# Mathematics Third Term Examination Questions 32019/2020 Session – Senior Secondary School Two( SSS 2)

**EDUDELIGHT GROUP OF SCHOOLS**

**1 Benson Avenue, Lekki Phase
1, Lagos.**

**3RD TERM EXAMINATION
2019/2020 SESSION**

**SUBJECT: FURTHER MATHEMATICS** **CLASS: SSS 2 TIME: 2HRS **

**SECTION A (OBJECTIVES)**

- Simplify: (A) – tan θ (B) –cos θ (C) tan θ (D) cos θ
- If (x+1) is a factor of the polynomial: ,find the value of p
- -2 (B)- 3 (C)- 4(D)15
- A polynomial is defined by find
*f*(2) (A) -8 (B) -4 (C) 4 (D) 2 - Differentiate with respect to x . (A) (B) – (C) (D)
- In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the
**correct**mean. (A)19 (B) 21 (C) 23 (D) 24 - Given that
^{n}P_{r}=90 and^{n}C_{r}=15, find the value of r. (A) 2 (B) 3 (C) 5 (D) 6 - Which of the following options is not a measure of Central Tendency (A) Mode (B) Variance (C) Mean (D) Median
- A fair die is tossed twice. Find the probability of obtaining a3 and a5.

(A) (B) (C) (D) - Find the number of different arrangements of the letters of the word IKOTITINA. (A) 30240(B) 60840 (C) 120960 (D) 362880
- A box contains 4 red and 3 blue identical balls. If two balls are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.(A) (B) (C) (D)
- If y = 3e
^{-4x}, find . (A) -3e^{-4x}(B) -12e^{-4x}(C) 12e^{-4x}(D) 4e^{-3x} - The reciprocal of tanx is (A) cosec
^{2}x (B) cot^{2}x (C) sec^{2}x (D) cotx - Differentiate sin 5x. (A) cos 5x (B) – 5sin 5x (C) 5 cos 5x (D) -5cos 5x
- The reciprocal of sin θ is (A) sec
*Ѳ*(B) cot*Ѳ*(C) tan*Ѳ*(D) cosec*Ѳ* - The reciprocal of cot θ is (A) sec
*Ѳ*(B) sin*Ѳ*(C) tan*Ѳ*(D) cosec*Ѳ* - Find the standard deviation of 2,3,5 and 6 (A) (B) (C) (D)
- If cotθ = , where θ is an acute angle, find sin θ. (A) (B) (C) (D)
- Find the gradient of the line passing through points P(1,1), and Q (2,5).

(A) 4 (B) 3 (C) 2 (D) 5 - Solve for x and y if x – y = 2 and x
^{2}-y^{2}= 8 (A) (1,3) (B) (-1,3) (C) (3,1) (D) (-3,1) - If x is inversely proportional to y and x = 2 when y = 2. Find x when y = 4

(A) 4 (B) 5 (C) 2(D) 1 - If (x-3) is a factor of 2x
^{3}+3x^{2}+17x-30, find the remaining factors

(A) (B) (C) (D) - Evaluate
^{5}C_{3}+^{5}C_{2}(A) 40 (B) 30 (C) 20 (D) 10 - Polynomial is defined by (A) -8 (B)-2 (C)12 (D)14
- If the mid-point of the line joining (1-k,-4) and (2,k+1) is (-k,k), find the value of k.(A) -4 (B) -3 (C)-2 (D) -1
- If find the values of x at the turning points.(A) (B) (C) 1, – (D) 1,
- A binary operation, ∆, is defined on the set of real numbers by
*a ∆ b = a + b + 4.*Find the identity element of operation ∆ . (A)4 (B)2 (C) (D) -4 - Express the product of 0.21 and 0.34 in standard form.

(A) 7.14 x 10^{-1}(B) 7.14 x 10^{-2}(C) 7.14 x 10^{-3}(D) 7.14 x 10^{-4} - Find k if 6k7
_{8}= 511_{8}. (A) 6 (B) 5 (C) 3 (D) 2 - Evaluate . (A) 6 (B) 5 (C) 3 (D) 2
- Evaluate . (A) 6 (B) 5 (C) 3 (D) 2
- If (3x – 1) is a factor of the polynomial f(x) = 4x
^{3}– 4x^{2}– X + P, find the value of constant p. (A) 7/27 (B) 17/27 (C) 5/27 (D) -7/27 - Evaluate (101
_{2})^{2}, leaving your answer in base two. (A) 10101_{2}(B) 10010_{2}(C) 11001_{2}(D) 11101_{2} - If (2x + 3)
^{3}= 125, find the value of x. (A) 0 (B) 1 (C) 2 (D) 3 - Evaluate . (A) -2 (B) 2 (C) 0 (D) 1
- Find the numbers of arrangement of 7 objects taking 3 at a time.

(A) 40 (B) 30 (C) 20 (D) 10 - Find the numbers of arrangement possible from the word SUCCESS.

(A) 30 (B) 50 (C) 180 (D) 210 - Eight football clubs are to play in a league on home and away basis. How many matches are possible? (A) 14 (B) 28 (C) 56 (D) 128
- Given that 2
^{x}= 0.125, find the value of x. (A) 0 (B) -1 (C) -2 (D) -3 - 40. If p and q are the roots of the equation 3X
^{2}– 16X + 2=0,

find the value of p + q(1+p). A. – 14 B. – 6 C. – 4 D.6

**SECTION B (THEORY)**

**Instruction: Answer any four questions in this section.**

(1a)
Differentiate (x-3)(x^{2}+5) with respect to x. (5marks)

(1b) Simplify –
(5marks)

(2a)
The ratio of the coefficients of x^{4} to x^{3} in the binomial
expansion of (1+2x)^{n} is

3:1. Find the value of n. (4marks)

(2b) given that A = ,
Show that AA^{-1} = I. (6marks)

(3a)
Find the gradient of x^{2} + y^{2} +3xy = 14 at the point (1,
3). (5marks)

(3b)If f(x) = 6x^{2 },
find Lim f( x+h) – f(x) (5Marks)

(4a) If = , find . (5marks)

(4b) If = -24. Find the value of x. (5marks)

(5a)Given
that Q(x) = ax^{2} + bx +5. If
Q(1)=6 and Q(-1)=12, determine thevalues of

a and b.
(4marks)

(5b) If the first three term of the expansion of (1+kx)^{n} in
ascending powers of x

are 1 + 20x + 160x^{2}. Find the value of n and k. (6marks)

(6) Using Matrix method solve the
equation below

3x – y – z = 11

x + 5y + 2z = -1

2x + 3y + z = 15.

(10marks)