# Further Mathematic First Term Examination Questions 2019/2020 Session – Senior Secondary School Two,Two(SSS 1, SSS 2)

**EDUDELIGHT SECONDARY SCHOOL**

** 1 BENSON AVENUE, LEKKI PHASE 1, LAGOS.**

** First Term Examination
2019/2020Academic Session**

**CLASS: S.S.S.1
SUBJECT: FURTHER MATHEMATICS TIME: 2
HOURS**

**
OBJECTIVE**

- Determine the value for -5*4 (a) ½ (b) – ½ (a) ¼ (d) – ¼
- Given that √2 = 1.414 and √3 = 1.732 simplify (a) 4.312 (b) 3.535 (c) 8.135 (c) 9.12
- Simplify 6/√3 (a) 3.462 (b) 3.921 (c) 9.312 (d) 1.23
- Given that P = {1, 2, 3, 4, 5, 6} and Q = {9, 6, 4, 8, 10, 12} find PnQ (a) {4, 3, 2} (b) {4, 6, 1} (c) {4, 6} (d) {7, 2}
- Given that F = {1, 2, 3, 4, 5} and G = {2, 3, 5, 7} find the sum of the power of the set (a) 32 (b) 48 (c) 89 (d) 100
- Find the value of x in log
_{10}^{x}= 4 (a) 10 (b) 2000 (c) 10000 (d) 10 - What is the value of log
_{4}^{14}– log_{4}^{7}(a) – 1/5 (b) ½ (c) 3.5 (d) 2.5 - Find the value of x in the logarithmic equation ½log
_{x}^{64}= 3 (a) 5 (b) 7 (c) 2 (d) 9 - What is the value of x in the exponential equation (a) x = 0 or – 3 (b) x = 4 or -1 (c) x = 5 or -2 (d) x = 4 or -5
- Write the basic surd to single surd 5√3 (a) √75 (b) √30 (c) √10 (d) √18
- Simplify √20 + √45 + √125 – 2√80 (a) 2√5 (b) 3√0 (c) 4√3 (d) 9√2
- If P = {a, b, c, d, e, f, g, h} and Q = {a, c, I, o, g, k( are only sub set of a universal set, find P
^{1}uQ (a) [a,b,c,d,e} (b) {a, c, i, o, g, k} (c) {a, b, c, d, e} (d) {a, b, c ,g} - Given that = 0.000001 find the value of x (a) -3 (b) 8 (c) 6 (d) -6
- Solve the exponential equation (a) x = 1 and 1 (b) x = 3, 5 (c) x = 1, 4 (d) x = 5 and 2
- Solve
the equation 3(3
^{x}) – 27 (a) x = 2 (b) x = 7 (c) x = 9 (d) x = 27

**SECTION B **

Answer question one and any other two

- Solve the following logarithmic equation

A(i)

(ii)

B simplify the following

C. Determine the value for

(i)
2*1 (ii) 3* – 1 (iii) ½ * ^{4}/_{3}

- In a casino of 32 gamblers a gambler can either play Naija bet or Baba Ijebu or both. If 16 gamblers play Naija bet and 18 play baba-ijebu, and 3 do none, find how many gamblers do both.

B. Given that the operation is defined on the set of real S = {0, 1, 2, 3, 4, 5,} by x∆y = x + y – xy. Find (a) 2 5 (b)0 4 (c) 3 1 (d) 4 5

C. Find the addition and multiplication of Modulo 9 and 10

- Given
that the universal set ξ = {1, 2, 4, 6, 9, 12}, A = {4, 6, 12} B = {2, 4, 9}
find (i) A
^{i}(ii) B^{i}(iii) A^{i}nB (iv) AnB (v) (AuB)^{i}

B. Simplify 3√2 – √32 + √50 + √98

Rationalize

- Given
that X {Whole numbers less than 24}, P {Prime number less than 24}, Q {Even
numbers less than 24}. Find (i) PnQ (ii) PuQ (iii) P
^{i}nQ (iv) (PuQ)^{i}

B. Given that = 0.477 and find

**EDUDELIGHT SECONDARY SCHOOL**

** 1 BENSON AVENUE, LEKKI PHASE 1, LAGOS.**

** Third Term Examination
2019/2020Academic Session**

**CLASS: S.S.S.2 SUBJECT: FURTHER MATHEMATICS TIME: 2 HOURS**

**
OBJECTIVE**

- Find the number of different permutation of the letters o the word EXCELLENCE (a) 3500 (b) 37800 (c) 1850 (d) 4000
- Out of seven women and nine men, a committee consisting of three women and four men is to be formed. In how many ways can this be done if any women and any man may be included (a) 4100 (b) 1400 (c) 3320 (d) 4410
- Find
the equation of the circle of centre (1,4) radius 3 units (a) x
^{2}+ y^{2}– 4x – 8y + 10 (b) x^{2}+ y^{2}– 2x – 8y + 8 (c) x^{2}+ y^{2}– x + y + 10 (d) x^{2}+ y^{2}– 12x – 8y + 16 - Find the length of tangent of the circle from the given point x2 + y2 + 5x + 4y -20 = 0 at point (2,3) (a) √30 (b) √21 (c) √15 (d) √4
- Simplify (a) 4200 (b) 2400 (c) 9800 (d) 1480
- If
f and h are mapping defined on the set of real numbers by f(x) = 3x + 1, g(x) =
2x – 1 and h (x) = x
^{2}find gof (a) 8x + 2 (b) 6x + 1 (c) 7x + 3 (d) 9x + 4 - Foh
(a) 3x + 1 (b) 3x
^{2}+ 1 (c) 3x^{4}+ 1 (d) 3x^{2}+ 1 - Find
15C
_{2}(a) 105 (b) 100 (c) 102 (d) 104 - Find the mid point of the line joining p(-3, 5) and Q(5, -3) (a) (4, -4) (b) (4, 4) (c) 2, 2 (d) 1, 1
- Determine
the value of ½*½ (a) -1/2 (b)
^{1}/_{3}(c) ½ (d)^{1}/_{5} - What
is the value of
^{15}C_{2}(a) 300 (b) 600 (c) 105 (d) 70 - In how many ways can 6 member of a board of director of a company be seated round a circular table. (a) 200 (b) 170 (c) 120 (d) 45
- What
is the length of the tangent circle from the given point x
^{2}+ y^{2}– 4x + 2y – 4 = 0 at (2, -4) (a) √30 (b) √21 (c) √9 (d) √81 - What
is the equation of the circle of centre (5, -4) with radius 10 units (a) x
^{2}+ y+ – 10x + 8y – 59= 0 (b) x^{2}+ y^{2 }– 20x + 16y – 50 = 0 (c) x^{2}+ y^{2}– 10x + y – 10 = 0 (d) 2x^{2}+ 2y2 – 45x + 20y – 80 = 0 - What is the mid point of the lines joining the following points A(3,5) and B(1,3) (a) (4,5) (b) 8,7 (c) 9, 4 (d) 2,4
- Find the gradient of the line joining (3,2) and (7,10) (a) 2 (b) 14 (c) 8 (d) 19
- From
question 16 what is the angle of slope of the line (a) 61.5
^{0}(b) 63.43^{0}(d) 18.1^{0}(d) 30.2^{0} - The distance between S(-3, 2) and T (1, -4) is (a) √20m (b) √18 (c) √50 (d) √70
- In how many ways can nine women be seated at a round table if two particular women must not sit next to each other (a) 8! (b) 7! (c) 9! (d) 10!
- Find the number of different arrangements of the letters of the words OGBOMOSO (a) 1600 (b) 1200 (c) 1680 (d) 2000

**SECTION B **

Instruction: Answer any two

1a. Find the number of ways a committee of 5 consisting of 3 males and 2 females, can be formed from a social club consisting of 8 males and 7 females.

b. Find the length of the following tangent

i.
x^{2} + y^{2} + 5x + 4y – 20 = o at (2, 3)

ii.
3x^{2} + 3y^{2} + 5x + 6y – 30 = 0 at (2, 2)

- 2x
^{2}+ 2y^{2}+ x – 2y – 17 = 0 at (5, -3)

c. Find the equation of the tangent and normal to the following circle at the given point of the circle

i.
3x^{2} + 3y^{2} – 8x – 6y – 61 = 0 at (4, 5)

2a. Find the centre and the following radii of the following

- X
^{2}+ y2 – 6x – 8y + 5 = 0 - 5x
^{2}+ 5y2 – 3x + 7y – 1 = 0 - 2x
^{2}+ 2y2 – x + y – 3 = 0

bi. Find the centre and radius of the circle
36x^{2} + 36y^{2} – 24x – 36y – 23 = 0

ii. What is the equation of the circle of r centre (-3, 2) with radius of 3 units

3a. Given that a = -5, b = -f and c = a^{2}
+ b^{2} – r^{2} from (x – a)^{2} + (y -b)2 = r^{2}
the general equation of a circle is x^{2} +y^{2} +2gx +2fy + c=
0

b. Out of seven women and nine men, a committee consisting of three women and four men is to be formed. In how many ways can this be done if

i. Any woman and any man may be include

ii. One particular man must be on the committee.

c. Simplify