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- An aeroplane that moves at a constant speed of 600 knots flies from town A (140N, 300W) southwards to town B (X0S, 300W) taking 3...(Solved)
An aeroplane that moves at a constant speed of 600 knots flies from town A (140N, 300W) southwards to town B (X0S, 300W) taking 3 1/2 hrs. It then changes direction and flies along latitude to town C (X0S, 600E). Given π = 3.142 and radius of the earth R= 6370 km
(a) Calculate
(i) The value of X
(ii) The distance between town B and town C along the parallel of latitude in km.
(b) D is an airport situated at (50N, 1200W), calculate
(i) The time the aeroplane would take to fly from C to D following a great circle through the South Pole.
(ii) The local time at D when the local time at A is 12.20 pm
Date posted: November 12, 2019. Answers (1)
- Two circles centres A and B have radii 2.5cm and 1.5cm respectively. The distance between A and B is 7cm.
(a) Draw the required circles and...(Solved)
Two circles centres A and B have radii 2.5cm and 1.5cm respectively. The distance between A and B is 7cm.
(a) Draw the required circles and construct the direct common tangents to the two circles.
(b) Measure the length of the tangent
Date posted: November 12, 2019. Answers (1)
- The figure below shows a frustum of a square based pyramid (not drawn to scale). The base ABCD is a square of sides 10cm. The...(Solved)
The figure below shows a frustum of a square based pyramid (not drawn to scale). The base ABCD is a square of sides 10cm. The top A’B’C’D’ is a square of side 4 cm and each slant edges of the frustum is 5cm long. Calculate the angle between AC’ and the line AC.
Date posted: November 12, 2019. Answers (1)
- Draw a line DF = 4.6cm.Construct the locus of point K above DF such that angle DKF = 700.(Solved)
Draw a line DF = 4.6cm.Construct the locus of point K above DF such that angle DKF = 700.
Date posted: November 12, 2019. Answers (1)
- Triangle ABC has vertices A(1,0), B(4,0) and C(1,4) is mapped onto A’B’C’ under a shear matrix, x axis invariant and C(1,4) is mapped onto C’(7,4)....(Solved)
Triangle ABC has vertices A(1,0), B(4,0) and C(1,4) is mapped onto A’B’C’ under a shear matrix, x axis invariant and C(1,4) is mapped onto C’(7,4). Find the shear matrix hence find the coordinates of the image of P(2,-3) and Q(-2,-3).
Date posted: November 12, 2019. Answers (1)
- Calculate all the values of x between -180° and +180° which satisfy the equation 6 cos (x - 30)° = -3.(Solved)
Calculate all the values of x between -180° and +180° which satisfy the equation 6 cos (x − 30)° = −3.
Date posted: November 12, 2019. Answers (1)
- The cost of a matatu was sh. 950 000.It depreciated in value by 5% per year for the first 2 years and 15% per for...(Solved)
The cost of a matatu was sh. 950 000.It depreciated in value by 5% per year for the first 2 years and 15% per for the subsequent years. Calculate the value of the matatu after 5 years.
Date posted: November 12, 2019. Answers (1)
- Given that P varies directly as V and inversely as the cube root of R and that P = 12 when V = 3 and...(Solved)
Given that P varies directly as V and inversely as the cube root of R and that P = 12 when V = 3 and R = 2,
(i) Find an equation connecting P, V and R.
(ii) Find the percentage change in P if V is increased by 12% and R decreased by 36%
Date posted: November 12, 2019. Answers (1)
- The radius and height of a cylindrical Kentank rounded to 1 cm are 105 cm and 300 cm respectively.
Calculate the percentage error in its volume.(Solved)
The radius and height of a cylindrical Kentank rounded to 1 cm are 105 cm and 300 cm respectively.
Calculate the percentage error in its volume.
Date posted: November 12, 2019. Answers (1)
- Given that and that a and b are rational numbers, find the values of a and b.(Solved)
Given that 
and that a and b are rational numbers, find the values of a and b.
Date posted: November 12, 2019. Answers (1)
- Use the method of completing the square to solve
4 - 9x - 3x2 = 0(Solved)
Use the method of completing the square to solve
4 − 9x − 3x2 = 0
Date posted: November 12, 2019. Answers (1)
- Solve for x in log3 = log5 0.5.(Solved)
Solve for x in log3 
= log5 0.5.
Date posted: November 12, 2019. Answers (1)
- (a) Expand and simplify (x - 1/2x)6 up to the term in x3 and state the constant term.
(b) Use this expansion to calculate to...(Solved)
(a) Expand and simplify (x − 1/2x)6 up to the term in x3 and state the constant term.
(b) Use this expansion to calculate to 4 d.p the value of (0.96)6.
Date posted: November 12, 2019. Answers (1)
- Make h the subject of the formula.(Solved)
Make h the subject of the formula.
Date posted: November 12, 2019. Answers (1)
- In this question, show all the steps in your calculations, giving the answer at each stage. Use logarithms correct to decimal places, to evaluate.
(Solved)
In this question, show all the steps in your calculations, giving the answer at each stage. Use logarithms correct to decimal places, to evaluate.
Date posted: November 12, 2019. Answers (1)
- The speed of projectile v m/s at a given time t is given by v=10(10t-t2)(Solved)
The speed of projectile v m/s at a given time t is given by v=10(10t-t2) calculate
a. The time when the velocity is maximum
b. The maximum velocity attained
c. The distance traveled by the body in the first 6 seconds
d. The acceleration of the projectile at t=6.5sec
Date posted: November 12, 2019. Answers (1)
- (a) Complete the table below for the function y = 2x2 + 3x – 5.(b) On the grid provided draw the graph of y =...(Solved)
(a) Complete the table below for the function y = 2x2 + 3x – 5.
(b) On the grid provided draw the graph of y = 2x2 + 3x – 5 for -4 = x = 2
(c) Use your graph to state the roots of
(i) 2x2 + 3x – 5 = 0
(ii) 2x2 + 6x – 2 = 0
Date posted: November 12, 2019. Answers (1)
- Four towns A, B, C and D are such that B is 84km direct to the north of A and C is on a bearing...(Solved)
Four towns A, B, C and D are such that B is 84km direct to the north of A and C is on a bearing of N 65oW from A at a distance of 60km. D is on a bearing of 340o from C at a distance of 30km. Using a scale of 1 cm rep 10km
a) Make an accurate scale drawing showing the relative positions of the towns
b) Find the distance and bearing of B from C
c) Find the distance and bearing of D from B
d) Find the bearing of A from D
Date posted: November 12, 2019. Answers (1)
- The figure above shows two circles ABPQ and ABSR intersecting at A and B. QART, PBS and ABU are straight lines. The line TSU is...(Solved)
The figure above shows two circles ABPQ and ABSR intersecting at A and B. QART, PBS and ABU are straight lines. The line TSU is a tangent to the circle ABSR at S. Given that ˂BPQ = 80o, ˂PBU = 115o and ˂BUS = 70o.
Find & state reasons for the following angles
a) ˂BRS
b) ˂BSU
c) ˂STR
d) ˂BAR
e) ˂ARB
Date posted: November 12, 2019. Answers (1)
- (a). The price of an article is marked as sh.12,000. Mr. Mulmulwas sold the article at a discount of 10% and still made a profit...(Solved)
(a). The price of an article is marked as sh.12,000. Mr. Mulmulwas sold the article at a discount of 10% and still made a profit of 5%. Calculate the cost of the article.
(b). Mr. Mulmulwas made a loss of 30% by selling an electric kettle at sh.700. What profit would he have made if she had sold it at sh.1150?
(c). Mr. Mulmulwas is a real estate agent who is entitled to a commission on all properties bought through him. During a certain month he sold 2 mansions at sh. 2.54 million each, 4 flats at sh. 582,000 each and 5 bungalows at sh.354,000 each and he was paid a total commission of sh.458,900. Calculate the percentage rate of commission he was paid.
Date posted: November 12, 2019. Answers (1)