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- The figure shows triangle OPQ in which QN : NP = 1 : 2, OT : TN = 3 : 2 and M is the...(Solved)
The figure shows triangle OPQ in which QN : NP = 1 : 2, OT : TN = 3 : 2 and M is the mid - point of OQ.
OP = p and OQ = q
a) Express the following in terms of p and q.
i) PQ
ii) ON
iii) PT
iv) PM
b) Hence show that P, T and M are collinear.
Date posted: May 6, 2019. Answers (1)
- Three pupils Irene, Mary and Atieno applied for a form one vacancy. The probability of Irene, Mary and Margaret
getting the chance in the school are...(Solved)
Three pupils Irene, Mary and Atieno applied for a form one vacancy. The probability of Irene, Mary and Margaret
getting the chance in the school are 0.5, 0.4 and 0.9 respectively. Determine the probability that
a) None gets the chance.
b) Only one gets the chance.
c) At most one of the three gets the chance.
d) At least one of the three gets the chance.
Date posted: May 6, 2019. Answers (1)
- A farmer wishes to keep some chicks and ducks. Chicks cost Ksh. 60 each while ducks costs Kshs. 80 each. She finds its
uneconomical to keep...(Solved)
A farmer wishes to keep some chicks and ducks. Chicks cost Ksh. 60 each while ducks costs Kshs. 80 each. She finds its
uneconomical to keep less than 250 birds. She also wishes to keep more chicks than ducks but the chicks must be less
than 200. She cannot afford to spend more than ksh. 24,000.
a) Taking x and y to be the number of chicks and ducks respectively rite down all the inequalities that satisfy the above
conditions.
b) Represent the inequalities graphically shading out the unwanted region.
c) If the farmer makes a profit of ksh. 200 per chicks and ksh. 250 per duck, find the number of chicks and ducks she must keep in order to maximize her profit. State the profit.
Date posted: May 6, 2019. Answers (1)
- The table below shows income tax rates for a certain year.(Solved)
The table below shows income tax rates for a certain year.
A secondary school teacher was earning a monthly basic salary of Ksh. 55,480 house allowance of Kshs. 12,000 and a
commuter allowance of ksh. 8000. He was entitled to a personal relief of Kshs. 1162 per month.
a) Calculate
i) The teacher’s taxable income.
ii) The teacher’s net monthly tax.
b) In addition to the tax the other deductions were per month as follows:
- Cooperative loan Ksh. 10,000
- Co-operative shares Ksh. 2,000
- Window and children’s pensions scheme at 2% of the basic salary.
Calculate the teacher’s net monthly pay.
Date posted: May 6, 2019. Answers (1)
- The figure below shows the pulleys with centres A and B and radii 13cm and 6cm respectively. The distance between
the centres is 25cm.(Solved)
The figure below shows the pulleys with centres A and B and radii 13cm and 6cm respectively. The distance between
the centres is 25cm.
A belt PRSTUP goes round the two pulleys. PQ and TS are also tangents.
a) Calculate
i) Length PQ
ii) Angle BAP
b) Hence or otherwise calculate the length of the belt.
Date posted: May 6, 2019. Answers (1)
- A businesswoman mixes three types of rice A, B and C in the ratio A : B = 1 : 2 and B : C...(Solved)
A businesswoman mixes three types of rice A, B and C in the ratio A : B = 1 : 2 and B : C = 4 : 5. The mixture is to
contain 60 bags of type B.
a) Find the ratio A : B : C
b) Find the required number of bags of type C.
c) The cost per bag of type A is Kshs. 7,500, type B Kshs. 5,000 and type C Kshs. 4,000.
i) Calculate the cost per bag of the mixture.
ii) Find the percentage profit if the selling price of the mixture is Ksh. 6,500 per bag.
Date posted: May 6, 2019. Answers (1)
- A vehicle initially moving at a velocity of 80m/s had breaks applied. The table below shows how velocity changed in
the next 14 seconds.(Solved)
A vehicle initially moving at a velocity of 80m/s had breaks applied. The table below shows how velocity changed in
the next 14 seconds.
Determine the average rate of deceleration between the fourth and the twelfth second.
Date posted: May 6, 2019. Answers (1)
- The gradient function of a curve is x3 - 4. If the curve passes through point (2, 3). Find the equation of the curve.(Solved)
The gradient function of a curve is x3 - 4. If the curve passes through point (2, 3). Find the equation of the curve.
Date posted: May 6, 2019. Answers (1)
- A plane flies from point P (400N,500E) towards West to a point Q. Given that the plane covers a distance of 10,000km what is the...(Solved)
A plane flies from point P (400N, 500E) towards West to a point Q. Given that the plane covers a distance of 10,000km what is the position of Q. (Take 𝜋= 22/7, radius of the earth 6370km)
Date posted: May 6, 2019. Answers (1)
- Francis bought a vehicle at ksh. 2 800 000. After three years he sold the vehicle at Kshs. 1,500,000. Determine the average rate of depreciation...(Solved)
Francis bought a vehicle at ksh. 2 800 000. After three years he sold the vehicle at Kshs. 1,500,000. Determine the average rate of depreciation per annum correct to one decimal place.
Date posted: May 6, 2019. Answers (1)
- Solve the simultaneous equations.(Solved)
Solve the simultaneous equations.
2x - y = 3
xy - y2 = 0
Date posted: May 6, 2019. Answers (1)
- The figure below represent a square based right pyramid ABCDV. AB = 10cm,AV = BV = CV = DV = 15cm.(Solved)
The figure below represent a square based right pyramid ABCDV. AB = 10cm,AV = BV = CV = DV = 15cm.
Calculate the angle between AV and the base ABCD to the decimal place.
Date posted: May 6, 2019. Answers (1)
- Solve for x without using mathematical tables or calculators.(Solved)
Solve for x without using mathematical tables or calculators.
Date posted: May 6, 2019. Answers (1)
- Expand (4 - x)7 upto to the term in x4. Hence find the appropriate value of (3.8)7.(Solved)
Expand (4 - x)7 upto to the term in x4. Hence find the appropriate value of (3.8)7.
Date posted: May 6, 2019. Answers (1)
- In a transformation, an object with area 9cm2 is mapped onto an image whose area is 54cm2. Given that the matrix of transformation is (Solved)
In a transformation, an object with area 9cm2 is mapped onto an image whose area is 54cm2. Given that the matrix of transformation is 
find the value of x.
Date posted: May 6, 2019. Answers (1)
- Determine the amplitude and period of the function 3y = 6sin (2x - 30).(Solved)
Determine the amplitude and period of the function 3y = 6sin (2x - 30).
Date posted: May 6, 2019. Answers (1)
- The table shows the frequency distribution of marks scored by students in a test.(Solved)
The table shows the frequency distribution of marks scored by students in a test.
Determine the median mark correct to one decimal point.
Date posted: May 6, 2019. Answers (1)
- The quantities P, Q and R are such that P varies directly as Q and inversely as the square of R. Given that P =...(Solved)
The quantities P, Q and R are such that P varies directly as Q and inversely as the square of R. Given that P = 2 when Q = 12 and R = 6. Determine the equation connecting the three.
Date posted: May 6, 2019. Answers (1)
- In the figure below PQR is the diameter of the circle centre O. Angle QPR = 200 and angle QTR = 800(Solved)
In the figure below PQR is the diameter of the circle centre O. Angle QPR = 200 and angle QTR = 800
Determine the size of
a) Reflex angle POS
b) Angle OSQ
Date posted: May 6, 2019. Answers (1)
- The first term of an arithmetic sequence is 5 and the common difference is 2.(Solved)
The first term of an arithmetic sequence is 5 and the common difference is 2.
a) List the first six terms of the sequence.
b) Determine the sum of the first 40 terms of the sequence.
Date posted: May 6, 2019. Answers (1)