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- Two towns on latitude 30oS are 3000km apart. Find the longitude different of the two towns(Solved)
(a) Two towns on latitude 30oS are 3000km apart. Find the longitude different of the two towns
(Take 
and the radius of the earth to be 6370km)
(b) The positions of airport P and Q are (60oN,45oN) and Q(60oN,KoE). It takes a plane 5 hrs to travel due east from P to Q at an average speed of 600 knots
(i) Calculate the value of K
(ii) The local time at P is 10.45am, what is the local time at Q when the plane reaches where?
(c) Calculate the shortest distance between (30oS,36oE) and (30oS,144oW) in nautical miles
Date posted: November 8, 2019. Answers (1)
- The cash price of a camera is Sh.42,200. Joseph bought the camera on hire purchase (H.P) term by paying a deposit of Sh.7,200 and cleared...(Solved)
The cash price of a camera is Sh.42,200. Joseph bought the camera on hire purchase (H.P) term by paying a deposit of Sh.7,200 and cleared the balance in 24 equal monthly installments each of Sh.2,250
(a) Find the amount of interest paid under hire purchase plan
(b) Ken took a loan from a financial institution and bought the camera with cash. He repaid the loan in two years at 18% interest compound semi-annualy. Find the total interest paid by Ken
(c) The cash price is taken as the value of the Camera. If the camera depreciated at a rate of 15% in the first year after buying and at P% p.a for rest of the time, calculate the value of p if the value of the camera after 5 years was Sh.23,534
Date posted: November 8, 2019. Answers (1)
- (a) A sequence is formed by adding corresponding terms of an A.P and a G.P. The first, second and third terms of the sequence formed...(Solved)
(a) A sequence is formed by adding corresponding terms of an A.P and a G.P. The first, second and third terms of the sequence formed after adding the first three terms of the sequences are 14,34 and 78 respectively. Given that the first term of the A.P is a and the first term of the G.P is b, and that the common ratio of the G.P is 3; Find the first term of the AP and G.P and the common difference of the A.P
(b)The second and third terms of a geometric progression are 24 and 12(x+1) respectively. Given that the sum of the first three terms of the progression is 76, find the whole number value of x and hence the first term
Date posted: November 8, 2019. Answers (1)
- The points A1B1 and C1 are the images of A(4,1), B(0,-2) and C(-2,4)(Solved)
(a) The points A1B1 and C1 are the images of A(4,1), B(0,-2) and C(-2,4) respectively under transformation represented by the matrix M= 
write down the coordinates of A1B1C1
(b) A11B11C11 are the images of A1B1C1 under another transformation whose matrix is 
write down the coordinates of A11B11C11
(c) Transformation m followed by N can be represented by a single transformation P. Determine the
matrix for P
(d) Another transformation has the matrix T = 
Determine the matrix for transformation m followed by N and T in that order
Date posted: November 8, 2019. Answers (1)
- The diagram below shows a square based pyramid V vertices above the middle of the base. PQ=10cm and VR=13cm M is the midpoint of VR(Solved)
The diagram below shows a square based pyramid V vertices above the middle of the base. PQ=10cm and VR=13cm M is the midpoint of VR
Find
(a)(i) the length PR
(ii) the height of the pyramid
(b)(i) the angle between VR and the base PQRS
(ii) the angle between PM and the base PQRS
(iii) the angle between the planes QVR and PQRS
Date posted: November 8, 2019. Answers (1)
- Given that OA= -i +j, OB=3i+5j and OC= 11i+13j. Show that A, B and C are collinear.(Solved)
Given that OA= -i +j, OB=3i+5j and OC= 11i+13j. Show that A, B and C are collinear.
Date posted: November 8, 2019. Answers (1)
- Three towns X,Y and Z are such that Y is 50km South of X and Z is on a bearing of 300o from Y. Calculate...(Solved)
Three towns X,Y and Z are such that Y is 50km South of X and Z is on a bearing of 300o from Y. Calculate the angle XZY given that XZ is 70km.
Date posted: November 8, 2019. Answers (1)
- A transformation matrix maps an object of area 21cm2 to an image of area 42cm2. Determine the value of p.(Solved)
A transformation matrix 
maps an object of area 21cm2 to an image of area 42cm2. Determine the value of p.
Date posted: November 8, 2019. Answers (1)
- The points P and Q are 7.4cm apart. By construction locate the locus R such that PR=2.5cm and angle PRQ=90o.(Solved)
The points P and Q are 7.4cm apart. By construction locate the locus R such that PR=2.5cm and angle PRQ=90o.
Date posted: November 8, 2019. Answers (1)
- Find the radius and the coordinates of the centre of the circle whose equation is
2x2 + 2y2 – 3x +2y + 1/2 = 0(Solved)
Find the radius and the coordinates of the centre of the circle whose equation is
2x2 + 2y2 – 3x +2y + 1/2 = 0
Date posted: November 8, 2019. Answers (1)
- A bag contains 2 white balls and 3 black balls. A second bag contained 3 white balls and 2 black balls. The balls are identical...(Solved)
A bag contains 2 white balls and 3 black balls. A second bag contained 3 white balls and 2 black balls. The balls are identical except for the colours. Two balls are drawn at random, one after the other from the first bag and placed in the second bag. Calculate the probability that the two balls are both white.
Date posted: November 8, 2019. Answers (1)
- A circle whose equation is x2+y2+4x-10y+4=0 touches a straight line (-7,3). Find the equation of the line(Solved)
A circle whose equation is x2+y2+4x-10y+4=0 touches a straight line (-7,3). Find the equation of the line
Date posted: November 8, 2019. Answers (1)
- Find the value of x given that the matrix is a singular matrix.(Solved)
Find the value of x given that the matrix is a singular matrix.
Date posted: November 8, 2019. Answers (1)
- Solve for x in the equation.
2sin2x-1 = cos2 x + sin x, where OO = x = 360o.(Solved)
Solve for x in the equation.
2sin2x-1 = cos2 x + sin x, where OO ≤ x ≤ 360o.
Date posted: November 8, 2019. Answers (1)
- Find the values of a and b where a and b are irrational numbers(Solved)
If, 
,find the values of a and b where a and b are irrational numbers
Date posted: November 8, 2019. Answers (1)
- The dimensions of a rectangle are 40cm and 45cm. If there is an error of 5% in the length and 8% in the width. Find...(Solved)
The dimensions of a rectangle are 40cm and 45cm. If there is an error of 5% in the length and 8% in the width. Find the percentage error I calculating the area of the rectangle.
Date posted: November 8, 2019. Answers (1)
- Use logarithms correct to 4 decimal places to evaluate.(Solved)
Use logarithms correct to 4 decimal places to evaluate.
Date posted: November 8, 2019. Answers (1)
- Given that x=2i+j-2k, y=-3i+4j-k, and z=-5i+3j+2k and p=3x-y+2z, calculate the magnitude of p correct to 3 significant figures(Solved)
Given that x=2i+j-2k, y=-3i+4j-k, and z=-5i+3j+2k and p=3x-y+2z, calculate the magnitude of p correct to 3 significant figures
Date posted: November 8, 2019. Answers (1)
- a) Using the trapezium rule with seven ordinates estimate the area of the region bounded by the
curve y= - x2 + 6x +1, the line...(Solved)
a) Using the trapezium rule with seven ordinates estimate the area of the region bounded by the
curve y= - x2 + 6x +1, the line x=0,y=0 and x=6.
b) Calculate:
i) The area of the region in (a) above by integration.
ii) The percentage error of the estimated area to the actual area of the region, correct to 2d.p.
Date posted: November 8, 2019. Answers (1)
- In the diagram, below LX = SLN
ON = a OL = b, LX = SLN, OM = 3a and MK = 2b.
a) Calculate:
i) LN in...(Solved)
In the diagram, below LX = SLN
ON = a OL = b, LX = SLN, OM = 3a and MK = 2b.
a) Calculate:
i) LN in terms of a and b.
ii) OK in terms of a and b.
b) i) Show that OX = sa + (1 - s) b where s is a scalar.
ii) Given also that OX = r OK, find the value of r and s.
iii) Determine the ratio OX: XK.
Date posted: November 8, 2019. Answers (1)