Ijumaa, 19 Julai 2013


NECTA 2012
Qn 1. (a) By using mathematical tables, evaluate 

to three significant figures.


Qn 2. (a) Find the value of x for which

(b) Solve

Qn 3. (a) Mr. Beans lived a quarter of his life as a child, a fifth as a teenager and a third as an adult. He then spent 13 years in his old age. How old was he when he died?

(b) A and B are subsets of the universal set U. Find
given that

Qn 4. Given that a= (3, 4), b= (1, -4) and c = (5, 2) determine:
(a) d = a + 4b – 2c;
(b) Magnitude of vector d , leaving your answer in the form ;
(c) The direction of the cosines of d and hence show that the sum of the squares of these directional cosines is one.
Qn 5 (a) If polygons X and Y are similar and their areas are 16 cm2 and 49 cm2 respectively, what is the length of a side of polygon Y corresponding side of polygon X is 28 cm.
(b) (i) show whether triangles PQR and ABC are similar or not.
(ii) Find the relationships between y and x in the triangles given above.

Qn 6 (a) The power (P) used in an electric circuit is directly proportional to the square of the (I). When the current is 8 Ampere (A), the power used is 640 Watts (W).

(i)Write down the equation relating power (P) and the current (I).
(ii) Calculate the current I when the circuit uses 360 Watts.

(b) If x*y is defined as . Find (5* - 2)*(3* -4).
Qn7 (a) By selling an article at shs. 22,500/= a shopkeeper makes a loss of 10%. At what price must the shopkeeper sell the article in order to get a profit of 10%.

(b) An alloy consists of three metals A, B, and C in the proportions A:B = 3:5 and B:C = 7:6. Calculate the proportion A:C.

Qn8. (a) If the 5th term of an arithmetic progression is 23 and the 12th term is 37, find the first term and the common difference.

(b) Find the sum of the first four terms of a geometric progression which has a first term of 1 and a common ratio of .

Qn9. (a) Find the length AC from the figure below.
(b) A ladder reaches the top of a wall 18m high when the other end on the ground is 8m from the wall. Find the length of the ladder.

\Qn10. (a) Solve for x if .

(b) If the sum of two numbers is 3 and the sum of their squares is 29, find the numbers.

Answer any four (4) questions

Qn11. Anna and Mary are tailors. They make x blouse and y skirts each week. Anna does all the cutting and Mary does all the sewing. To make a blouse it takes 5 hours of cutting and 4 hours of sewing. To make a skirt it takes 6 hours of cutting and 10 hours of sewing. Neither tailor works for more than 60 hours a week.
(a) For sewing, show that .
(b)Write down another inequality in x and y for the cutting.
(c) If they make at least 8 blouses each week, write down another inequality.
(d)Using 1 cm to represent 1 unit on each axis, show the information in parts (a), (b) and (c) graphically. Shade only the required region.
(e) If the profit on a blouse is shs. 3,000/= and on a skirt is shs. 10,000/=, calculate the maximum profit that Anna and Mary can make in a week.

Qn12. 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 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

Qn13.(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 the wood used.

(b) Find the distance (in km) between towns      and  
  along a line of latitude, correctly to 4 decimal places.

Qn14. (a) the following balances were extracted from the ledger of Mr & Mrs
Mkomo business 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/=

Qn 15. (a) Find the value of k such that the matrix is singular.

(b) The vertices of triangle 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.

Qn16. 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 color
(d) Find the probability that the first is black and the second is red.
(e) Verify the probability rule by using the results in part (b).

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