- The equation of a curve is given as y = x3 – 3x + 2.
Determine
a) the value of y when x = 2
b) the...(Solved)
The equation of a curve is given as y = x3 – 3x + 2.
Determine
a) the value of y when x = 2
b) the gradient of the curve at x = 3.
c) the turning points of the curve and their nature.
Date posted: November 5, 2019. Answers (1)
- The table below gives some of the values of x and y for the function y = 1/2x2 + 2x + 1 in the interval...(Solved)
The table below gives some of the values of x and y for the function y = 1/2x2 + 2x + 1 in the interval 0 ≤ x ≤ 6
a) Use the values in the table to draw the graph of the function on the grid provided.
b) i) Using the graph and the mid-ordinate rule with six (6) strips, estimate the area bounded by the
curve, the x – axis, the y- axis and the line x = 6.
ii) If the exact area of the region described in (b) (i) is 78cm2; calculate the percentage error
made when the mid-ordinate rule is used.
Date posted: November 5, 2019. Answers (1)
- a) Given that the matrix find A-1, the inverse of A.
b) Kariuki bought 400 goats and 600 sheep for a total of Kshs 1.7m....(Solved)
a) Given that the matrix 
find A-1, the inverse of A.
b) Kariuki bought 400 goats and 600 sheep for a total of Kshs 1.7m. Maina bought 180 goats and 240 sheep for a total of Kshs 720,000. If the price of a goat is sh. X and that of a sheep is shs y,
i) Form two equations to represent the above information.
ii) Use the matrix A-1 to find the price of one goat and one sheep.
c) John bought 450 goats and 720 sheep. He was given a total discount of shs 66,600.
Date posted: November 5, 2019. Answers (1)
- In the figure below OA = a, OB = b, OA : AE = 2 : 3 and OB : OC = 1 : 2
a)...(Solved)
In the figure below OA = a, OB = b, OA : AE = 2 : 3 and OB : OC = 1 : 2
a) Express AC and BE in terms of a and b
i) AC
ii) BE
b) If DC = kAC and BD = mBE where k and m are scalars.
By expressing DC in two ways, determine the values of k and m.
c) Find the ratio of BD : DE
Date posted: November 5, 2019. Answers (1)
- A house is to be sold either on a cash basis or through a loan. The cash price is Kshs. 750,000. The loan conditions are...(Solved)
A house is to be sold either on a cash basis or through a loan. The cash price is Kshs. 750,000. The loan conditions are as follows: there is to be a down payment of 10% of the cash price and the rest of the money to be paid through a loan of 10% per annum compound interest.
A customer decided to buy the house through a loan.
a) i) Calculate the amount of money loaned to the customer.
ii) The customer paid the loan in 3 years.
Calculate the total amount paid for the house.
b) Find how long the customer would have taken to fully pay for the house if she paid a total of Kshs 891,750.
Date posted: November 5, 2019. Answers (1)
- A cylindrical water tank is of diameter 7 metres and height 2.8 metres.
a) Find the capacity of the water tank in litres.
b) Six members...(Solved)
A cylindrical water tank is of diameter 7 metres and height 2.8 metres.
a) Find the capacity of the water tank in litres.
b) Six members of a family use 15 litres each per day. Each day 80 litres are used for cooking and washing and a further 60 litres are wasted.
Find the number of complete days a full tank of water would last the family.
c) members of the family were absent for 90 days. During the 90 days, wastage was reduced by 20% but cooking and washing remained the same. Calculate the number of days a full tank would now last the family.
Date posted: November 5, 2019. Answers (1)
- Divide line AB such that AP = 2/5 AB(Solved)
Divide line AB such that AP = 2/5 AB
Date posted: November 5, 2019. Answers (1)
- Use the matrix method to find the co-ordinates of the points of intersection of the line
3x - 4y = 1 and y + 7x =...(Solved)
Use the matrix method to find the co-ordinates of the points of intersection of the line
3x - 4y = 1 and y + 7x = 23
Date posted: November 5, 2019. Answers (1)
- In the figure below the lines AB and CD are parallel. AD and CB intersect at X. AB = 6cm, CD = 9cm and DX...(Solved)
In the figure below the lines AB and CD are parallel. AD and CB intersect at X. AB = 6cm, CD = 9cm and DX = 3 cm.
a) Calculate the length of AX.
b) The area of ΔABX is 6cm2. Calculate the area of ΔCXD.
Date posted: November 5, 2019. Answers (1)
- Without using a calculator evaluate(Solved)
Without using a calculator evaluate
Date posted: November 5, 2019. Answers (1)
- A line L is perpendicular to the line Given that L passes through (3, 10).
Find the
a) Gradient of L
b) Equation of L in...(Solved)
A line L is perpendicular to the line 
Given that L passes through (3, 10).
Find the
a) Gradient of L
b) Equation of L in form of y = mx + c where m and c are constants.
Date posted: November 5, 2019. Answers (1)
- Find the value of(Solved)
Find the value of
Date posted: November 5, 2019. Answers (1)
- Simplify the expression(Solved)
Simplify the expression
Date posted: November 5, 2019. Answers (1)
- Find all the integers satisfying the inequalities.
3 - 2x < x - 3 = 4(Solved)
Find all the integers satisfying the inequalities.
3 - 2x < x - 3 ≤ 4
Date posted: November 5, 2019. Answers (1)
- Given Sin (90 – a) = 1/2 , find without using tables or calculators the value of Cos a.(Solved)
Given Sin (90 – a) = 1/2 , find without using tables or calculators the value of Cos a.
Date posted: November 5, 2019. Answers (1)
- Solve the equation below.(Solved)
Solve the equation below.
Date posted: November 5, 2019. Answers (1)
- Use logarithms to evaluate(Solved)
Use logarithms to evaluate
Date posted: November 5, 2019. Answers (1)
- Without using a calculator, evaluate.
(Solved)
Without using a calculator, evaluate.
Date posted: November 5, 2019. Answers (1)
- A (50oN, 40oW) and B(50oN, 80oE) lie on the surface of the earth. (take R=6370km, p = 22/7)
(a) Calculate the distance along the small circle...(Solved)
A (50oN, 40oW) and B(50oN, 80oE) lie on the surface of the earth. (take R=6370km, π = 22/7)
(a) Calculate the distance along the small circle between A and B, giving your answer in
i) Nautical miles
ii) Kilometers
(b) Find the distance between A and B along a great circle (over North pole) in
i) Nautical miles
ii) Kilometres
c) Find the time at A if the local time at B is 12:00 noon
Date posted: November 2, 2019. Answers (1)
- Use a ruler and compasses only for all the constructions in this question.
(a) Construct a triangle ABC such that angle BAC = 30o, AB=4cm and...(Solved)
Use a ruler and compasses only for all the constructions in this question.
(a) Construct a triangle ABC such that angle BAC = 30o, AB=4cm and AC = 6cm
b) Construct a circle passing through points A, B and C
c) On the opposite side of point C, locate point on the circumference such that
ACD= BCD. Measure length CD
Date posted: November 2, 2019. Answers (1)