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Mock SS3 Maths questions

```
MOCK EXAMINATION, 2010/2011 SESSION.
SUBJECT: MATHEMATICS 1(OBJECTIVE)		                                                        CLASS: SSS 3  	         	         TIME ALLOWED: 1½HRS

1)The simple interest on ?P for 4 years at 3 % per annum is ?42,000.00. What is the value of P?
A. ?342,000.00		B. ?300,000.00	C. ?258,000.00
D. ?150,000.00
2)   Make R the subject in the relation.
A. 		B. 		C. 		D. 
3)   Evaluate: 21 x 12
A. 1022		B. 1122		C. 1202		D. 2122
4)  If find K.
A. 1			B. 2			C. 3			D. 4
5)  Simplify: , correct to two significant figures.
A. 75.0		B. 15.0			C. 8.7			D. 3.9
6)  If y is inversely proportional to x and x = 3 when y = 4, find y when x = 2.
A. 1			B. 3			C. 6			D. 9
7)  Which set of values is represented on the number line below?

A. -2 =  x = 4		B. -2 = x = 4		C. -2 =  x = 4		D. -2 =  x = 4
8)  Find the value of yz from equations: 4y = 3z and 8y = 9z + 12.
A. 12		B. 7			C. -7			D. -12
9)  Factorize the expression: .
A. 	B. 	C. 	D. 
10)  A sector of a circle of radius 3 cm subtends an angle of 80° at the centre. Find, in terms of p,
the area of the sector.
A. 3p  		B. 		C. 2p		D.
11) What is the coefficient of xy in the expansion of 
A. -11		B. -5			C. 5			D. 11

12)  If  and find 
A. 4.3088		B. 6.1544		C. 6.3088		D. 8.6176
13)  Evaluate: .
A. 1			B. 3			C. 16			D. 48
A distance of 5.6km is represented by a length of 28mm on a map. Use this information to answer questions 16 and 17.
14)  What is the scale of the map?
A. 2	B. 		C. 		D. 
15)  What length on the ground does 10cm on the map represent?
A. 2 km		B. 20 km		C. 200 km		D. 2000 km
16)  Simplify: .
A. 		B.			C. 		D. 
17)

In the diagram, O is the centre of the circle. If the reflex angle ZOY = 260°, find <  ZXY
60°   	         B. 50°		C. 40°			D. 30°

18)  Express as a single fraction: 
A. 	B. 	C. 	D. 
19)  A rectangular lawn is (x – 2) m long and (x – 3) m wide. If the perimeter is 70 m, calculate    the area of    the lawn.		A. 289                B. 306               C. 324                    D. 400

20)  In the diagram below, PS//RQ /RQ/ = 6.4cm and the perpendicular /PH/ = 3.2cm. Find the area of SQR

A. 12               B. 9.60                 C. 10.24                    D. 20.48
21) In a circle, an arc of length 55cm subtends an angle of 105° at the centre. Find the radius of
the circle. (Take p = 
A. 75cm		B. 60cm		C. 55cm		D. 30cm
22)  In the diagram below, < MNL = 30°, < JKL = 73° and <  MLK = x°. Find x.
A. 77°
B. 81°
C. 103°
D. 107°

23) Find the equation whose roots are 2 and.
A. 			B. 
C. 				D. 
24) By selling an article for ?650.00, Abu gained 10% of the cost price. Find the cost price.
A. ?550.00		B. ?525.00		C. ?500.00		D. ?475.00
25) If  0 =  = 90°, express  in terms of .
A. 		B. 		C.   		D. 
26) Find the values of  for which the expression  is undefined.
A. -3 or 3		B. -1 or 4		C. 1 or 4		D. 1 or 3
27) If  is a perfect square, what is the value of ?
A. 25		B. 			C. 		D. -25
28) Obi has four times as many sweets as Olu. If he gives 21 sweets to Olu, they will of equal
number of sweets. How many sweets has Obi?
56		B. 52			C. 48			D. 44
29) Calculate the total surface area of a cube of side 5 cm.
A. 		B. 		C. 		D. 
30)

Which of these statements is not true about the Venn diagram?
I. 	II. 	III. ?		IV. 
A. I only		B. II only		C. III only		D. IV only

31) In the diagram below, O is the centre of the circle with radius 10cm.If < QKR = 90° and
/PK/ = 6cm, find /KQ/.

2 cm
3 cm
4 cm
5cm

32)                                                                    The diagram shows a cone which was formed from
a sector of a circle. Calculate, correct to the nearest
degree, the angle of the sector of the circle from
which the cone was formed.

A. 332°		B. 277°		C. 150°		D. 138°

33) In the figure below PQRSU is a circle, /ST/ = /RS/ and <  TSR = 52°. Find the value of m.
A. 128°
B. 52°
C. 104°
D. 64°

34) In the figure below FGHK is a rhombus. What is the value of angle x?
A. 90°
B. 30°
C. 120°
D. 150°

35) In the diagram below, DE//BC, DB//FE. /DE/ = 2cm /FC/ = 3cm, /AE/ = 4cm. Determine the
length of /EC/.
8cm
6cm
4cm
-4cm

36) Which of the following statements is wrong?
A. If a triangle is equiangular then it is also equilateral.
B. If a triangle is equilateral then it is also equiangular.
C. If two triangles are congruent then they are also similar.
D. If two triangles are similar then they are also congruent.37) Given that  and, find 
A. -1.3010		B. -0.6990		C. 1.3010		D. 0.6990
38) One of the roots of the equation   is 3. The value of  and the other root are
respectively
-2,5		B. 5,2			C. 2,-5			D. -5,-2

39) In the diagram below, <  QPS = <  SPR, /PR/ = 9cm, /PQ/ = 4cm and /QS/ = 3cm. Find /SR/.
A. 6 cm
B. 3 cm
C. 4 cm
D. 2 cm

40) Two triangles have the same area if;
A. One side and the opposite angle in one triangle are equal to one side and the opposite
angle in the other triangle.
Three angles in one triangle are equal to three angles in the other triangle.
Three sides in one triangle are equal to the three sides in the other triangle.
Two angles in one triangle are equal to two angles in the other triangle.
41) In a class of 45 students, every student has to offer either chemistry or economics or both. If
25 students offer chemistry while 34 offer economics, how many students offer both subjects
20			B. 15			C. 14			D. 11

42) When a plane is 800m above the ground, its angle of elevation from a point P on the ground
is 30°. How far is the plane from P by line of sight?
A. 400m		B. 800m		C. 1500m		D. 1600m
43) The locus of a point which moves in a plane such that it is equidistant from two fixed points
A and B is;
The perpendicular bisector of the line segment AB.
A line parallel to the line segment AB.
Internal angle bisector of the line segment AB.
A circle with the line segment AB as the diameter.

44) Each side of a regular convex polygon subtends an angle of 30° at its center. Calculate each
interior angle.
75°		`	B. 150°		C. 160°		D. 168°
45) The solid below is a cylinder surmounted by a hemispherical bowl. Calculate its volume.
A. 2259cm
B. 1540cm
C. 3080cm
D. 4518cm

46) If the mean of the numbers 0, x + 2, 3x + 6 and 4x + 8 is 4, find their mean deviation.
A. 4			B. 3		C. 2			D. 0
47) An aircraft flies from a point X(30°S, 44°E) to a point Y(30°S, 28°W) in 8 hours. If the
radius of the Earth is 6,370Km, p = , and the plane flies along the parallel of latitude, its
average speed, to the nearest kilometer is;
462Kmh		B. 620Kmh		C. 770Kmh		D. 800Kmh

48) In the diagram below, O is the center of the circle and <  TOS = 100°, if <  SQR = 70°,
what is <  QTO?

A.30°
B.40°
C.60°
D.20°

49) A man walks 2Km due east and then 4Km due south. Find correct to the nearest degree, his
bearing from his original position.
027°		B. 033°		C. 063°		D. 153°

50) Find the inequality which represents the shaded portion in the diagram below.

A.
B.
C. ? 0
D. ? 0

MOCK EXAMINATION, 2010/2011 SESSION.
SUBJECT: MATHEMATICS 2(THEORY)
CLASS: SSS 3  	         	         TIME ALLOWED: 2½HRS

Instruction: Answer all questions in part A and any five(5) questions in part B.
Paper 2(THEORY).                                                                               Time;2hrs30mins.
PART A
1)a. Solve the inequality  and sketch a number line graph for the solution.
b. A sum of money invested at 8% compound interest amount to ?4,408 after 5 years, find the sum invested.
2)a. Calculate the mean deviation of the following marks; 50,55,58,50,52,54,57,56.
b. Express each of the following as a single logarithm in its simplest forms;
i) 
ii) .
3)a. An article was bought for ¢450,000 in Ghana. An import duty of 50% was paid on entering
Nigeria. Given that ?1 = ¢20, what was the total cost of the article in naira?.
b. Evaluate the following;
i) 
ii) 
4)a. In triangle ABC, c = 8.44m, a = 7.92m and B = 151.3°, calculate /AC/.
b. A shot-put sphere of radius 3cm is of mass 22Kg. Find the density of the sphere.
(Hint: density = )
5)a. Make  the subject of the formula in 
b. A ladder 8m long leans against a vertical wall so that it makes an angle of 60° with wall.
How far is the distance of the foot of the ladder from the wall?

PART B
6)a. Use the logarithm tables to evaluate;  to three significant figures.
b. The second and fourth terms of a G.P are 6 and 54 respectively, find the 6th term and the
sum of the first six terms.
7)   There are 80 people in a sport camp and each plays at least one of the following games;
Volleyball, football and handball. 31play volleyball, 36 play football and 42 play handball.
If 8 play volleyball and football, 11 play volleyball and handball and 13 play football and
Handball.
Draw a venn diagram to illustrate this information, using x to represent the number that plays all the three games.
How many of them play;
All the three games.
Exactly two of the three games.
Exactly one of the three games.
Handball only.
8)   A car was driven along a very straight road from a point A to another point B, 5km away on
a bearing of 137°. From the point B the car was driven 12km along another straight road to
another point C on a bearing of 025°.
How far is the car from the starting point?
What is the bearing of the starting point from the car?
What is the bearing of the car from the starting point?

9)  The following are marks by 50 candidates who take part in a mathematics examination;
93	70	35	51	83	60	61	73	44	90
64	88	56	34	52	61	43	57	40	58
95	71	52	71	25	86	79	35	73	44
82	67	63	53	48	78	65	98	28	72
68	50	46	54	62	35	70	41	63	73
Using class intervals of 21 – 30, 31 – 40, 41 – 50 . . .
Form the frequency table for the distribution.
Calculate the mean mark of the distribution.
Draw the cumulative frequency curve of the distribution and use it to find;
The median,
The 6th deciles,
iii) The inter-quartile range.
10)a. Using a ruler and a pair of compasses only, construct a parallelogram RXYZ such that
/XY/ = 7.5cm, <  RXY = 60°, /YZ/ = 4.7cm.
b. Locate the point P on /XY/ such that /XP/: /PY/ is 3 : 2
c. Construct the locus  of points which is 4cm from P.
d. Construct the locus of points which is equidistant from R and Z.
e. Locate the points of intersection  and  of  and . Measure //.

11)a. A plane moves from a point P on latitude 70°N and flew due south on the same longitude to
another point Q at an average speed of 875km/h for 4hours. What is the latitude of Q?

b. In the diagram below triangle ABD is right angled at B./AB/ = 3cm, /AD/ = 5cm,
<  ACB = 61° and <  DAC = °. Calculate correct to one decimal place, the value of .

D

12)a. Copy and complete the table of values below for  to one decimal place.

0°
30°
60°
90°
120°
150°
180°
120°



10.3


-0.2
-5.3

-10.3


b. Using a scale of 2cm to 30° on the  and 1cm to 1unit on the , draw the
graph of  for 0 = = 210°
c. Use the graph to solve the equation;
i) ,
ii) , correct to the nearest degree.
d. Find the maximum value of , correct to one decimal place.
13) a.	When the price of an apple increase by ?5.00, 18 apples cost ?60.00 more than 20 apples cost before the increase. Find the new price of an apple.
The cost of sinking a well varies partly as the depth of the well and partly as the number of laborers used for the job. If it cost ?1500 to sink a well of 6 meters deep with 2 laborers and ?2500 to sink a well of 9 meters deep with 5 laborers. Find the
Law of variation
Cost of sinking a well 15 meters deep with 6 laborers
Number of laborers that would sink a well of 12 meters deep at ?3000

```

Mock SS3 Maths guide

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