- The displacement S metres of a body moving along a straight line after t seconds is given by(Solved)
The displacement S metres of a body moving along a straight line after t seconds is given by
(a) Find its initial acceleration.
(b) Calculate:-
(i) The time when the body was momentarily at rest.
(ii) Its displacement by the time it comes to rest momentarily
(c) Calculate the maximum velocity attained
Date posted: September 6, 2019. Answers (1)
- In the figure, E is the midpoint of AB and OD:OB = 2:5 and F is the point of intersection of OE and AD.(Solved)
In the figure, E is the midpoint of AB and OD:OB = 2:5 and F is the point of intersection of OE and AD.
(b) Given further that AF = tAD and OF = hOE where t and h are scalars, find the values of t and h
(c) Show that the points O, F and E are collinear
Date posted: September 6, 2019. Answers (1)
- The figure below shows a model of a solid in the shape of a frustum of a cone with a hemispherical top.(Solved)
The figure below shows a model of a solid in the shape of a frustum of a cone with a hemispherical top.
The diameter of the hemispherical top is 70cm and is equal to the diameter of the top of the frustum. The
frustum has a base diameter of 28cm and a slant height of 60cm.
(a) Calculate the area of the hemispherical surface.
(b) Calculate the slant height of the cone from which the frustum was cut.
(c) Calculate the total surface area of the model
Date posted: September 6, 2019. Answers (1)
- The diagram below shows two circles centre A and B which intersect at point P and Q. Angle PBQ = 400 and angle PAQ =...(Solved)
The diagram below shows two circles centre A and B which intersect at point P and Q. Angle PBQ = 400 and angle PAQ = 700, and PA = AQ = 8cm.
Use the diagram to calculate to two d.p
(a) The length PQ
(b) The length PB
(c) Area of minor segment of circle centre A
(d) Area of minor segment of circle centre B
(e) The area of shaded region.
Date posted: September 6, 2019. Answers (1)
- Three partners Mutua, Muthoka and Mwikali contributed Sh. 600,000, Sh. 400,000 and Sh. 800,000
respectively(Solved)
Three partners Mutua, Muthoka and Mwikali contributed Sh. 600,000, Sh. 400,000 and Sh. 800,000
respectively to start a business of a matatu plying Mbumbuni – Machakos route. The matatu carries 14
passengers with each paying Sh. 250. The matatu makes two round trips each day and ever full. Each day
Sh. 6000 is used to cover running costs and wages.
(a) Calculate their net profit per day.
(b) The matatu works for 25 days per month and is serviced every month at a cost of KSh.10, 000. Calculate their monthly profit in June.
(c) The three partners agreed to save 40% of the profit, 24% to be shared in the ratio of their contribution. Calculate Muthoka’s share in the month of July
(d) The matatu developed mechanical problems and they decided to sell it through an agent who charged a commission of 5% on selling price. Each partner received KSh. 475,000 from the agent after he had taken his commission. Determine the price at which the agent sold the matatu.
Date posted: September 6, 2019. Answers (1)
- In the figure below O is the centre of circle PQRS.(Solved)
In the figure below O is the centre of circle PQRS. angle PTS = 560 and angle PQS = 280 and TPQ is a straight line
Find:
(a) angle TSP
(b) angle PRQ
Date posted: September 6, 2019. Answers (1)
- Mutua bought 8 pairs of trousers and six shirts at Sh. 4160.(Solved)
Mutua bought 8 pairs of trousers and six shirts at Sh. 4160. Had he bought twice as many shirts and half
as many trousers, he would have saved Sh. 160. Find the cost of each item.
Date posted: September 6, 2019. Answers (1)
- Use a calculator to work out.(Solved)
Use a calculator to work out.
Date posted: September 6, 2019. Answers (1)
- The figure below AB//CD, AD and BC intersect at T.(Solved)
The figure below AB//CD, AD and BC intersect at T. Given that AT:TD = 1:3 and CB = 12cm.
Calculate the length of TB
Date posted: September 6, 2019. Answers (1)
- Solve for x in the equation(Solved)
Solve for x in the equation
Date posted: September 5, 2019. Answers (1)
- In the figure below PQRS is a rectangle in which PS = 10cm and PQ = 6cm(Solved)
In the figure below PQRS is a rectangle in which PS = 10cm and PQ = 6cm. M and N are midpoints of
QR and RS respectively. Find the area of the shaded part.
Date posted: September 5, 2019. Answers (1)
- Solve the following inequalities and represent the solution on a number line and hence state the integral
values of x(Solved)
Solve the following inequalities and represent the solution on a number line and hence state the integral
values of x
Date posted: September 5, 2019. Answers (1)
- A line L passes through point (3, 1) and is perpendicular to the line 2y = 4x + 5.(Solved)
A line L passes through point (3, 1) and is perpendicular to the line 2y = 4x + 5. Determine the equation
of L
Date posted: September 5, 2019. Answers (1)
- Evaluate:(Solved)
Evaluate:
Date posted: September 5, 2019. Answers (1)
- Without using a calculator evaluate(Solved)
Without using a calculator evaluate
Date posted: September 5, 2019. Answers (1)
- The displacement of a particle S metres, t seconds after passing a fixed point O is given by
S=3+2t-5t2(Solved)
The displacement of a particle S metres, t seconds after passing a fixed point O is given by
S=3+2t-5t2
Calculate:
(a) The displacement of the particle 2 seconds later
(b) The time taken for the particle to return to O
(c) The maximum displacement of the particle
(d) The initial velocity of the particle
(e) The acceleration of the particle after t seconds
Date posted: September 5, 2019. Answers (1)
- The figure below shows a prism whose cross section is a regular pentagon of side 6cm and whose length is 20cm(Solved)
The figure below shows a prism whose cross section is a regular pentagon of side 6cm and whose length is 20cm joined to a cylinder of radius 14cm and height 6cm to form a the model of a solid
(a) Calculate the cross section area of the pentagon
(b) Calculate the total volume of the solid
(c) The model represents a pillar of total height 5.2m, calculate the volume of the actual solid
in m3
Date posted: September 5, 2019. Answers (1)
- A matatu left Oyugis for Homabay town 51km away at an average speed of 48km/h at 7.00am.(Solved)
A matatu left Oyugis for Homabay town 51km away at an average speed of 48km/h at 7.00am. At 7.30am a Boda boda left Homabay for Oyugis travelling along the same route at an average speed of 60km/h
(a) The time when Boda boda meet the matatu
(b) How far from Oyugis did the Boda boda meet the matatu
(c) After meeting the Boda boda the matatu stopped for fifteen minutes before resuming the journey. At what speed should it travel then to reach Homabay at the same time when the Boda boda reached Oyugis
Date posted: September 5, 2019. Answers (1)
- The table shows the marks obtained by 40 candidates in an examination(Solved)
The table shows the marks obtained by 40 candidates in an examination
(a) Find the value of x
(b) On the grid provided below draw a histogram to represent the data
(c) By drawing a straight line on the graph above determine the median mark
Date posted: September 5, 2019. Answers (1)
- Four schools Wiobiero, Asumbi, Nyawita and Angiro are such that Wiobiero is 15km from Asumbi on a bearing of 158o(Solved)
Four schools Wiobiero, Asumbi, Nyawita and Angiro are such that Wiobiero is 15km from Asumbi on a bearing of 158o, Nyawita is to the west of Asumbi and 20km away while An’giro is to the South of Nyawita and on a bearing of 240o from Wiobiero.
(a) Using a scale of 1:400,000 draw a scale diagram showing the relative positions of the four schools.
(b) Using your diagram determine the distance and bearing of Ang’iro from Asumbi
(c) A mast is to be erected so that its equidistant from Asumbi and Nyawita and 20km from Ang’iro on the same diagram show the position of the mast and find its distance from Wiobiero
Date posted: September 5, 2019. Answers (1)