- (a) A rectangular tank of base 2.4m by 2.8m and a height of 3m contains 3600 litres of water initially.Water flows into the tank at...(Solved)
(a) A rectangular tank of base 2.4m by 2.8m and a height of 3m contains 3600 litres of water initially.Water flows into the tank at the rate of 0.5 litres per second. Calculate:
(i) The amount needed to fill the tank
(ii) The time in hours and minutes required to fill
(b) Pipe A can fill an empty tank in 3 hours while pipe B can fill the same tank in 6 hours. When the
tank is full, it can be emptied by pipe C in 8 hours. Pipes A and B are opened at the same time when the tank is
empty. If one hour later pipe C is also opened, find the total time taken to fill the tank.
Date posted: April 26, 2019. Answers (1)
- Three warships A, B and C are at sea such that ship B is 500km on a bearing N300E from ship A. Ship C is...(Solved)
Three warships A, B and C are at sea such that ship B is 500km on a bearing N300E from ship A. Ship C is 700km from
ship B on a bearing of 1200. An enemy ship D is sighted 800km due south of ship B.
(a) Taking a scale of 1cm to represent 100km, locate the positions of ships A,B, C and D. (4 Marks)
(b) Find the bearing of:
(i) Ship A from D
(ii) Ship D from C
(c) Use scale drawing to determine the distance between
(i) D and A
(ii) C and D
(d) Measure angle DAC and angle BCD
Date posted: April 26, 2019. Answers (1)
- An ant moved from Y to X the midpoint of RS through P in the right pyramid below.(Solved)
An ant moved from Y to X the midpoint of RS through P in the right pyramid below.
Draw the net of the pyramid showing the path of the ant hence find the distance it moved.
Date posted: April 26, 2019. Answers (1)
- The G.C.D. and L.C.M of three numbers are 3 and 1008 respectively. If two of the numbers are 48 and 72, find the least
possible value...(Solved)
The G.C.D. and L.C.M of three numbers are 3 and 1008 respectively. If two of the numbers are 48 and 72, find the least
possible value of the third number.
Date posted: April 26, 2019. Answers (1)
- A woman walks directly from point A towards the foot of a tall building 240m away. After covering 180m, he observes
that the angle of elevation...(Solved)
A woman walks directly from point A towards the foot of a tall building 240m away. After covering 180m, he observes
that the angle of elevation of the top of the building is 450. Determine the angle of elevation of the top of the building
from A.
Date posted: April 26, 2019. Answers (1)
- ABCD is a rhombus. A is the point(2,1) and C is the point (4,7). Find the equation of the diagonal BD in the form ax...(Solved)
ABCD is a rhombus. A is the point(2,1) and C is the point (4,7). Find the equation of the diagonal BD in the form ax + by = c
Date posted: April 26, 2019. Answers (1)
- The ratio of the lengths of the corresponding sides of two similar rectangular petrol tanks is 3:5. The volume of the
smaller tank is 8.1m3. Calculate...(Solved)
The ratio of the lengths of the corresponding sides of two similar rectangular petrol tanks is 3:5. The volume of the
smaller tank is 8.1m3. Calculate the volume of the larger tank.
Date posted: April 26, 2019. Answers (1)
- A regular n-sided polygon has its interior angle equal to 4 times its exterior. Find n.(Solved)
A regular n-sided polygon has its interior angle equal to 4 times its exterior. Find n.
Date posted: April 26, 2019. Answers (1)
- A school decided to make a beautiful picnic site to be used by students and teachers as a resting point. The site was
designed to be...(Solved)
A school decided to make a beautiful picnic site to be used by students and teachers as a resting point. The site was
designed to be triangular in shape measuring 40 metres, 60 metres and 80 metres. Calculate the area of the picnic site.
(Answer correct to 1 d.p)
Date posted: April 26, 2019. Answers (1)
- During a certain month, the exchange rates in a bank were as follows;(Solved)
During a certain month, the exchange rates in a bank were as follows;
A tourist left Kenya to the United States with KSh. 1,000,000.At the airport he exchanged all the money to dollars and
spent 190 dollars on air ticket. While in US he spent 4500 dollars for upkeep and proceeded to Europe. While in Europe he spent a total of 2000 Euros. How many Euros did he remain with?
Date posted: April 26, 2019. Answers (1)
- Without using calculator, evaluate.(Solved)
Without using calculator, evaluate.
leaving the answer as a mixed fraction.
Date posted: April 26, 2019. Answers (1)
- Find the integral values of x which satisfy the inequality.(Solved)
Find the integral values of x which satisfy the inequality.
3(1 + x)< 5x – 11
Date posted: April 26, 2019. Answers (1)
- Marwa bought a refrigerator on hire purchase by paying monthly installments of KSh. 2000 per month for 40 months
and a deposit of KSh. 12,000. If...(Solved)
Marwa bought a refrigerator on hire purchase by paying monthly installments of KSh. 2000 per month for 40 months
and a deposit of KSh. 12,000. If this amounted to an increase of 25% of the original cost of the refrigerator, what was
the cash price of the refrigerator?
Date posted: April 26, 2019. Answers (1)
- A two digit number is such that the one’s digit is four more than the tens digit, and the sum of the digits is 14....(Solved)
A two digit number is such that the one’s digit is four more than the tens digit, and the sum of the digits is 14. Find the
number.
Date posted: April 26, 2019. Answers (1)
- All prime numbers less than ten are arranged in ascending order to form a number.(Solved)
All prime numbers less than ten are arranged in ascending order to form a number.
(a) Write down the number formed.
(b) Express the number in (a) above in expanded form.
Date posted: April 26, 2019. Answers (1)
- Simplify(Solved)
Simplify
Date posted: April 26, 2019. Answers (1)
- Given that;(Solved)
Given that
Use mathematical tablets to find the value of x in standard form correct to 3 significant figures.
Date posted: April 26, 2019. Answers (1)
- The law E = KXn gives an expression for the energy E joules stored in a spring for the extension xcm. The table below
shows the...(Solved)
The law E = KXn gives an expression for the energy E joules stored in a spring for the extension xcm. The table below
shows the value of E and the corresponding value of X.
Determine graphically the values of k and n. Write the equation connecting E and X.
Date posted: April 26, 2019. Answers (1)
- The first term of an Arithmetic Progression (AP) is 200. The sum of the first 10 terms of AP is 24500.(Solved)
The first term of an Arithmetic Progression (AP) is 200. The sum of the first 10 terms of AP is 24500.
(a) (i) Find the common difference.
(ii) Given that the sum of the first n terms of the AP is 80100, find n.
(b) The 3rd, 5th and 8th terms of another AP, form the first three terms of a Geometric Progression (GP). If the common
difference of AP is 5, find:-
(i) The first term of the GP.
(ii) The sum of the first 12 terms of the GP, to four significant figures.
Date posted: April 26, 2019. Answers (1)
- In the figure below, QT = a and QP = b.(Solved)
In the figure below, QT = a and QP = b.
(a) Express the vector PT in terms of a and b.
(b) If PX = kPT, express QX in terms of a, b and k, where k is a scalar.
(c) If QR = 3a and RS = 2b, write down an expression for QS in terms of a and b.
(d) If QX = tQS, use your result in (b) and (c) to find the value of k and t.
(e) Find the ratio PX : XT.
Date posted: April 26, 2019. Answers (1)