- 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)
- Five towns A,B,C,D and E are such that B is on a bearing of 040o and 6km from E.(Solved)
Five towns A,B,C,D and E are such that B is on a bearing of 040o and 6km from E. D is due west of E on a bearing of 340o from E. A is due North of E on a bearing of 045o from D. C is on a bearing of 250o from B and due North of E.
(a) Make a scale drawing showing the positions of the five towns.(Use a scale of 1cm to represent 1km)
(b) Use your drawing to determine;
(i) the bearing and distance of B from A.
(ii) the bearing and distance of C from D.
(iii) the distance between A and E.
Date posted: September 3, 2019. Answers (1)
- The sides of a rectangle are increased by 10%. By what percentage is the area increased(Solved)
The sides of a rectangle are increased by 10%. By what percentage is the area increased
Date posted: September 3, 2019. Answers (1)
- Rono left Kenya for Ethiopia with Ksh. 16, 742, which he changed at the airport to Ethiopian Birr
currency at the rate of Kshs.1=7.772 Birr.(Solved)
Rono left Kenya for Ethiopia with Ksh. 16, 742, which he changed at the airport to Ethiopian Birr
currency at the rate of Kshs.1=7.772 Birr. He spent 71,502.40 Birr and returned to Kenya with the balance that he changed back to Kenya shillings, at a new rate of Ksh. 1=8.211 Birr. How much, to the nearest cents, in Kenya shillings did Rono get?
Date posted: September 3, 2019. Answers (1)
- Solve the following equation for x without using tables or calculators.(Solved)
Solve the following equation for x without using tables or calculators.
Date posted: September 3, 2019. Answers (1)
- Each interior angle of n-sided polygon is 350o(Solved)
Each interior angle of n-sided polygon is 350o.
(a) Find n.
(b) What is the name of the polygon?
Date posted: September 3, 2019. Answers (1)
- A milk vendor bought 20 litres of milk at Ksh.15 per litre and added 5 litres of water to the milk.(Solved)
A milk vendor bought 20 litres of milk at Ksh.15 per litre and added 5 litres of water to the milk. If he
sold the mixture at Ksh.18 per litre, what was the percentage profit.
Date posted: September 3, 2019. Answers (1)
- The figure below shows the graph of velocity Vm/s against time t seconds of a car. (Solved)
The figure below shows the graph of velocity Vm/s against time t seconds of a car. If the car traveled a
distance of 32 metres, in the first four seconds, calculate the average velocity for the whole journey.
Date posted: September 3, 2019. Answers (1)
- Find the integral values of x which satisfy the simultaneous inequalities.(Solved)
Find the integral values of x which satisfy the simultaneous inequalities.
3x-2<10+x <10+x
Date posted: September 3, 2019. Answers (1)
- A sector of a circle of radius 10cm has an arc that subtends an angle of 270o at the centre.(Solved)
A sector of a circle of radius 10cm has an arc that subtends an angle of 270o at the centre.
Calculate the vertical height of the cone formed by the sector.
Date posted: September 3, 2019. Answers (1)
- In the figure below MPN is a tangent to the circle at P. Find ?SPQ and ?NPQ, stating your reasons. (Solved)
In the figure below MPN is a tangent to the circle at P. Find angle SPQ and angle NPQ, stating your reasons. Angle SRQ=120o and angle PQR=62o
Date posted: September 3, 2019. Answers (1)
- The line passing through the points P(5, b), Q(2,3) is parallel to the line 2y=-x+2. determine the value
of b.(Solved)
The line passing through the points P(5, b), Q(2,3) is parallel to the line 2y=-x+2. Determine the value
of b.
Date posted: September 3, 2019. Answers (1)
- A prism of length 15cm has a uniform triangular cross section of sides measuring 8cm, 7cm and 5cm.
(Solved)
A prism of length 15cm has a uniform triangular cross section of sides measuring 8cm, 7cm and 5cm. Determine the volume of the prism.
Date posted: September 3, 2019. Answers (1)
- Simplify the expression(Solved)
Simplify the expression
Date posted: September 3, 2019. Answers (1)
- Without using mathematical table of calculator, evaluate:(Solved)
Without using mathematical table of calculator, evaluate:
Date posted: September 3, 2019. Answers (1)
- Find the integral values that satisfy the inequalities(Solved)
Find the integral values that satisfy the inequalities
Date posted: September 3, 2019. Answers (1)
- Kamau bought five exercise books and three geometrical sets for sh.725.(Solved)
Kamau bought five exercise books and three geometrical sets for sh.725. If he had bought four similar exercise books and five geometrical sets, he would have paid sh.375 more. How much would he pay for two exercise books and six geometrical sets.
Date posted: September 3, 2019. Answers (1)