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### Further Mathematics. Third Term SS2.

THIRD TERM  EXAMINATION, 2009/2010 SESSION.
SUBJECT: FURTHER MATHEMATICS (1)
CLASS: SSS 2                 TIME ALLOWED: 2HRS

If P={x:1=x=6}and
Q={x:2<x<9}
where x
R,
find PnQ (a) {x:2=x=6}
(b) {x:2=x<6} (c) {x:2<x<6} (d) {x:2<x=6}
simplify -2/3 (a) -4 (b) -1/4 (c) 1/8 (d) 4

A binary operation * is defined on the set R of real numbers by a*b=
find the value of v2*v6 (a) v3 (b) 3v2/4 (c) v3/2 (d)

If (x-3) is a factor of 2x3+3x2-17x-30 find the remaining factors (a) (2x-5)(x-2) (b) (2x-5)(x+2) (c) (2x+5)(x-2) (d) (2x+5)(x+2)

Given that (v3-5v2)( v3+v2)=P+qv6 find q (a) 4 (b) -4 (c) -5 9d) -7

Find the coefficient of x4 in the binomial expansion of (1-2x)6 (a) 320 (b) 240 (c) -240 (d) -320

Find the equation of the line passing through (0,-1) and parallel to the y-axis (a) y=-1 (b) y=0 (c) x=0 (d) x=-1

Find the sum of the exponential series 96+24+6+�. (a) 144 (b) 128 (c) 72 (d) 64

Evaluate Log0.258 (a) 3/2 (b)2/3 (c) -2/3 (d) -3/2

Evaluate (a)1 (b)1/2 (c)0 (d) -1
A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man (a) 15 (b) 40 (c) 70 (d) 175

Simplify (a) 24 (b) 18   (c) 12  (d) 6
.
The area of a sector of a circle is 3cm2 if the sector subtends an angle of 1.5 radians at the centre calculate the radius of the circle. (a) 1cm (b)v2cm (c)2cm (d) 4cm

In a firing contest the probabilities that Joy and Oyinkansola in the target are 2/5 and 1/3 respectively. What is the probability that none of them will hit the target (a)1/5 (b) 2/5 (c) 3/5 (d) 4/5

The equation of the line of best fit for variable x and y is y=19.33+0.42x, where x is the independent variable. Estimate the value of y when x=15 (a) 18.91 (b) 19.74 (c) 25.63 (d) 38.23

Find the coordinates of the centre of the circle 4x2+4y2-5x+3y-2=0 (a) (-5/4,3/4) (b) (3/8,-5/8) (c) (5/8,-3/8) (d) (-5/4,-3/4)
A and B are two independent events such that P(A)=2/5 and P(AnB)=1/15

find P(B) (a) 3/5 (b) 1/3 (c) 1/6 (d) 2/15

Calculate correct to one decimal place the angle between 5i+12j and 2i+3j (a)54.8� (b) 56.3� (c) 66.4� (d) 76.3�

The sum of the first three terms of an Arithmetic progression (A.P) is 18. if the first term is 4. find the product (a)130 (b) 192 (c)210 (d) 260

The gradient of a line passing through the points P (4, 5) and Q(x, 9) is �. Find the value of x (a) -4 (b) 0 (c) 4 (d) 12
Simplify       (a) � (b) �v3 (c) 3 (d)2v3

Given that log2y1/2=log5125 find the value of y (a) 16 (b)  25 (c)36 (d) 64
Simplify (a)3v2 (b)2v3 (c) v3 (d) v2

Find the area of the circle whose equation is x2+y2-4x+8y+11=0 (a)3

Find the surd form the value of tan 15� (a) (2+v3) (b) (1+v3) (c) (3-v1) (d) (2-v3)

A bag contains 2 red and 4 green sweet each from the box one after the other without replacement. What is the probability that at a sweet with green wrapper is picked (a)1/5 (b)2/5 (c)8/15 (d)14/15

Evaluate   (a) 4   (b) 3 (c) 2 (d) 0
Find the value of p which will make (x2-x+P) a perfect square (a) -1/2 (b)1/4 (c)1/2 (d) 1

The equation of a circle is given by x2+y2-4x+2y-3 find the radius and the coordinates of its centre (a) 3,(-1,2) (b) 2v2,(2,-1) (c)2v2,(2,1) (d) 9,(2,-1)
The Polynomial g(x) =2x3+3x2+qx-1 has the same remainder when divided by (x+2) and (x-1). Find the value of constant q (a) -11 (b) -9 (c) -3 (d) -1

How many ways can 12 people be divided into three group of 2,7 and 3 in that order (a) 7,920 (b) 792 (c)187 (d)42

Given that P=4i +3j find the unit vector in the direction of P (a) 1/3(4i+3j) (b) 1/3(3i+4j) (c)1/5(3i+4j) (d)1/5(4i+3j)

Three students are working independently on a further mathematics problem. Their respective probabilities of solving the problem are 0.6, 0.7 and 0.8. what is the probability that at least one of them solves the problem (a) 0.024 (b) 0.336 (c) 0.664 (d) )0.976

A group of 5 boys and 4 girls is to be chosen from a class of 8 boys� and 6 girls. In how many ways can this be done? (a) 840 (b) 480 (c)408 (d) 380

Calculate correct to one decimal place the standard deviation of the numbers -1,5,0,2 and 9  (a) 7.2   (b) 6.6   (c) 3.6   (d) 3.2

Two statements are represented by p and q as follows: P: he is brilliant q: he is regular in class. Which of the following symbols represent the statement �he is regular in class but dull�? (a) qv~P  (b) q^~p   (c) ~q^~p   (d) ~q?~p

Find the coefficients of x4 in the binomial expansion of (2+x)6 (a)120 (b)80 (c)60 (d)15

Given f(x) = 4x3+2x2+5 find f1(2) (a)56 (b)75 (c)90 (d)45

Find the derivative of     (a)2x + 2 -    (b) 2x � 2 - (c) 2x+2-3x4 (d) 2x-  2+

THIRD TERM  EXAMINATION, 2009/2010 SESSION.
SUBJECT: FURTHER MATHEMATICS (2)
CLASS:  SSS 2                  TIME ALLOWED:2�HRS

SECTION A: Answer ALL Questions in this section (48 marks)
Solve the simultaneous equation log2x-log2y=2, log2(x-2y)=3
Given that tan 2A =  evaluate tan 15�

Express in the form mv2+nv5 where m and n are rational numbers

Differentiate with respect to x, x3+2x from the first principles

The sum of 2nd and 5th terms of an arithmetic progression (A.P) is 42. if the difference between the 6th and 3rd term is 12 find the
Common difference
First term
20th term

The table shows the distribution of the ages of a group of people in a   village

(in Years)
15-18
19-22
23-26
27-30
31-34
35-38

Frequency
40
33
25
10
8
4

Using an assumed mean of 24.5     calculate the mean of the distribution

If (x+2) and (x-1) are factors of f(x) =6x4+mx3-13x2+nx+14 find the
Values of m and n
Remainder where f(x) is divided by (x+1)

An object is projected vertically upward with a velocity of 80ms-1 find the
Maximum height reached;

SECTION B: Answer FOUR question only from this section (52 Marks)
All questions carry equal marks

9(a). The 3rd and 6th terms of a geometric progression (G.P) are 2 and 54 respectively. Find the
Common ratio
First term
The sum of the first 10 term; correct to the nearest whole number.

(b). The points (7,3), (2,8) and (-3,3) lie on a circle find the
(i) Equation
10. The table below shows the distribution of hours spent at work by
employees of a factory in a week

Time (hours)
20-29
30-39
40-49
50-59
60-69
70-79

No. of persons
8
11
23
25
8
5

(a). Draw an Ogive for this distribution
(b). Using your graph estimate the

(i) Median (ii) Lower quartile (iii) 40th
percentile
(iv) number of employees� that spent at least 50 hours 30 minutes

11. The table below shows the corresponding value of two variables X and Y
X
33
31
28
25
23
22
19
17
16
14

Y
4
6
4
10
12
10
14
15
18
22

(a). Plot a scatter diagram to represent the data
(b). Calculate
(c). Draw the line of best fit to pass through ( )
(d). from your graph in C, determine the
(i) relationship between X and Y
(ii) Value of Y and X is 24
A survey indicated that 65% of the families in an area have cars. Find correct to three decimal places the probability that among 7 families selected at random in the area
exactly 5
3 or 4
At most 2 of them have cars
13a. If 18Cr = Cr+2, find rC5
(b). Five (5) female and seven (7) male teachers applied for 4 vacancies in    a junior High Scholl. The teachers are equally qualified. Find the numbers of ways of employing the 4 teachers. If
(i) There is no restriction
(ii) at least 2 of them are females
14a. Write down the first four terms of the binomial expansion of (2  - 1/2x)5 in   ascending powers of x
14b.Use your expansion in (a) to find correct to two decimal places the value     of (1.99)5
15a.  Resolve into partial fractions
15b. The Position vectors of point P,Q and R with respect to the origin are (4i-  5j), (i+3j) and      (-   5i+2j) respectively. If PQRM is parallelogram find
the position vector of M

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# Further Mathematics. Third Term SS2.

THIRD TERM  EXAMINATION, 2009/2010 SESSION.
SUBJECT: FURTHER MATHEMATICS (1)
CLASS: SSS 2                 TIME ALLOWED: 2HRS

If P={x:1=x=6}and
Q={x:2<x<9}
where x
R,
find PnQ (a) {x:2=x=6}
(b) {x:2=x<6} (c) {x:2<x<6} (d) {x:2<x=6}
simplify -2/3 (a) -4 (b) -1/4 (c) 1/8 (d) 4

A binary operation * is defined on the set R of real numbers by a*b=
find the value of v2*v6 (a) v3 (b) 3v2/4 (c) v3/2 (d)

If (x-3) is a factor of 2x3+3x2-17x-30 find the remaining factors (a) (2x-5)(x-2) (b) (2x-5)(x+2) (c) (2x+5)(x-2) (d) (2x+5)(x+2)

Given that (v3-5v2)( v3+v2)=P+qv6 find q (a) 4 (b) -4 (c) -5 9d) -7

Find the coefficient of x4 in the binomial expansion of (1-2x)6 (a) 320 (b) 240 (c) -240 (d) -320

Find the equation of the line passing through (0,-1) and parallel to the y-axis (a) y=-1 (b) y=0 (c) x=0 (d) x=-1

Find the sum of the exponential series 96+24+6+�. (a) 144 (b) 128 (c) 72 (d) 64

Evaluate Log0.258 (a) 3/2 (b)2/3 (c) -2/3 (d) -3/2

Evaluate (a)1 (b)1/2 (c)0 (d) -1
A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man (a) 15 (b) 40 (c) 70 (d) 175

Simplify (a) 24 (b) 18   (c) 12  (d) 6
.
The area of a sector of a circle is 3cm2 if the sector subtends an angle of 1.5 radians at the centre calculate the radius of the circle. (a) 1cm (b)v2cm (c)2cm (d) 4cm

In a firing contest the probabilities that Joy and Oyinkansola in the target are 2/5 and 1/3 respectively. What is the probability that none of them will hit the target (a)1/5 (b) 2/5 (c) 3/5 (d) 4/5

The equation of the line of best fit for variable x and y is y=19.33+0.42x, where x is the independent variable. Estimate the value of y when x=15 (a) 18.91 (b) 19.74 (c) 25.63 (d) 38.23

Find the coordinates of the centre of the circle 4x2+4y2-5x+3y-2=0 (a) (-5/4,3/4) (b) (3/8,-5/8) (c) (5/8,-3/8) (d) (-5/4,-3/4)
A and B are two independent events such that P(A)=2/5 and P(AnB)=1/15

find P(B) (a) 3/5 (b) 1/3 (c) 1/6 (d) 2/15

Calculate correct to one decimal place the angle between 5i+12j and 2i+3j (a)54.8� (b) 56.3� (c) 66.4� (d) 76.3�

The sum of the first three terms of an Arithmetic progression (A.P) is 18. if the first term is 4. find the product (a)130 (b) 192 (c)210 (d) 260

The gradient of a line passing through the points P (4, 5) and Q(x, 9) is �. Find the value of x (a) -4 (b) 0 (c) 4 (d) 12
Simplify       (a) � (b) �v3 (c) 3 (d)2v3

Given that log2y1/2=log5125 find the value of y (a) 16 (b)  25 (c)36 (d) 64
Simplify (a)3v2 (b)2v3 (c) v3 (d) v2

Find the area of the circle whose equation is x2+y2-4x+8y+11=0 (a)3

Find the surd form the value of tan 15� (a) (2+v3) (b) (1+v3) (c) (3-v1) (d) (2-v3)

A bag contains 2 red and 4 green sweet each from the box one after the other without replacement. What is the probability that at a sweet with green wrapper is picked (a)1/5 (b)2/5 (c)8/15 (d)14/15

Evaluate   (a) 4   (b) 3 (c) 2 (d) 0
Find the value of p which will make (x2-x+P) a perfect square (a) -1/2 (b)1/4 (c)1/2 (d) 1

The equation of a circle is given by x2+y2-4x+2y-3 find the radius and the coordinates of its centre (a) 3,(-1,2) (b) 2v2,(2,-1) (c)2v2,(2,1) (d) 9,(2,-1)
The Polynomial g(x) =2x3+3x2+qx-1 has the same remainder when divided by (x+2) and (x-1). Find the value of constant q (a) -11 (b) -9 (c) -3 (d) -1

How many ways can 12 people be divided into three group of 2,7 and 3 in that order (a) 7,920 (b) 792 (c)187 (d)42

Given that P=4i +3j find the unit vector in the direction of P (a) 1/3(4i+3j) (b) 1/3(3i+4j) (c)1/5(3i+4j) (d)1/5(4i+3j)

Three students are working independently on a further mathematics problem. Their respective probabilities of solving the problem are 0.6, 0.7 and 0.8. what is the probability that at least one of them solves the problem (a) 0.024 (b) 0.336 (c) 0.664 (d) )0.976

A group of 5 boys and 4 girls is to be chosen from a class of 8 boys� and 6 girls. In how many ways can this be done? (a) 840 (b) 480 (c)408 (d) 380

Calculate correct to one decimal place the standard deviation of the numbers -1,5,0,2 and 9  (a) 7.2   (b) 6.6   (c) 3.6   (d) 3.2

Two statements are represented by p and q as follows: P: he is brilliant q: he is regular in class. Which of the following symbols represent the statement �he is regular in class but dull�? (a) qv~P  (b) q^~p   (c) ~q^~p   (d) ~q?~p

Find the coefficients of x4 in the binomial expansion of (2+x)6 (a)120 (b)80 (c)60 (d)15

Given f(x) = 4x3+2x2+5 find f1(2) (a)56 (b)75 (c)90 (d)45

Find the derivative of     (a)2x + 2 -    (b) 2x � 2 - (c) 2x+2-3x4 (d) 2x-  2+

THIRD TERM  EXAMINATION, 2009/2010 SESSION.
SUBJECT: FURTHER MATHEMATICS (2)
CLASS:  SSS 2                  TIME ALLOWED:2�HRS

SECTION A: Answer ALL Questions in this section (48 marks)
Solve the simultaneous equation log2x-log2y=2, log2(x-2y)=3
Given that tan 2A =  evaluate tan 15�

Express in the form mv2+nv5 where m and n are rational numbers

Differentiate with respect to x, x3+2x from the first principles

The sum of 2nd and 5th terms of an arithmetic progression (A.P) is 42. if the difference between the 6th and 3rd term is 12 find the
Common difference
First term
20th term

The table shows the distribution of the ages of a group of people in a   village

(in Years)
15-18
19-22
23-26
27-30
31-34
35-38

Frequency
40
33
25
10
8
4

Using an assumed mean of 24.5     calculate the mean of the distribution

If (x+2) and (x-1) are factors of f(x) =6x4+mx3-13x2+nx+14 find the
Values of m and n
Remainder where f(x) is divided by (x+1)

An object is projected vertically upward with a velocity of 80ms-1 find the
Maximum height reached;

SECTION B: Answer FOUR question only from this section (52 Marks)
All questions carry equal marks

9(a). The 3rd and 6th terms of a geometric progression (G.P) are 2 and 54 respectively. Find the
Common ratio
First term
The sum of the first 10 term; correct to the nearest whole number.

(b). The points (7,3), (2,8) and (-3,3) lie on a circle find the
(i) Equation
10. The table below shows the distribution of hours spent at work by
employees of a factory in a week

Time (hours)
20-29
30-39
40-49
50-59
60-69
70-79

No. of persons
8
11
23
25
8
5

(a). Draw an Ogive for this distribution
(b). Using your graph estimate the

(i) Median (ii) Lower quartile (iii) 40th
percentile
(iv) number of employees� that spent at least 50 hours 30 minutes

11. The table below shows the corresponding value of two variables X and Y
X
33
31
28
25
23
22
19
17
16
14

Y
4
6
4
10
12
10
14
15
18
22

(a). Plot a scatter diagram to represent the data
(b). Calculate
(c). Draw the line of best fit to pass through ( )
(d). from your graph in C, determine the
(i) relationship between X and Y
(ii) Value of Y and X is 24
A survey indicated that 65% of the families in an area have cars. Find correct to three decimal places the probability that among 7 families selected at random in the area
exactly 5
3 or 4
At most 2 of them have cars
13a. If 18Cr = Cr+2, find rC5
(b). Five (5) female and seven (7) male teachers applied for 4 vacancies in    a junior High Scholl. The teachers are equally qualified. Find the numbers of ways of employing the 4 teachers. If
(i) There is no restriction
(ii) at least 2 of them are females
14a. Write down the first four terms of the binomial expansion of (2  - 1/2x)5 in   ascending powers of x
14b.Use your expansion in (a) to find correct to two decimal places the value     of (1.99)5
15a.  Resolve into partial fractions
15b. The Position vectors of point P,Q and R with respect to the origin are (4i-  5j), (i+3j) and      (-   5i+2j) respectively. If PQRM is parallelogram find
the position vector of M