
12. In a survey of the number of children in 12 houses, the following data resulted: 1, 2, 3, 4, 2, 2, 1, 3, 4, 3,
5, 3
(a) Show this data in a frequency distribution table.
(b) Draw a histogram and a frequency polygon to represent this data.
(c) Calculate the mean and mode number of children per house.
13. (a) An open rectangular box measures externally 32cm long, 27cm wide and 15cm deep. If the box
is made of wood 1cm thick, find the volume of wood used.
(b) Find the distance (in km) between towns P (12.4°S, 30.5°E) and Q(12.4°S, 39.8°E) along a line
of latitude, correctly to 4 decimal places.
14. (a) The following balances were extracted from the ledgers of Mr. and Mrs. Mkomo business on
31st January. Prepare a trial balance.
Capital 30,000/= Insurance 3,000/=
Furniture 25,000/= Cash 18,000/=
Motor vehicle 45,000/= Discount received 7,000/=
Sales 68,000/= Discount allowed 4,000/=
Purchases 54,000/= Drawing 12,000/=
Creditors 76,000/= Electricity 5,000/=
Debtors 15,000/=
(b) Determine the gross profit and the net profit from the information given below.
Sales 38,000/=
Opening stock 8,000/=
Purchases 25,000/=
Electricity 4,000/=
Discount allowed 2,000/=
Closing stock 5,000/=
15. (a) Find the value of k such that the matrix is singular.
(b) The vertices of ABC are A(1, 2) , B(3, 1) and C(− 2, 1) . If triangle ABC is reflected on the
x-axis, find the coordinates of the vertices of its image.
(c) Solve the following simultaneous equations by matrix method.
16. A box contains 7 red balls and 14 black balls. Two balls are drawn at random without replacement.
(a) Draw a tree diagram to show the results of the drawing.
(b) Find the probability that both are black.
(c) Find the probability that they are of the same colour.
(d) Find the probability that the first is black and the second is red.
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