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Form 4 Mathematics Paper 2 Topical Questions and Answers

Lessons (48)

1. The probability that three girls Fatuma, Jane and Adede will pass this year’s exam is #2/3 ,2/5 and 3/4 #respectively. Using a tree diagram, determine the probability that a).All three will fail b).All three will pass c).Only two will pass
11m 11s
2. Five bags of coffee and three bags of tea have a total mass of 716 kg. Three bags of coffee and five bags of tea weigh 216 kg less. Determine the total mass of one bag of coffee and seven bags of tea.
6m 35s
3. The seventh and eighth terms of an AP are 42 and 45 respectively. Find the sum of the third and fifth terms of the AP.
3m 52s
4. Given that log x = m,log y = n and log z = p,express in terms of m,n and p. #Log((x^(2 ) y^4)/(sqrtz)^3 )#
3m 3s
5. Solve the following quadratic equation using the completing square method. #5x^2 – 19x +12#
5m 11s
6. The price of two grades of tea T1 and T2 ,is sh 180 and sh 120 per kg respectively. Kiprono mixed T1 and T2 in a ratio such that by selling the mixture at sh 175 per kg, he made a profit of 25%. Determine the ratio T1 :T2 in the mixture.
6m 12s
7. Solve the following simultaneous equations #x^2 -xy =2# x+y = 3
3m 46s
8. The volume V of a cylinder varies jointly with its height h and the square of its radius r. Determine the percentage increase in the volume of the cylinder if its radius increases in the ratio 3:2 and its height decreases by 30%.
5m 19s
9. Given that vectors a = #((1),(-2),(3)),b =((-2),(3),(-1)) and c = ((-3),(-1),(-4))# and that p = 2a – b + c,find to one decimal place the length of vector p.
4m 0s
10. Two towns R and S are situated on a river bank 64 km apart. A boat can travel at a speed of 36km/h in still water. The boat travelled from town R downstream to town S and back to town R in 3 hours 36 minutes. Determine the speed of the river current.
9m 51s
11. A tea broker bought Kenyan tea at sh 150 per kg,Ugandan tea at sh 120 per kg and Zairean tea at sh 82.50 per kg. He mixed them in the ratio 2:3:4 by mass to make a blend which he sold at a profit of 50%.Determine the price at which he sold one kg of the blend.
3m 51s
12. Given that 2n, 3n and 4n +2 are consecutive of a geometric progression determine a).the common ratio b).the value of n
2m 51s
13. Given that #3x^2 -11x +m# is a perfect square, find the value of m.
2m 35s
14. The cash price for an article is sh 15000.The article can be bought by hire purchase which requires the customer to pay one-third of the HP value as deposit followed by equal monthly instalments of sh 1625 each.The HP value is 30% more than the cash price how many instalments will be required.
3m 31s
15. The equation of a circle is #x^2 + y^2 -4x + 8y -29 =0#. Find the coordinates of the centre of the circle and its radius.
3m 41s
16. Without using a calculator or mathematical tables, evaluate #5log_10 2 - 1/2 log_10 16 + 3 log_10 5#
1m 53s
17. Solve the equation #a/(a+3) - 2/(a-3) = 1#
2m 24s
18. The velocity V metres per second of a particle in motion is given by #V = 4t^2 -2t +7# Where t is time in seconds. Determine the total distance moved by the particle between the second and third seconds of its motion.
5m 54s
19. Three quantities F,L and Q are connected by the equation F=L +Q. The quantity L varies as r and Q varies as the square of r. Given that F =54 when r = 3 and F =140 when r =5,find the value of F when r = 6.
5m 24s
20. Make D the subject of the formula #T = k/(2f)(s^2- D^2 )#
1m 54s
21. Simplify the following surd by writing in the form #a +sqrtb#. #1/(4- sqrt15)#
1m 37s
22. Solve the following quadratic equation by completing the square #5x^2 -11x -12 =0#
4m 32s
23. Three quantities X, Y and Z are such that X varies jointly with Y and the square of Z. Given that X =160 when Y =10 and Z = 2, Find a).The equation connecting X,Y and Z. b).The value of X when Y=6 and Z= 3
3m 24s
24. The velocity V metres per second of a moving object is given by #V = 4t^3 -3t^2 +10t -3# Where t is time in seconds after the object passes a fixed point O. Determine the total distance moved by the object in the first 2 seconds.
3m 44s
25. The expression #25x^2 -80x + k# is a perfect square. Find the value of k.
2m 57s
26. Make d the subject of the formula #P =sqrt((d^(2 )+x)/(d^2 x))#
2m 4s
27. The present value of a matatu is sh 764 500.For the last 4 years the value has been depreciating at a uniform rate of 4% per annum. Calculate to the nearest one thousand shillings, the value of the matatu at the start of the 4 year period.
8m 12s
28. The equation of a curve is #y =2x^2 + 4x +5#. Determine the coordinates of the turning point of the curve
2m 46s
29. The matrix #T = ((k-3,4),(k,k+2))# has no inverse. a).Find two possible values of k b).Write down two possible matrices for T.
4m 33s
30. The sum of the first n terms of the series 3.5 +10.5 +17.5 +24.5+.. is 224.Find the value of n.
2m 52s
31. Use the matrix method to solve the simultaneous equations 6a -2b =16 4a – 3b = 14
6m 53s
32. The position vectors of C is #((-1),(3),(-2))# and vector CD is #((4),(-5),(-2))#.Determine the coordinates of D.
2m 4s
33. The vectors x =#((-2),(4),(-8))#,y =# ((1),(-2),(1))# and z = #((6),(-3),(3))# are such that #p = 1/2 x +y -2/3 z# a).Express p as the column vector. b).Hence calculate /p/ to 2 decimal places.
4m 14s
34. The equation of a circle is #x^2 -4x +y^2 +6y = 3#. Determine the centre and the radius of the circle.
3m 31s
35. A transformation is represented by the matrix T =#((2,1),(-1,3))# A triangle ABC whose area is #13.5cm^2# is mapped onto triangle A’B’C’ by transformation T. What is the area of triangle A’B’C’?.
2m 46s
36. Find the value of x which satisfy the equation #(2x-1)/6 =(x+1)/(3x)#
3m 13s
37. Two bags A and B each contain a mixture of red balls and green balls. Bag A contains red balls and green balls in the ratio 8:7.Bag B contains a total of 18 balls out of which 6 are green. A student picked a bag at random and from it picked a ball at random. What is the probability that the ball picked was red.
4m 13s
38. Without using a calculator or mathematical tables, evaluate the expression. #4log_10 5 -1/2 log_10 16 + 6log_10 2#
3m 20s
39. Two grades of coffee A and R cost sh 200 per kg and sh 120 per kg respectively. Wangare mixed the two grades and sold the mixture at sh 195 per kg.If in so doing she made a profit of 30%,find the ratio in which she mixed them.
5m 4s
40. Given the matrices A =#((2,1),(3,-4))# and B = #((p,q),(q-1,-q))# and C =#((4,5),(-5,13))# are such that AB = C.Find the values of p and q.
5m 45s
41. Two quantities E and x are such that E partly varies as x and partly varies as the square root of x. When x=4,E =50 and when x = 9,E =105.Determine a).the equation which relates E and x b).The value of E when x = 16.
5m 43s
42. The curve which passes through the point (0, 8) has a gradient function #dy/dx = 2x -6# Find the equation of the curve and hence determine the coordinates of its turning point.
3m 55s
43. Sorghum costs sh 90 per kg and millet sh 40 per kg. A trader mixed sorghum and millet and sold the mixture at sh 84 per kg.If in so doing he made a profit of 40%,find the ratio in which he mixed them.
4m 17s
44. Given the matrices P = #((3,x),(-2,x))# Q = #((y,2),(-3,1))# ,R =#((-3,8),(-8,-2))# and that PQ = R, Find the values of x and y.
3m 59s
45. Given that #(sqrt6)/(2-sqrt3) = hsqrt6 + ksqrt2#,Find the values of the rational numbers h and k.
2m 54s
46. The position vector of B is 4i +j -3k and vector AB= 6i -3j +2k.Express the position vector of A in terms of i,j and k and hence state the coordinates of A.
3m 5s
47. The acceleration a m/#s^2# of a moving particle is given by a = 2t -3 where t is time seconds. Determine a).An expression for the velocity V m/s of the particle given that the initial velocity is 5m/s. b).The total distance moved by the particle in the first 3 seconds of motion.
5m 13s
48. Given the equation below express in fraction form sin x #6cos^2x –sin x -4=0#
5m 31s

Form 4 Mathematics Paper 2 Topical Questions and Answers

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