Calculate the height of the water in the container in centimeters.
4m 6s
10. Factorize the expression #28x^2 – 7y^2# completely and hence or otherwise find its value when x =5 and y = 6
5m 23s
11. Simplify the expression 2(2a - 3b-4c)-3(a-2b +2c) -4(b-2c-a)
2m 56s
12. An article was sold to a customer for sh 510 after allowing him a 15% discount on the marked price. Find the price at which the article was marked.
1m 27s
13. Evaluate #( 81/16)^(-3/4) times (9/4)^(1/2) times (27)^(2/3)#
2m 59s
14. Hamisi bought 3 shirts and 2 trousers at a total cost of sh 1575.If he had bought 2 shirts and 3 trousers he would have spent sh 225 more. Find the cost of 5 shirts and 2 trousers.
5m 43s
15. Given that x = 2,y= 3 and z = - 2,find the value of #(3x^2 yz^2 - 4xy^2 z^2 + 5x^2y^2z^2)/(4xy^2z^2 - 2x^2yz + 4x^2y^2z)#
6m 20s
16. The table below shows the heights to the nearest centimeter of 40 students in a form 2 class a) State the modal class b) Calculate the median height
7m 44s
17. Giving your answer in the simplest terms possible, Express the expression #(3x-y)^2 – (x-2y)(2x+y)# In terms of x only given that y = x-2
6m 25s
18. The dimensions of a rectangle whose area is #104cm^2# are such that its width is 5cm shorter than its length. a).Taking l to be the length of the rectangle, write down a simplified quadratic equation for the area of the rectangle and hence find its dimensions. b).Calculate the perimeter of the rectangle.
5m 45s
19. The straight line joining the points P(a,7) and Q(13,a) is parallel to the line whose equation is 3y+2x = 9.Find the value of a.
2m 54s
20. Given that the ratio x:y = 3:5,find the ratio (x+y):(3x –y)
1m 14s
21. Simplify the following expression by reducing it to a single fraction in its simplest form #(3x-2)/2 - (2x-3)/3 - (3-x)/ 6#
3m 1s
22. By writing your answer in the form ay simplify #(3^(5x)times 5^(2x) times 3^(-x) ÷ 5^(-2x))^(1/4#
2m 19s
23. Solve for x #27^x times 3^(2x-2) =9^(x +2)#
2m 8s
24. Form the quadratic equation whose roots are #x = (-5)/2# and x = 3
2m 16s
25. Solve the inequality #(2x)/3 +2 ge (5x)/2-9#
1m 59s
26. Factorize #2x^2 –x -3#
1m 11s
27. The sum of 4 consecutive odd numbers is 72.find the numbers.
2m 21s
28. Simplify #(x+4)/(x-4) -(5x+20)/(x^2-16)#
4m 15s
29. After allowing his customer a #12 1/2%# discount a trader sold an article at sh 350.Find the price at which the article was marked.
1m 38s
30. Simplify as far as possible #((2x- y)^2 - (y + 2x)^2)/((y - x)^2 - (y + x)^2)#
6m 46s
31. The position vectors of points A,B and C are a,b and c respectively and C is the mid-point of AB a).Find a relationship between vectors a,b and c b).Given that a =( -2,7 ) and b = ( -4,1) ,Find c and hence state the coordinates of point C.
4m 51s
32. A car which consumes 1 litre of petrol for every 12 km uses 48 litres of petrol for a certain journey. Find how many litres of petrol a matatu which consumes 1 litre for every 8 km uses for the same journey.
1m 47s
33. A truck left town A at 9:35a.m and travelled towards town B at an average speed of x km/h. At the same time a lorry left town B and travelled towards town A along the same road. The distance between the two towns is 322km and the two vehicles met at 2:11p.m.Given that the lorry travelled 20km/h faster than the truck, find the value of x.
4m 27s
34. Two coils which are made by winding aluminium wire of different gauges and length have the same mass.The first coil is made by winding 270 metres of wire with cross-sectional diameter 2.8mm while the second coil is made by winding a certain length of wire with cross-sectional diameter 2.1mm.Find the length of the wire in the second coil.
5m 40s
35. The wheel of a racing bicycle has a diameter of 80cm and rotates at the rate of 2.5 revolutions per second. Calculate to one decimal place the speed in km/h at which the bicycle is moving.#(Take pi = 3.142)#
3m 12s
36. The straight line whose double intercept equation is #x/a + y/b = 1# Passes through the points A(6,-4) and B(-3, 8).Find the equation of the line in the form y =mx +c and determine the values of a and b.
5m 32s
37. Pipe A can fill a drum in 6 minutes while pipe B can fill it in 10minutes.A drainage pipe C can empty the full drum in 5 minutes. Pipes A and B are opened and left running for 3 minutes. The drainage pipe C is then opened and all three left running. Find how many more minutes it takes to fill the drum.
3m 23s
38. On arrival to Kenya a Canadian tourist exchanged his Canadian dollars for ksh 199690.Given that the currency exchange rate was 1 Canadian dollar = ksh 52.55 and that the bank charged him 5% commission, find the number of dollars he exchanged.
2m 56s
39. The radius of a cylinder is increased by 15% while its height is decreased by 20%.Find the percentage increase in the volume of the cylinder.
3m 59s
40. The straight line passing through the point A (-3,-4) is perpendicular to the line whose equation is 2y +3x = 8.The line passing through A cuts the x-axis and the y-axis at P and Q respectively. Find the equation of the line and hence determine the coordinates of P and Q.
4m 36s
41. In a school there are 30 more boys than girls. One-quarter of the boys and two-thirds of the girls are boarders. If there are 255 boarders, find the number of students in the school.
3m 36s
42. Without using mathematical tables evaluate #(sin60. tan30. cos 60 + sin 30. cos 45. sin45)/(sin90. cos45. sin45 - sin60. cos30. sin30)#
8m 59s
43. Omare uses one half of his farm for planting maize, one-fifth for tea, one-third of the remainder for mixed farming and the rest for grazing. If he uses 3.5 hectares for grazing, Calculate how many hectares he puts under maize.
2m 42s
44. A cylindrical container of diameter 35cm and height 20cm is two-fifths full of water. The container is filled using a smaller cylindrical can of diameter 7cm and height 10cm.Find the number of cans that must be drawn in order to fill the container.
2m 47s
45. A trader bought an article at sh 600 and marked it at a price such that after allowing his customer a 10% discount he would make a profit of 35%.Find the marked price of the article.
1m 47s
46. Factorize the expression #5x^2 + x -4# and hence solve the quadratic equation #5x^2 + x -4 = 0#
2m 7s
47. In order to complete building a house in 30 days, a contractor employs 18 men to work at the rate of 8 hours a day. Find how many more days it would take 12 men working at the rate of 10 hours a day to complete the house.
2m 19s
48. Without using mathematical tables or a calculator, Evaluate #(41.58 times 4.095)/(1.365 times 20.79)#
3m 40s

Form 4 Mathematics Paper 1 Solved Questions

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