- Point T is the mid-point of a straight line AB. Given that the position vectors of A and T are i-j+k and 2i + 1½...(Solved)
Point T is the mid-point of a straight line AB. Given that the position vectors of A and T are i-j+k and 2i + 1½ k
respectively, find the position vector of B in terms of i , j and k.
Date posted: April 29, 2019. Answers (1)
- (a) Draw a regular pentagon of side 4cm
(b) On the diagram drawn, construct a circle which touches all the sides of the pentagon(Solved)
(a) Draw a regular pentagon of side 4cm
(b) On the diagram drawn, construct a circle which touches all the sides of the pentagon
Date posted: April 29, 2019. Answers (1)
- a)Expand (1-x)5 up to the term in x3.(Solved)
a)Expand (1-x)5 up to the term in x3.
(b) Use the expansion in (a) to approximate the value of (0.98)5 correct to 3 decimal places
Date posted: April 29, 2019. Answers (1)
- In the figure below, AT is a tangent to the circle at A. Angle ATB = 480, BC = 5cm and CT = 4cm. Calculate...(Solved)
In the figure below, AT is a tangent to the circle at A. Angle ATB = 480, BC = 5cm and CT = 4cm. Calculate the length
AT.
Date posted: April 29, 2019. Answers (1)
- Find the relative error in the difference between 26.0cm and 14.2cm(Solved)
Find the relative error in the difference between 26.0cm and 14.2cm
Date posted: April 29, 2019. Answers (1)
- Simplify the expression below (Solved)
Simplify the expression given below
Date posted: April 29, 2019. Answers (1)
- The image of P(0,2), under an enlargement with a scale factor 3 is P’ (4,6). Find the centre of enlargement.(Solved)
The image of P(0,2), under an enlargement with a scale factor 3 is P’ (4,6). Find the centre of enlargement.
Date posted: April 29, 2019. Answers (1)
- Two dice are tossed together.(Solved)
Two dice are tossed together.
a) Draw a probability space to show all the possible outcomes
b) Find the probability that the sum of the two upper faces will be 9
Date posted: April 29, 2019. Answers (1)
- In the figure below, 0 is the centre of the circle. Find (Solved)
In the figure below, 0 is the centre of the circle. Find 
Date posted: April 29, 2019. Answers (1)
- Solve the inequality 2x + 3> 5x – 3> - 8 and represent your answer on the number line(Solved)
Solve the inequality 2x + 3> 5x – 3> - 8 and represent your answer on the number line
Date posted: April 29, 2019. Answers (1)
- Make P the subject of the formula(Solved)
Make P the subject of the formula
Date posted: April 29, 2019. Answers (1)
- Tap P can fill a tank in 2 hours and tap Q can fill the same tank in 4 hours. Tap R can empty the...(Solved)
Tap P can fill a tank in 2 hours and tap Q can fill the same tank in 4 hours. Tap R can empty the tank is 3 hours.
a) If tap R is closed, how long would it take taps P and Q to fill the tank?
b) Calculate how long it would take to fill the tank when the three taps P, Q and R are left running.
Date posted: April 29, 2019. Answers (1)
- Use logarithms to evaluate, correct to 4 decimal places.(Solved)
Use logarithms to evaluate, correct to 4 decimal places.
Date posted: April 29, 2019. Answers (1)
- The frequency table shows masses, to the nearest kilogramme of fish caught by a fisherman in a day.(Solved)
The frequency table shows masses, to the nearest kilogramme of fish caught by a fisherman in a day.
(a) Draw a histogram to represent the above information
(b)(i) State the class in which the median mass lies
(ii) Draw a vertical line in the histogram, showing where the median mass lies
(iii) Calculate the median mass in kilogrammes of the fish caught
Date posted: April 29, 2019. Answers (1)
- In the figure below OY = 20B, OX = 5/2 OA, OA = a and OB = b(Solved)
In the figure below OY = 20B, OX = 5/2 OA, OA = a and OB = b
a) Express the following in terms of a and b
(i) AB
(ii) XY
(b) Given that AC = 6AB, express OC & XC interms of a and b
(c) Show the points X, Y and C are collinear
(d) State the ratio in which C divides XY
Date posted: April 29, 2019. Answers (1)
- The displacement, S metres, of a moving particle after t seconds is given by
S = 40t3 – t2 + 3t + 3. Determine:(Solved)
The displacement, S metres, of a moving particle after t seconds is given by
S = 40t3 – t2 + 3t + 3. Determine:
(a) The velocity of the particle when t= 3 seconds
(b) The value of t when the velocity of the particle is 4M/S
(c) The displacement when the particle velocity is 4M/S
(d) The acceleration of the particle when t = 3 seconds
Date posted: April 29, 2019. Answers (1)
- In triangle ABC, BC = 3.2cm, AC = 4.8cm and angle ABC = 1200.(Solved)
In triangle ABC, BC = 3.2cm, AC = 4.8cm and angle ABC = 1200.
(a) Construct the triangle and a circumscribed circle and measure its radius.
(b) If BC is the base of the triangle, calculate correct to one decimal place.
(i) The perpendicular height of the triangle.
(ii) The area of the minor segment substended by the Chord AC.
(iii) The size of angle ABC
Date posted: April 29, 2019. Answers (1)
- (a) The product of the matrices is a singular matrix. Find the value of y.(Solved)
(a) The product of the matrices.
Is a singular matrix. Find the value of y.
(b) In a certain week, a businessman bought 18 bicycles and 16 radios for a total of Kshs. 113,640. In the following week,
he bought 14 bicycles and 12 radius for a total of Kshs. 87,480. Using matrix method, find the price of each bicycle and
each radio that he bought.
(c) In the third week, the price of each bicycle was reduced by 10% while the price of each radio was raised by 10%. The
businessman bought as many bicycles and as many radios as he had bought in the first two weeks. Find by matrix
method, the total cost of the bicycles and radios that the businessman bought in the third week.
Date posted: April 29, 2019. Answers (1)
- The diagram below shows a cross-section of a bottle. The lower part ABC is a hemisphere of radius 5.2cm and the
upper part is a frustrum...(Solved)
The diagram below shows a cross-section of a bottle. The lower part ABC is a hemisphere of radius 5.2cm and the upper part is a frustrum of a cone. The top radius of the frustrum is one third of the radius of the hemisphere. The hemisphere part is completely filled with water as shown in the diagram.
(a) Determine the height of the frustrum part.
(b) Find the surface area of the frustrum part of the bottle.
Date posted: April 29, 2019. Answers (1)
- The distance between towns M and N is 280km. A car and a lorry travel from M to N.
The average speed of the lorry is...(Solved)
The distance between towns M and N is 280km. A car and a lorry travel from M to N.
The average speed of the lorry is 20km/h less than that of the car. The lorry takes 1h 10min more than the car to
travel from M to N.
a) If the speed of the lorry is xkm/h, find x
b) The lorry left town M at 8.15am. The car left town M later and overtook the lorry at 12.15pm. Calculate the time the car left town M.
Date posted: April 29, 2019. Answers (1)