SERIES
2
FORM
FOUR WEEKLY MATH’S QUESTIONS
NECTA
2012
SECTION
A:
Qn
1. (a) By using mathematical tables, evaluate
to three significant
figures.
(b)Rationalize
(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 cm^{2
}and
49 cm^{2
}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.
(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 5^{th} term of an arithmetic progression is 23 and the 12^{th} 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.
SECTION B:
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 31^{st}
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 xaxis, 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).
FORM FOUR 1^{ST} ELEARNING SERIES
Answer all questions:
Qn.1 Write 300.3264 correct to:
(a) Three significant figures.
(b) Three decimal places.
Qn.2 Rationalize the denominator and simplify.
Qn.3 (a) Evaluate
(b)Find
x to three significant figures if 10^{x}=5
Qn. 4 (a)Draw the graph given by
(b ) What are the Domain and
Ranges of the relation R?
(c) If
Qn. 5 Use the following frequency
distribution table to answer (a) to (c) below:
Marks

09

1019

2029

3039

4049

5059

6069

Frequency

1

2

5

11

21

20

17

Marks

7079

8089

9099

100109

110119


Frequency

10

6

4

4

1

(a) Draw the histogram and the frequency
polygon.
(b) Find the modal class.
(c) Calculate the mode.
(d) Calculate the median.
(e) Calculate the mean.
ANSWERS:
SOLUTIONS TO FORM FOUR SERIES ONE
WEEKLY QUESTIONS:
QN 1:;
solution
(a) Three significant figures 300.0
(b) Three decimal places 300.326
QN2:
solution
Rationalization of the denominator
QN3:
(a) solution
(b) solution
QN4 (a) solution
Table of values for the function
(b) The domain and ranges for the
relation are such that
QN5.
Solution:
Marks  Class Marks(x)  Frequency (f)  f.x  Cumulative Frequency 
09  4.5  1  4.5  1 
1019  14.5  2  29  3 
2029  24.5  5  122.5  8 
3039  34.5  11  379.5  19 
4049  44.5  21  934.5  40 
5059  54.5  20  1090  60 
6069  64.5  17  1096.5  77 
7079  74.5  10  745  87 
8089  84.5  6  507  93 
9099  94.5  4  378  97 
100109  104.5  4  418  101 
110119  114.5  1  114.5  102 
TOTAL  102  5819 
(a)Histogram and Frequency Polygon see
figure 1.
(b) The modal class refers to the class
with the highest frequency which in this case is 4049.
(c) Solution:
(d) Calculating the median
But before anything you should find the
median class by calculating the middle term of the cumulative
frequency which is usually the number which is equal to the half of
the total of frequency or just above.
Which in this case 102/2 = 51
So we choose the class with a
cumulative frequency of 60.
Hence the median class is 5059
Histogram and Frequency Polygon
FREQUENCY POLYGON
Maoni 4 :
asante sana kaka kweli umetuokoa akina kayumba. Munhu akuzidishie
Nimependa sana notes zenu ni nzuri sana. Shukurani zangu ziwafikie. Mmeniokoa katika ugumu wa kupata material
jamani, naomba kupata analysis ya passed like a shaddow
This is really good I love math my God math is de best
Chapisha Maoni