# Mathematics Second Term Examination Questions 2019/2020 Session – Senior Secondary School Three ( SSS 1, SSS 2)

**EDUDELIGHT GROUP OF SCHOOLS**

**2 ^{ND} EXAMINATION 2019/2020**

** SUBJECT: **MATHEMATICS **CLASS: **S.S. 1

**SECTION A**

- Expand ( 2x – 5 )(x – 3) A. x
^{2}– 11x -5 B. x^{2}– 11x + 15 C.2 x^{2}– 5x -8 D. x^{2}– 5x -15 - The roots of a quadratic equation are – ¼
and 3. The quadratic equation is A. 4 x
^{2}– 13x -3=0 B. 4 x^{2}– 11x -3 = 0 C. 4 x^{2}+11x -3 = 0 D. 3 x^{2}– 11x -3 = 0 - The angle of a sector of a circle of radius
35cm is 288
^{0}. Find the perimeter of the sector A.246cm B. 44cm C.114cm D. 141cm - If sin β = cos β for β ≤
0 ≤ 360
^{0 }find the value of β A.135^{0}, 315^{0}B 45^{0}, 225^{0}C. 45^{0}, 315^{0}D. 135^{0}, 225^{0} - If
tan x = 2
^{2}/_{5}find the value of x; 0 < x < 90^{0}A.^{5}/_{13 }**B.**^{12}/_{13 }C.^{2}/_{5}D.^{13}/_{5} - Cos
65
^{0}has the same value as A.Sin 65^{0}*B.*Cos 295^{0 }C. Cos 115^{0}D. Cos 205^{0} - A chord is 5cm from the centre of a circle of diameter 26cm. find the length of the chord. A. 16cm B. 24cm C.18cm D.25.51cm
- The
n
^{th}3 x 2^{(2-n)}. Write down the first three terms of the sequence. A.^{3}/_{2},3,6 B. 6,3,^{ 3}/_{2}C.^{ 3}/_{2},3,1/2 D.^{ 3}/_{2},0,6 - Solve
the equation 5×2 – 4x -1 = 0 A.-1,
^{1}/_{5}B. –^{1}/_{5,},1_{ }C. 1,^{1}/_{5}D. -1,5 - P and q are two positive numbers such that p > 2q. Which of the following statement is true? A. –p > -2q B. . –p < -2q C. –q < 2p D. q < ½
- If P = {3,7,11,13} and Q = {2,4,8,16}, which of the following statement is correct ? A.( P n Q) = {2,3,4,13} B. P n Q = Ø C. . P u Q = Ø D.n( P u Q ) = 4
- A group of eleven people can speak either English or French or both. Seven can speak English and six can speak French. How many students can speak both languages? A.3 B 2 C. 1 D. 13
- The sides of a right angled triangle , in an ascending order of magnitude are 8cm,( x – 2) cm and x cm. find the value of x. A.16 B. 17 C. 34 D. 60
- Express 398753 correct to 3 significant figure A.398000 B.399000 C. 398700 D. 398800
- Which of the following bearing is
equivalent to S 50
^{0}W? A. 040^{0}B 230^{0}C. 130^{0 }D. 220^{0} - If N varies directly as M and N= 8 when M = 20, find M when N = 7. A.13 B. 17 ½ C. 15 D. 18 ½
- A sector of a circle subtends 172
^{0}at the centre of the circle has a perimeter of 600cm. find correct to the nearest cm, the radius of the circle. A. 116 cm B. 120 cm C.107 cm D. 100cm - Factorize completely 32x
^{2}y – 48x^{3}y^{3}A. 8xy ( 4x – 6x^{2}y^{2}) B. 16x^{2}y (2 – 3xy^{2}) C. 16xy (2x – 3x^{2}y^{2}) D. 8x^{2}y (4 – 6xy^{2}) - If cos ( x + 40 )
^{0}0.0872, what is the value of x . A. 65^{0}B. 45^{0}C.85^{0}D.75^{0} - Convert 35
_{10}to a number in base 2 A.1011 B. 100011 C.110011 D. 10011

Section Two. Answer any four questions from this section.

- In a school, 120 students offer Biology or Mathematics or both. 125 offer Biology and 110 offer Mathematics. How many offer Biology but not Mathematics
- a. factorize px – 2qx – 4qy = 2py b. given that the universal set U
={1,2,3,4,5,6,7,8,9,10} P={
1,2,3,4,6,10} Q ={ 1,2,3,4,5,6,7,8,9,10} show that ( P u Q ) = P
^{1}n Q^{1} - The product of two consecutive positive odd numbers is 195. Find the two numbers
- find the area of a circle with radius 7cm,
which subtends an angle of 120
^{0}at the centre. - Find the total surface area of a cylinder covered at both end of length 12cm, and radius 6cm.

**EDUDELIGHT GROUP OF SCHOOLS**

**2 ^{ND} EXAMINATION 2019/2020**

** SUBJECT:
** MATHEMATICS **CLASS:
**S.S. 2

**SECTION A**

INSTRUCTION: Answer all the questions in this section

- Find
(101
_{2})^{2}express your answer in base 2 (a) 10101 (b) 11001 (c) 19119 (d) 1101 - Simplify: 0.027
^{-1/3}(a) 3^{1}/_{3}(b) 3 (c)^{1}/3 (d)^{3}/10 - Solve
the inequality:
^{1}/_{3}(2x-1)<5 (a) x < -6 (b) x < 8 (c) x < -5 (d) x < 16 - What
is the smaller value of x for which x
^{2}+ 3x + 2 = 0? (a) -1 (b) -2 (c) 1 (d) 2 - Factorize the expression x(a-c) + y(c-a) (a) (a-c) (y-x) (b) (a-c) (x-y) (c) (a+c) (x-y) (d) (a-c) (x + y)
- Solve
the equation 3x
^{2}+ 2x – 18 = 0 (a) -3, 2 (b)^{-2}/_{3}, 9 (c) -2, 9 (d) -2, 3 - Solve the equation (x+2) (x-7) = 0 (a) 1 or 8 (b) 2 or 7 (c) -4 or 5 (d) -5 or -2

In ABC above BC is produced to D,
/AB/ = /AC/, <BAC = 50^{0}.
Find <ACD (a) 50 (b) 65
(c) 60 (d) 115

- The bearing of two point Q and R from a point
Q are 030
^{0}and 120^{0}respectively. If /PQ/= 2m and /PR/ = 5m. Find the distance QR (a) 13m (b) 11m (c) 9m - Find
dy/dx of x
^{3}– 6x^{2}+ 12x – 8 (a) 3x^{3}– 12x + 12 (b) 3x^{2}– 12x + 12 (c) 3x^{2}+ 12x – 12 (d) 3x^{2}= 12x -8 - If dy/dx moves from the positive to a negative number there arises a (a) Maximum point (b) minimum point (c) point of inflection (d) stationary point
- If two point A(2, -3), b(3, 4) are points on the graph. What is the gradient of the curve (a( 1 (b) 7 (c) -7 (d) -1
- If x varies over the set of real numbers which of the following is illustrated in the diagram above? (a) -2 < x < 3 (b) -2 < x < 3 (c) -2 < x < 3 (d) -2 < x < 3

-4 -3 -2 -1 0 1 2 3 4 x

- In triangle XYZ below XM is the altitude from X to YZ. XY = 15cm, and YM = 5cm. find the length of YZ. (a) 9cm (b) 14 cm (c) 12cm (d) 19.85cm
- Two
angles of a triangle are 41
^{0}and 49^{0}which of the following is true? It is (a) An equilateral triangle (b) a right angled triangle

X

13cm 15cm

Y 5cm M Z

- If sin
~~O~~=^{ -1}/_{2}, find the value of~~O~~between 0^{0}and 360^{0}(a) 120^{0}, 240^{0}(b) 210^{0}, 330^{0}(c) 120^{0}, 180^{0}(d) 210^{0}, 300^{0}

A tree is 8km due south of a building, Kofi is standing 5km west of the tree. Use this information to answer question 17 and 18.

- How far is K from the building (a) 4 2km (b) 8km (c) 8 2km (d) 16km
- Find
the bearing of Kofi from the building
(a) 315
^{0}(b) 270^{0}(c) 225^{0}(d)135^{0} - Find
the bearing of equivalent to 550
^{0}W (a) 040^{0}(b) 130^{0}(c) 220^{0}(d) 230^{0}

- If sin
2
~~ө~~= cos~~ө~~find~~ө~~(a) 40 (b) 22.5 (c) 45 (d)50 - If Sin 2 Ө = Cos Ө find Ө (a) 40 (b) 22.5 (c) 45 (d) 2.30

**THEORY**

Answer question number one and any other two questions

- Find the turning points on the curve and determine whether
the stationary points are maximum, minimum or points of inflexion in Y = x
^{2}– 3x + 5. - (a) A point P is 40km
from Q on a bearing of 061
^{0}calculate, correct to one decimal place, the distance of P to (i) North of Q (ii) East of Q

(b) Illustrate graphically and shade the region in which the inequalities Y – 2x < 5. 2y = x > 4

- Using the first principle, differentiate 2 x
^{2}+ 2x – 3. - Two men P and Q set off from a base camp R
prospecting for oil. P moves 20 km on a
bearing of 205
^{0}and Q move, 15km on a bearing of 060^{0}. calculate the (a) distance of Q from P (b) bearing of Q from P (Give your answer in each case correct to the nearest whole number)