- A passenger train travelling at 25km/hr is moving in the same direction as the truck travelling at 30km/hr.(Solved)
A passenger train travelling at 25km/hr is moving in the same direction as the truck travelling at 30km/hr. the railway line runs parallel to the road and the track takes 1 ½ to overtake the train completely
(a) Given that the truck is 5 metres long determine the length of the train in metres
(b) The track and the train continue moving parallel to each other at the original speeds. Calculate the distance between them after 4 minutes and 4 seconds after the track overtake the train
(c) The track stopped 45 minutes after overtaking the train. How long did the train take to catch up with the truck
Date posted: September 4, 2019. Answers (1)
- Four towns A,B,C and D are such that B is on a bearing of 247o and 6km from A.(Solved)
Four towns A,B,C and D are such that B is on a bearing of 247o and 6km from A. C is due SSE and 4.8km from B. D is to the south of A and the bearing of C from D is S44oW
(a) Make a scale drawing showing the relative positions of A,B,C and D using the scale 1cm represents 1km
(b) Use your drawing to determine
(i) The bearing of A from C
(ii) The distance between C and D
(iii) How far D is east of B
(c) The average speed of a cyclist from C to A if he takes 30 minuets between A and D and 20 minutes between D and A
Date posted: September 4, 2019. Answers (1)
- A cold water tap can fill a bath in 3 minutes while a hot tap can fill in 5 minutes.(Solved)
A cold water tap can fill a bath in 3 minutes while a hot tap can fill in 5 minutes. The drain pipe can empty the bath in 3 ¾ minutes. The two taps and the drain pipe are fully open for 2 minutes, after which the drain pipe is closed.
(a) What fraction of the bath is filled after the first two minutes
(b) How many seconds are required for the bath to be completely filled?
(c) Given that the cold water tap delivers water at the rate of 200cm3/s
Determine
I. The capacity of the bath in litres
II. The rate of flow of the hot water tap
Date posted: September 4, 2019. Answers (1)
- Given that OA= i + 2j and OB= 2i-3j.(Solved)
Given that OA= i + 2j and OB= 2i-3j. Find the magnitude of AB to three significant figures
Date posted: September 4, 2019. Answers (1)
- Three years ago, James was three times as old as his Peter.(Solved)
Three years ago, James was three times as old as his Peter. In five years time, the sum of their ages will be 76. Determine their present ages
Date posted: September 4, 2019. Answers (1)
- In the figure below, AB is parallel to DE, DE bisects angle BDG, angle DCF=60o angle CFG=110o(Solved)
In the figure below, AB is parallel to DE, DE bisects angle BDG, angle DCF=60o angle CFG=110o
Find
(a) angle CDF
(b) angle ABD
Give reasons for your answers
Date posted: September 4, 2019. Answers (1)
- Find the range values that satisfy the inequality (Solved)
Find the range values that satisfy the inequality
Date posted: September 4, 2019. Answers (1)
- A contractor was to finish a piece of work in 80 days. He employed 150 workers to work for 6 hours a day.(Solved)
A contractor was to finish a piece of work in 80 days. He employed 150 workers to work for 6 hours a day. After 30 days he found out that only a quarter of the work had been done. How many more workers did he require to finish the work in time
Date posted: September 4, 2019. Answers (1)
- Without using a calculator or mathematical tables find the value of(Solved)
Without using a calculator or mathematical tables find the value of
Date posted: September 4, 2019. Answers (1)
- The resistance to the motion of a car is partly constant and partly varies as the square of the speed.(Solved)
The resistance to the motion of a car is partly constant and partly varies as the square of the speed. At
40km/h-1 the resistance and at 60kmh-1 it is 730N. What will be the resistance at 70kmh-1?
Date posted: September 4, 2019. Answers (1)
- Solve for x and y in the simultaneous equations given below (Solved)
Solve for x and y in the simultaneous equations given below
21x-12y=-29
12x+5y=19
Date posted: September 4, 2019. Answers (1)
- In the figure below PS=PR PS=13 cm, RS=10 cm and angle QSR=30o. (Solved)
In the figure below PS=PR PS=13cm, RS=10cm and angle QSR=30o. Find the length of QS
Date posted: September 4, 2019. Answers (1)
- Factorise 90x2-40y2(Solved)
Factorise 90x2-40y2
Date posted: September 4, 2019. Answers (1)
- A line Ax +3y-6=0 is perpendicular to the line 5x+7y-k=0.(Solved)
A line Ax +3y-6=0 is perpendicular to the line 5x+7y-k=0. If 5x+7y-k=0 passes through the point (4,3). Determine the values of A and K
Date posted: September 4, 2019. Answers (1)
- The radius of a cone is given as 4.2cm while its height is given as 9.7cm.(Solved)
The radius of a cone is given as 4.2cm while its height is given as 9.7cm. Find the percentage error in
the estimation of the volume of the cone
Date posted: September 4, 2019. Answers (1)
- Evaluate using logarithm
(Solved)
Evaluate using logarithm
Date posted: September 4, 2019. Answers (1)
- Two circles of radii 3.5cm and 4.2cm with centres O1 and O1 respectively intersect at points A and B as shown in the figure below.(Solved)
Two circles of radii 3.5cm and 4.2cm with centres O1 and O2 respectively intersect at points A and B as shown in the figure below. The distance of the centres is 6cm.
Calculate
(a) angle AO1B to the nearest degree
(b) angle AO2B to the nearest degree
(c) Area of the quadrilateral O1AO2B, correct to 2 decimal places.
(d) The shaded area correct to two significant figures.(Take π =22/7)
Date posted: September 3, 2019. Answers (1)
- On a squared paper draw the graph of y=(1-2x)(x+4) for the range -6(Solved)
(a) On a squared paper draw the graph of y=(1-2x)(x+4) for the range -6
(b) On the same grid draw the line y=2-3x.
(c) Use your graphs to solve the equations
(i) (1-2x)(x+4)=-5
(ii) 2-4x-2x2=0
Date posted: September 3, 2019. Answers (1)
- The diagram below shows a frustrum made by cutting of a small cone on a plane parallel to the base of
the original cone. (Solved)
The diagram below shows a frustrum made by cutting of a small cone on a plane parallel to the base of
the original cone. The frustrum represents a bucket with the open-end diameter of 28cm and the bottom diameter of 21cm. The bucket is 20cm deep. Calculate to 1 decimal place, the capacity of the bucket in litres.
Date posted: September 3, 2019. Answers (1)
- The figure below shows a metal solid consisting of a right cone mounted onto a hemisphere.(Solved)
(a)The figure below shows a metal solid consisting of a right cone mounted onto a hemisphere. The height h of the cone is twice the radius r. if the volume of the solid is 36cm3, find the radius of the hemisphere.
(b) The solid is totally immersed in water contained in a cylindrical tin of radius 9cm. through what height does the water level in the tin rise.
(c) The solid is melted and recast into a right pyramid of vertical height 4.2cm. Find the base area of the pyramid.
(d) If the solid is of mass 14.4g. Find its density in kg/m3.
Date posted: September 3, 2019. Answers (1)