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- Without using a calculator evaluate.(Solved)
Without using a calculator evaluate.
Date posted: November 13, 2019. Answers (1)
- The table below shows the income tax ratesJuma is a salaried employee who is given an automatic house allowance of sh. 8000 monthly. He also gets...(Solved)
The table below shows the income tax rates
Juma is a salaried employee who is given an automatic house allowance of sh. 8000 monthly. He also gets a single relief of Ksh1320. If his P.A.Y.E is Ksh 5420 a month,
(a) Find his total tax in shillings per annum
(b) How much does he earn per month?
Date posted: November 12, 2019. Answers (1)
- The table below gives the marks obtained in a mathematics test by 47 students.
(a) State the modal class
(b) Draw a cumulative frequency curve to...(Solved)
The table below gives the marks obtained in a mathematics test by 47 students.
(a) State the modal class
(b) Draw a cumulative frequency curve to represent the above data.
(c) Use your graph to estimate
(i) Median
(ii) Lower quartile
(iii) Upper quartile
(d) Calculate the quartile deviation
Date posted: November 12, 2019. Answers (1)
- (a) Using trapezoidal rule estimate the area bounded by the curve y=3x2 - 2 and the lines x=-4 ,x=4 and x-axis.
(b) find the actual area...(Solved)
(a) Using trapezoidal rule estimate the area bounded by the curve y=3x2 − 2 and the lines x=−4 ,x=4 and x−axis.
(b) find the actual area bounded by the curve y=3x2 − 2 and the lines x=−4 ,x=4 and x−axis.
(c) Calculate the percentage error when trapezoidal rule is used.
Date posted: November 12, 2019. Answers (1)
- The probability that a boy goes to school by bus is 1/3 and by matatu is ½. If he uses a bus the probability that...(Solved)
The probability that a boy goes to school by bus is 1/3 and by matatu is ½. If he uses a bus the probability that he is late to school is 1/5 and if he uses a matatu the probability of being late is 3/10. If he uses other means of transport, the probability of being late is 1/20. What is he probability that;
(a) He will be late to school
(b) He will not be late to school
(c) He will be late to school if he does not use a matatu
(d) He neither uses a bus nor matatu but arrives to school early.
Date posted: November 12, 2019. Answers (1)
- The first term of A.P is 3.5, the common difference is d if the difference of 20th and 6th terms is 40.
(a) (i)find the common...(Solved)
The first term of A.P is 3.5, the common difference is d if the difference of 20th and 6th terms is 40.
(a) (i)find the common difference, d
(ii) calculate the sum of the first 40 terms of the AP
(b) The progression is such that the 2nd , 14th and 85th terms of the AP forms the first 3 terms of a G.P. If the common difference of A.P is 2.5
Find
(i) 2nd term of the G.P
(ii) Sum of the two 10 terms of G.P
Date posted: November 12, 2019. Answers (1)
- 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)