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## maths ss1 exam questions

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SECOND TERM  EXAMINATION, 2010/2011 SESSION.
SUBJECT: MATHEMATICS 2(THEORY)
CLASS:SSS 1	       	         	    TIME ALLOWED: 2HRS

PART A (Answer all questions in this part)
(a) Evaluate and express your answer in statndard form:                                                (b) Without using mathematical tables or calculator, evaluate: (73.8)2 – (26.2)2                           (c) Simplify ; , expressing your answer in the form  where a and b are positive integers.
(a) Simplify                                                                                                                (b) A cylindrical well of radius 1m is dug out to the depth of 8m. Calculate in m3, the volume of soil dug out.
(a) A sector of a circle of radius 6cm has an angle 105° at the centre. Calculate                             (i) its perimeter										               (ii) Area                                           [Take ]                                                                       (b) If = {2,3,4,5,6,7}										      P = {2,4,6} 										               and    Q = {2,3,5,7}      find							                             (i) P’										                            (ii) Q’											               (iii) (PQ)’
(a) Out of 30 candidates applying for a post, 17 have degrees, 15 diplomas and 4 have neither degree nor diploma, how many has both?                                                                                        (b) Simplify 

PART B : Answer any three questions
A paper cone has a base diameter of 8cm and a height of 3cm                                                          (a) Calculate the volume of the cone in terms of                                                                          (b) Calculate its slant height, hence                                                                                                  (c) Calculate the curved surface area of the cone in terms of                                                                                                                                                                                                                          (d) If the cone is cut opened into a sector of a circle, find the angle of the sector.

(a)
10cm

O   63°
10cm
Calculate the area of the shaded segment of the circle shown above. [Take ]                  (b) A tin has a radius 8cm and height 6cm. Find                                                                             (i) the total surface area of the tin                                                                                                    (ii) the volume of the cylindrical tin
(a) A cylindrical pipe is 28m long. Its internal radius is 3.5cm and external radius 5cm. Calculate                                                                                                                              (i) the volume in cm3 of metal used in making the pipe                                                                 (ii) the volume of water in litres that the pipe can hold when full, correct to 1 decimal place. [Take ]								                                        (b) Solve the equation;  2x2 – 11x + 15 = 0
(a) Use tables to calculate  		                                                                (b) Find the equation whose roots are  - and   - 		                                                   (c) Express as a single fraction : 
In a market survey, 100 traders sell fruits. 40 sell apples, 46 oranges, 50 sell mangoes, 14 sell apples and oranges, 15 sell apples and mangoes and 10 sell all the three fruits. Each of the traders sell at least one of the three fruits.                                                                                                    (i) Represent the information on a Venn diagram                                                                                 (ii) How many sell oranges and mangoes only?

SECOND TERM  EXAMINATION, 2010/2011 SESSION.
SUBJECT: MATHEMATICS 1(OBJECTIVE)
CLASS: SSS 1	       	         	      TIME ALLOWED: 2HRS

Find the radius of a circle whose area is 154cm2. [Take ]                                                       (a) 2.7cm    (b) 5cm   (c) 7 cm  (d) 22 cm
Find the total area of the surface of a solid cylinder whose base radius is 4 cm and height is 5cm       (a) 5 cm2    (b) 72cm2   (c) 96cm2   (d) 192cm2
Fiind the area of the curved surface area of a cone whose base radius is 6cm and whose height is 8cm. [Take ]    (a) 188.57cm2   (b) 188.08cm2   (c) 188cm2   (d) 100cm2
The angle of the sector of a circle of radius 35cm is 288. Find the perimeter of the sector [Take ]  (a) 114cm   (b) 141cm   (c) 211cm   (d) 246cm
In a circle, a chord 8cm long is at distance of 3cm from its centre. Find the length of the chord which is at a distance of 4cm from the centre of the same circle.                                                                     (a) 5cm   (b) 6cm   (c) 9cm   (d) 10cm
Simlify  (a) ½   (b) 2   (c) 1   (d) 0
A right circular cone of height h cm has a base diameter of x cm. Find the length of the slanting side  (a)  (b)   (c)    (d) 
An arc of a circle of radius 6cm is 8cm long. Find the area of the sector.                                            (a) 5cm2  (b) 24cm2   (c) 36cm2   (d) 48cm2
A solid cylinder of radius 3cm has a total surface area of 36cm2. Find its height.                             (a) 2cm   (b) 3cm  (c) 4cm   (d) 5cm
Calculate the perimeter, interma of , of a sector of a circle of radius 8cm and angle 45°.                 (a) 2    (b) 8 + 2   (c) 16 + 2   (d) 16 + 16
The area of a circular field is 154m2. What is the perimeter of the field? [Take ]                 (a) 44m    (b) 49m   (c) 88m   (d) 176m
Simplify             (a)     (b)    (c)    (d) 
Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm.                       (a) 1920cm2    (b) 592cm2   (c) 296cm2   (d) 148cm2
A right circular cone of base radius 14cm and height 30cm was filled with water. The content was emptied into a cylindrical can of radius 10cm. Find the height of the water in the can.  (a) 58.8cm   (b) 24.4cm   (c) 19.6cm   (d) 6.5cm
A chord of a circle 8cm long subtands an angle of 120° at the centre. Find the radius of the circle.     (a) 6.93cm   (b) 5.00cm   (c) 3.46cm   (d) 4.62cm
Simplify    (a) 3xy3   (b) 3xy6   (c) 9xy3    (d) 9y3

The radius of a tyre 1 ½ m. Find correct to the nearest whole number, the number of revolutions       (a) 10   (b) 11   (c) 21   (d) 22
Find the quadratic equation whose roots are c and –c    (a) x2 + c2 = 0     (b) x2 – c2 = 0      (c) x2 + 2cx + c2 = 0   (d) x2 – 2cx + c2 = 0
Factorise 8a2 – 18b2    (a) (4a + 3b)(2a – 3b)    (b) (4a – 3b)(2a + 3b)    (c) 2(4a – 3b)(c + 3b)           (d) 2(2a – 3b)(2a + 3b)
If R = {x: x2 = 16, x>5}, then R is   (a) 0   (b) {0}   (c)   (d) {}
A cone with a sector of angle 45° is cut off a circle of radius r cm. Find the base radius of the cone.   (a)    (b)    (c)    (d) 
Given that the circumference of a circle is 72cm. Calculate its radius. [Take ]                               (a) 11.45cm   (b) 11.54cm   (c) 11.55cm   (d) 10.45cm
A chord of a circle radius subtends an angle of 120° at the centre of the circle. Find the length of the chord  (a)   (b)   (c)  cm   (d) 3cm
Which of the following statements is true  for the set P = {- 3.2 = x =5}, where x is an integer?        (a) Least value of x is – 3.2   (b) least value of x is – 3  (c) Greatest value of x is 4.9    (d) greatest value of x is 5
A sector of aa circle of radius 14cm is folded into a cone of base radius 7cm. If the base of the cone is closed, find the total surface area of the cone.                                                                                       (a) 154cm2   (b) 308 cm2   (c) 462cm2   (d) 562cm2
If X = {a,b,c}, Y = {a,b,c,d,e} and Z = {a,b,c,d,e,f,g} then (XY)  (XZ)  is                                     (a) {a,b,c}   (b) {a,b,c,d,e}   (c) {a,b,c,d,e,f,g}    (d) 
Evaluate    (a)    (b)    (c)  (d) 
The arc of a circle whose radius is 10.5cm subtends an angle of 60° at the centre. Find the length of the arc. [Take ]   (a) 10.5cm  (b) 11cm  (c) 21cm  (d) 22cm
The angle of elevation of the top of a tower from a point on the ground which is 36m from the foot of the tower is 30°. Calculate the height of the tower.                                                                               (a) 62.35m   (b) 20.78m   (c) 18.00m   (d) 10.39m
An arc of a circle of radius 2cm subtends an angle of 60° at the centre. Find the area of the sector.    (a)    (b)   (c)    (d) 
If I is the set of positive integers and P = {x : x I, x2 < 10 and x 0}, then                                      (a)  P = {10,1}   (b)   {0,1,2,3}    (c) P = {1,2,3}   (d) P is an infinite set
Solve the equation 10 – 3x – x2= 0.    (a) x = 2 or – 5   (b) x = - 2 or 5    (c)  x = 1 or 10  (d) x = 2 or 5
An open rectangular box is made of wood 2cm thick. If the internal dimensions of the box are 50cm long, 36cm wide, and 20cm deep. The volume of the wood in the box is                                            (a) 11,520cm3   (b) 36,000cm3   (c) 38,200cm3   (d) 47,520cm3

In a circle of radius 12cm, a sector formed by two radii subtends an angle of 105° at the centre of the circle. Find the perimeter of the sector formed.                                                                                     (a) 24.0cm   (b) 40.0cm   (c) 46.0cm   (d) 47.2cm
Find the area of a rectangle of length 4cm and whose diagonal is 8cm. (Leave your answer in surd form)  (a) 8cm2   (b) 12cm2   (c) 16cm2  (d) 16cm2
Find the value of x for which 3(2x-3) = 384   (a) 4   (b) 9   (c) 10   (d) 15
A cylinder of height h and radius r is open at one end. Its surface area is                                            (a)    (b)   (c)   (d) 
The areas of the major and minor sectors of a circle are 63cm2 and 27cm2 respectively. Calculate the angle of the minor sector   (a) 27°    (b) 54°   (c) 108°   (d) 126°
A bicycle wheel of radius 42cm is rolled over a distance of 66 metres. How many revolutions does it make? [Take ]   (a) 2.5   (b) 5   (c) 25   (d) 50
Simplify    (a) 2n   (b) 2   (c) 2n – 1   (d) 1
Given that  = {1,2,3,...,10}, P = {x: x is prime} and Q = { y: y is odd}, find P’Q                        (a) {2}     (b) {1,9}   (c) {3,5,7}     (d) {4,6,8,10}
Factorise 2e2 – 3e + 1  (a) (2e – 1)(e – 1)   (b) (e + 1)(2e + 1)   (c) (2e + 3)(e – 2)    (d) (2e – 3) (e – 1)
Find the area of the curved surface of a cone generated by a sector of a circle radius 6cm when the base radius of the cone is cm. [Take ]                                                                                  (a) 66cm2   (b) 77cm2   (c) 132cm2   (d) 34cm2
The lengths of the parallel sides of sides of a trapezium are 5cm and 7cm. If its area is 120cm2, find the perpendicular distance between the parallel sides.                                                                          (a) 5.0cm   (b) 6.9cm   (c) 10.0cm   (d) 20.0cm
The height of a pyramid on a square base is 15cm. If the volume is 8cm3, find the length of the side of the base   (a) 3.3cm   (b) 5.3cm   (c) 4.0cm   (d) 8.0cm
Evaluate    (a)   (b) 3   (c)    (d) 
P = {3,9,11,13} and Q = {3,7,9,15} are subsets of the universal set µ = {1,3,7,9,11,13,15}. Find P’Q’  (a) {1, 11}   (b) {1}  (c) n{5,7,15}   (d) {3,9}
Construct a quadratic equation whose roots are – ½ and 2  (a) 3x2 – 3x + 2 = 0  (b) 3x2 + 3x – 2 = 0   (c) 2x2 – 3x + 2 = 0   (d) 2x2 – 3x – 2 = 0
The total surface area of the walls of a room 7m long, 5m wide and x m high is 96m2. Find the value of x   (a) m   (b) 2m   (c) 4m   (d) 8m
Expand (2x – 3y)(x – 5y)    (a) 2x2 + 13xy – 15y2   (b) 2x2 – 13xy – 15y2    (c) 2x2 + 13xy + 15xy2   (d) 2x2 – 13xy + 15y2

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### maths ss1 exam guide

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