- (a) An arithmetic progression is such that the first term is -5, the last is 135 and the sum of progression is...(Solved)
(a) An arithmetic progression is such that the first term is -5, the last is 135 and the sum of progression is 975. Calculate
(i) The number of terms in the series.
(ii) The common difference of the progression.
(b)The sum of the first three terms of a geometric progression is 27 and first term is 36.
Determine the common ratio and the value of the fourth term.
Date posted: September 17, 2019. Answers (1)
- The figure below shows a right pyramid VABCD with a square base of side 6 cm. VA = VB = VC = VD =...(Solved)
The figure below shows a right pyramid VABCD with a square base of side 6 cm. VA = VB = VC = VD = 12 cm
Calculate;
(i) The height of the pyramid correct to 2 d.p
(ii) The angle between the planes VAD and VBC correct to 2 significant figures.
Date posted: September 17, 2019. Answers (1)
- The taxation rate, for 2007 were as in the table below. In certain month in 2007, Mutai paid a tax of Ksh. 3000...(Solved)
The taxation rate, for 2007 were as in the table below.
In certain month in 2007, Mutai paid a tax of Ksh. 3000 after having been given a personal relief of Ksh. 1056 per month.
(a)How much tax per month could he have paid if he did not get tax relief.
(b)Calculate the his total taxable income in Ksh. P.m.
(c)Given that his total taxable allowance amount to Ksh. 4520 P.m. Calculate his monthly basic
salary in Kenya shillings.
Date posted: September 17, 2019. Answers (1)
- The graph below is part of the straight line graph obtained from the initial equation y = axn use the graph to calculate...(Solved)
The graph below is part of the straight line graph obtained from the initial equation y = axn use the graph to calculate the value of a and n,
Date posted: September 17, 2019. Answers (1)
- The area of a triangle where height is 4.4cm measured to the nearest millimeter is 13.2cm2. Determine the maximum possible length of the base of...(Solved)
The area of a triangle where height is 4.4cm measured to the nearest millimeter is 13.2cm2. Determine the maximum possible length of the base of the triangle to 4 s.f.
Date posted: September 17, 2019. Answers (1)
- The figure below shows a circle with secants ABE and CDE, if AB = 4cm and BE = 6cm and DE =...(Solved)
The figure below shows a circle with secants ABE and CDE, if AB = 4cm and BE = 6cm and DE = 4cm. find the length of CD.
Date posted: September 17, 2019. Answers (1)
- Find the value of X in the equation ( log3X)2 + 3 log 3X = 4(Solved)
Find the value of X in the equation ( log3X)2 + 3 log 3X = 4
Date posted: September 17, 2019. Answers (1)
- Nairobi and Kisumu lie on the same longitude. The latitude of Nairobi is 1o12’s and that of Kisumu is 5o50’N. Calculate the distance between them...(Solved)
Nairobi and Kisumu lie on the same longitude. The latitude of Nairobi is 1o12’s and that of Kisumu is
5o50’N. Calculate the distance between them in nautical miles
Date posted: September 17, 2019. Answers (1)
- Find the distance between the centre A of a circle whose equation is 2x2 + 2y2 + 6x + 10y + 7 = 0 ...(Solved)
Find the distance between the centre A of a circle whose equation is 2x2 + 2y2 + 6x + 10y + 7 = 0 and the point B ( -4 ,1).
Date posted: September 17, 2019. Answers (1)
- There are three athletes A,B, C in a 100m race. A is twice as likely to win as B, while B is twice as...(Solved)
There are three athletes A,B, C in a 100m race. A is twice as likely to win as B, while B is twice as likely to win as C. Find the probability that A does not win the 100m race.
Date posted: September 17, 2019. Answers (1)
- Taps A and B can fill a tank in 4 and 9 hours respectively. Both taps are turned on for 2 hours after which ...(Solved)
Taps A and B can fill a tank in 4 and 9 hours respectively. Both taps are turned on for 2 hours after which tap A is closed. Find how long tap B takes to fill the remaining part of the tank
Date posted: September 17, 2019. Answers (1)
- In the figure below, A triangle A1B1C1 is the image of triangle ABC under a rotation centre O.
By constructor, find and label centre...(Solved)
In the figure below, A triangle A1B1C1 is the image of triangle ABC under a rotation centre O.
By constructor, find and label centre O. Hence determine the angle of rotation.
Date posted: September 17, 2019. Answers (1)
- If (x + 3) ( x + 4) is equivalent to ( x + a)2+b. Find the values of a and...(Solved)
If (x + 3) ( x + 4) is equivalent to ( x + a)2+b. Find the values of a and b.
Date posted: September 17, 2019. Answers (1)
- Two variables P and Q are such that P varies partly as Q and partly as the square root of Q. Determine
the...(Solved)
Two variables P and Q are such that P varies partly as Q and partly as the square root of Q. Determine
the equation connecting P and Q when Q = 16, P = 500 and when Q = 25, P = 800.
Date posted: September 17, 2019. Answers (1)
- The figure below represent a solid frustum. The faces ABCD and EFGH are parallel squares of sides 10cm and 6 cm respectively. Each...(Solved)
The figure below represent a solid frustum. The faces ABCD and EFGH are parallel squares of sides 10cm and 6 cm respectively. Each of the slanting edges AE, BF, CG and DH are equal to 4cm.
Determine:
a)The length of the projection of AE on the plane ABCD
b)The angle between the line AE and the plane ABCD
c)The angle between the plane BCGF and ABCD
Date posted: September 17, 2019. Answers (1)
- A bag contains blue, green and red pens of the same type in the ratio 8:2:5 respectively. A pen is picked at random without...(Solved)
A bag contains blue, green and red pens of the same type in the ratio 8:2:5 respectively. A pen is picked at random without replacement and its colour noted.
a)Determine the probability that the first pen picked is
i)Blue
ii)Either green or red.
b)Using a tree diagram, determine the probability that
i)The first two pens picked are both green
ii)Only one of the first pens picked is red.
Date posted: September 17, 2019. Answers (1)
- Lengths of 100 mango leaves from a certain mango tree were measured to the nearest centimeter and recorded as per the table below,
a) draw a...(Solved)
Lengths of 100 mango leaves from a certain mango tree were measured to the nearest centimeter and recorded as per the table below,
a) draw a cumulative frequency graph to represent this data.
b)Use your graph to estimate
i)The median length of the leaves
ii)The number of leaves whose lengths lie between 13cm and 17cm.
Date posted: September 17, 2019. Answers (1)
- A globe representing the earth has a radius of 0.5m. point A(00, 100W), B (00, 350E), P(600N, 1100E) and Q(600N, 1200W) are marked on...(Solved)
A globe representing the earth has a radius of 0.5m. point A(00, 100W), B (00, 350E), P(600N, 1100E) and Q(600N, 1200W) are marked on the globe.
a)Find the length of arc AB, leaving your answer in term of π
b)If O is the centre of the latitude 600N, find the area of the minor sector OPQ
c)Of the local time at Q is 10.30 a.m. on Monday, Determine the local time and day at P.
Date posted: September 17, 2019. Answers (1)
- The table below shows the current taxation rates in Kenya
A member of parliament’s monthly earnings are as follows: Basic salary Kshs. 300 000, commuted mileage...(Solved)
The table below shows the current taxation rates in Kenya
A member of parliament’s monthly earnings are as follows: Basic salary Kshs. 300 000, commuted mileage allowance of Kshs. 75 000, entertain allowance Ksh. 60 000, extraneous allowance Ksh. 30 000, house allowance Kshs. 70,000, car maintaince allowance Kshs 247 000. he is entitled to a personal relief of Kshs. 1162 every month.
a)If before the promulgation of the new constitution all the MP’s allowances were tax free, calculate the PAYE the MP’s used to pay
b)In the new constitution all the MP’s are taxed just like the other Kenyans. Calculate the percentage increase in the MP’s PAYE after the new law was passed.
Date posted: September 17, 2019. Answers (1)
- The line PQ is 6cm long. On one side of the line,
a)Draw the locus of T such that the area of triangle PTQ =...(Solved)
The line PQ is 6cm long. On one side of the line,
a)Draw the locus of T such that the area of triangle PTQ = 12cm2
b)Determine two points on the locus obtained in part a) above such that angle PTQ = 700 and
label them as T1 and T2.
Date posted: September 17, 2019. Answers (1)