Excerpt
ii
EMBASSY MATHEMATIC SERIES(E.M.S)
MATHEMATICS FOR JUNIOR HIGH SCHOOLS
(1,2&3)
QUESTIONS AND ANSWERS
From 1990 to Date
Solutions to both objectives and theory questions with guided explaination.
Learning Mathematics is like learning how to ride a bicycle.
You never know how to ride by watching others ride but learning
how to ride on your own.
3
PREFACE
Embassy Mathematics Series (EMS) has been written to meet the needs of students and
teacher in revising for internal and external examinations in Mathematics.
This book contains past questions (BECE) and solutions for both the objective test and essay
type questions from 1990 to 2015.
Most students in reading Mathematics texts have always been confronted with the issue of
not understanding the steps taken in solving the questions, this gap has been filled as every
step in our working has been explained to help the students understand what is been done.
The book will also help teachers in setting questions for class exercises, class tests and end of
term exams. The book will possibly expose teachers to certain aspects of certain topics which
are unfamiliar to them or which are not treated into great lengths, or not treated at all in most
text books.
Much pain has been taken to check mistakes and misprints but if a few of them have gone
unnoticed, I will gladly accept them and included them in the next edition.
iv
ACKNOWLEGEMENT
I will like to thank the Almighty God for the successful completion of this first edition.
A great book like this cannot be done without the help of others. I will like to
acknowledgement the help of the following individuals and organizations.
I wish to give my heart felt appreciation to Adongo Ebenezer, a Maths tutor of Zorko senior
School for his insightful suggestions and editing part of this book.
My gratitude also extends to Richmond Akumbobe for reading through the entire book.
The author is indeed grateful to Jonathan Tee, an efficient ICT tutor of Big Boss for helping
him with the paging of the book.
Special mention must be made of the West African Examinations Council. The author used
materials from this institution and is very thankful.
The author is graciously thankful to Dzadza Isaac and David Zeng for giving him a chance in
life.
I want to also thank Directors, head teachers, teachers and students of Fountain Gate
international School, Bolga and Aim Preparatory Junior High School, Bolga.
v
TABLE OF CONTENT PAGE
PREFACE ... iii
ACKNOWLEGEMENT ... iv
TABLE OF CONTENT... v
OBJECTIVE TEST B.E.C.E 1990 ... 1
ESSAY QUESTIONS B.E.C.E 1990 ... Error! Bookmark not defined.6
OBJECTIVE TEST B.E.C.E 1991 ... 8
ESSAY QUESTIONS B.E.C.E 1991 ... 13
OBJECTIVE TEST B.E.C.E 1992 ... 15
ESSAY QUESTIONS- B.E.C.E 1992 ... 21
OBJECTIVE TEST-B.E.C.E 1993 ... 24
ESSAY QUESTIONS- B.E.C.E 1993 ... 30
OBJECTIVE TEST B.E.C.E 1994... 32
ESSAY QUESTIONS-B.E.C.E 1994 ... 38
OBJECTIVE TEST B.E.C.E 1995... 41
ESSAY QUESTIONS-B.E.C.E 1995 ... 46
OBJECTIVE TEST B.E.C.E 1996... 49
ESSAY QUESTIONS B.E.C.E 1996 ... 54
OBJECTIVE TEST- B.E.C.E1997 ... 57
ESSAY QUESTIONS B.E.C.E 1997 ... 62
OBJECTIVE TEST- B.E.C.E1998 ... 65
ESSAY QUESTIONS B.E.C.E 1998 ... 70
OBJECTIVE TEST B.E.C.E 1999 ... 73
ESSAY QUESTIONS B.E.C.E 1999 ... 78
OBJECTIVE TEST- B.E.C.E 2000 ... 81
ESSAY QUESTIONS B.E.C.E 2000 ... 86
OBJECTIVE TEST - B.E.C.E 2001 ... 89
ESSAY QUESTIONS B.E.C.E 2001 ... 94
OBJECTIVE TEST- B.E.C.E 2002A ... 97
ESSAY QUESTINS B.E.C.E 2002A... 103
vi
OBJECTIVE TEST- B.E.C.E 2002B ... 106
ESSAY QUESTIONS B.E.C.E 2002B ... 111
OBJECTIVE TEST B.E.C.E 2003 ... 114
ESSAY QUESTIONS- B.E.C.E 2003 ... 119
OBJECTIVE TEST B.E.C.E 2004 ... 121
ESSAY QUESTIONS B.E.C.E 2004 ... 126
OBJECTIVE TEST-B.E.C.E 2005 ... 129
ESSAY QUESTIONS- B.E.C.E 2005 ... 133
OBJECTIVE TEST -B.E.C.E 2006 ... 136
ESSAY QUESTIONS B.E.C.E 2006 ... 141
OBJECTIVE TEST- B.E.C.E 2007 ... 145
ESSAY QUESTIONS B.E.C.E 2007 ... 150
OBJECTIVE TEST- B.E.C.E 2008 ... 154
ESSAY QUESTIONS B.E.C.E 2008 ... 158
OBJECTIVE TEST- B.E.C.E 2009 ... 163
ESSAY QUESTIONS- B.E.C.E 2009 ... 168
OBJECTIVE TEST- B.E.C.E 2010 ... 172
ESSAY QUESTIONS B.E.C.E 2010 ... 177
OBJECTIVE TEST-B.E.C.E 2011 ... 181
ESSAY QUESTIONS- B.E.C.E 2011 ... 186
OBJECTIVE TEST-B.E.C.E 2012 ... 190
ESSAY QUESTIONS B.E.C.E 2012 ... 195
OBJECTIVE TEST-B.E.C.E 2013 ... 199
ESSAY QUESTIONS B.E.C.E 2013 ... 204
OBJECTIVE TEST B.E.C.E 2014 ... 207
ESSAY QUESTIONS B.E.C.E 2014 ... 212
OBJECTIVE TEST-B.E.C.E 2015 (PRIVATE) ... 216
ESSAY QUESTIONS B.E.C.E 2015(PRIVATE) ... 221
OBJECTIVE TEST B.E.C.E 2015... 224
ESSAY QUESTIONS B.E.C.E 2015A ... 230
ESSAY QUESTIONS- B.E.C.E 2015 B ... 234
1
OBJECTIVE TEST B.E.C.E 1990
1.
If P ={ 7,9,13} and Q={1,7,13},
find P n Q .
A { 1,7,13} B. { 1,9,13}
C. { 7,13} D. {7,9,13}.
Solution
P
Q= { 7,13}. Ans. C.
2.
In the Venn diagram , Q is the set
of numbers inside the circle and T
is the set of numbers inside the
rectangle. Find QUT.
A. {5} B. {6,7}
C. { 3,4,5,6,7} D. { 5,6,7}.
Solution
QUT = { 3,4,5,6,7} . Ans. C.
3.
Given that (23
find the exact value of
.
A. 14.8994 B. 148.994
C. 1489.94 D. 14899.4.
Solution
=1489.94, we
move the decimal point two places
backward. Ans. C.
4.
Convert 25
ten
to base two numeral .
A. 100001 B. 10011
C. 10101 D. 11001.
Solution
Number base Remainder
25
12
6
3
1
2
2
2
2
1
0
0
1
25
ten
= 11001
2
. Ans. D.
5.
If
Find the value of a.
A. 3.0 B. 5.8 C. 6.0 D. 9.0
Solution
Comparing both sides of the
equation 18 = 3a
Ans. C.
6.
If 26039 oranges are shared equally
among 13 women, how many
oranges does each woman receive?
A. 23 B. 203 C. 230 D. 2003.
Solution
Number of oranges each woman
receive =
Ans.D.
7.
Mr Mensah withdrew some money
from the bank. He gave
to his
daughter. If he had 500.00 left,
how much did he take from the
bank?
A. 600.00B.750.00
C. 1,500.00 D.3,000.00.
Solution
Let
Fraction left
(
*
. Ans. D.
8.
Simplify
(
)
Solution
(
)
(
)
(
]
(
*
(
)
Ans. B.
9.
If 21:2
=7:10. Find the value of
Solution
2
Ans. C.
10.
X is a point of the line segment
| |
| |
| | | |
Solution
| | | |
| | | | Ans.D.
11.
In an examination 60% of the
candidates passed. The number of
candidates who passed was 240.
How many failed?
A. 140 B. 160 C. 360 D.400.
Solution
Let the number of candidates who
failed be x
60 = 240
40 = x
60x = 9600
.Ans. B.
12.
A table which cost 2,400.00 to
manufacture was sold for
3,000.00. Find the profit percent.
A. 80% B. 25% C. 20% D. 11%.
Solution
Profit = Selling price Cost price =
3000-2400= 600.00.
Profit percent =
Ans.B.
13.
If
find the
value of a.
A. 2
9
B. 2
5
C. 2
2
D.2.
Solution
Ans. D.
14.
The distance between two towns is
12875 km. Express this distance in
standard form.
A.
.
Solution
12875=
. Ans. A.
The pie chart shows the monthly
expenditure of Mr Awuah whose
monthly income is 18,000.00.
Use the chart to answer questions
15 to 17.
15.
What fraction of Mr Awuahs
income is spent on food?
A.
Solution
Fraction spent on food =
Ans. C.
16.
How much does Mr Awuah spent
on rent?
A. 9,000.00 B. 4,500.00
C.9000.00 D.16,200.00
Solution
Amount spent on rent =
. Ans. B.
17.
What is the size of the angle
representing savings?
A. 40
0
B. 60
0
C. 130
0
D. 230
0
.
Solution
Angle representing savings =
360
0
-(90
0
+60
0
+50
0
+120
0
)=
360
0
-320
0
=40
0
. Ans. A.
18.
Find the missing addend:
2 0 4 5
* * * *
1 9 1 8
------------
4 4 3 0
----------
3
A. 8393 B. 1967
C. 2512 D. 467.
Solution
Add 2045 to 1918 and subtract it
from 4438.
2045
1918
--------
3963
---------
Now we subtract
4430
3963
--------
467
------- Ans. D.
19.
Remove the brackets
Solution
.
Ans. C.
20.
Simplify:
Solution
Ans. C.
21.
If
A. 225 B. 150 C. 237.5 D. 55
Solution
. Ans. B.
22.
If
find a.
A. 225 B. 150 C. 135 D. 30
Solution
Ans. A.
23.
Find the least common multiple of
7,14 and 18.
A. 71418 B. 1764 C. 252 D. 126
Solution
7={
} { }
{
}
Ans. D.
24. In
| | | |
| | area of the
triangle is 30cm
2
.
A. 25cm B. 14cm
C. 12.5cm D. 5cm.
Solution
Area of triangle =
| | | |
| |
| |
| |
| | Ans. D.
25.
Write 1204
five
as number in base
ten.
A.995 B. 179 C. 39 D. 35.
Solution
1204
5
=
Ans. B.
26.
Multiply
Solution
Ans. A.
27.
A watchman was paid basic wage
of
250.00 a day. If he worked
4
every day in the month, calculate
his basic wage for February ,
1988.
A.6,250.00 B.7,200.00
C.7,250.00 D.7,500.00.
Solution
Number of days in February 1988=
29 days,
Wage for 29 days = 29
. Note: 1988 is a leap
year with 29 years. Ans. C.
28.
A tank contains 250 litres of
water. If 96 litres is used, what
percentage of the original quantity
is left?
A. 61.6% B. 60.5%
C. 59.0% D. 54.2%.
Solution
Litres left = 250
. Ans. A.
29.
Evaluate 10
(
)
Solution
10
(
)
(
)
(
)
Ans. A.
30.
A bag contains 24 marbles, 10 of
which are blue and the rest are
green. A boy picks a marble at
random from the bag . what is the
probability that he picks a green
marble?.
A.
Solution
P(picking a green marble)
=
No. of green marbles = 24
Ans. D.
31.
Which of the following inequalities
is represented on the number line,
where
{ }
Solution
n is greater than -3.Ans. D.
32.
What is the name of the line
segment drawn to join any two
points on the circumference of a
circle?
A. Radius B. segment
C. Sector D. Chord.
Solution
Ans. D.
Use the mapping below to answer
questions 33 and 34.
( *
33.
Find the value of
A. 9.42 B.12 C. 18 D. 18.84.
Solution
The mapping is of the form
ABC
B= 2
A, C= B 3.14,
x= 6
.Ans. D.
34.
Find the value of
A. 2 B. 5 C. 7 D. 9.
Solution
B = 2 x A
.Ans.B
35.
The area of a square is 49cm
2
. Find
the perimeter of the square.
A. 7cm B. 51cm
C. 28cm D. 49cm.
Solution
Area of square =
.
Perimeter = 4l = 4(7) = 28 cm.
5
Ans. C.
36.
The least number in a set of real
numbers is 24 and the greatest is
30. Which of the following is the
correct interpretation of the
statement.
A.
Solution
Note: 24 & 30 are members of the
set.
Ans.A.
37.
Find the area of the trapezium
MNOP.
A. 120cm
2
B. 72cm
2
C. 60cm
2
D. 48cm
2
Solution
Area of trapezium =
(sum of parallel) height=
Ans. C.
38.
The length of a field, 128km is
represented on a map by a line
40mm long. What is the scale of
the map?
A. 1:100 B. 1:300
C. 1:1000 D. 1:30,000.
Solution
Scale = map distance : actual
distance
.
Ans. D.
39.
The diagram shows the
construction for.
A. Copying a given line.
B. bisecting a line segment
C. drawing a perpendicular to a
given line
D. bisecting a given angle.
Solution
Ans. D.
40.
Simplify
(
) (
)
(
) (
)
(
) (
)
Solution
(
) (
) (
) Ans. B.
6
ESSAY QUESTIONS B.E.C.E 1990
Q1
a)
List the members of each of
the sets
B= {whole numbers from
20 to 30}
D = { factors of 63}
List the members of
i)
B
D
ii)
B U D
b)
In a class of 60 students, 46 passed
mathematics and 42 passed English
language. Every student passed at
least one of the two subjects.
i)
Illustrate this information on a
Venn diagram
ii)
How many students passed in both
subjects. Let n represent the
number of students who passed in
both subjects.
Solution
B = { 20,21,22,23,24,25,26,
27,28,29, 30 }
D = { 1,3,7,9,21,63 }
i)
B n D = { 21}
ii)
B U D = { 1,3,7,9,20,21,22,23,24,
25,26, 27,28,29,30,63 }
b)
U = {number of students in
class}= 60
M ={those who passed in maths} =
46
E= {those who passed in English}=
42
n= n(M n E)
students passed in both
subjects
Q2
a)
Factorise completely
b)
Solve
c)
Illustrate the answer on the number
line.
Solution
a)
=
b)
c)
Q3
a)
Using a ruler and a pair of
compasses only,
i)
Construct a triangle PQR such that
| | | |
ii)
Construct perpendicular bisectors
(mediators) of
and
Name
the intersection of the mediators O.
7
iii) Draw a circle with O as the centre
and OQ as radius.
b) i) |
|
ii)
Solution
|
|
ii) angle QPR = 33
0
Q4
The following is the results of a
survey conducted in a class of a
Junior Secondary School to find
the favourite soft drink of each
pupil in the class.
Soft drink Number of
pupils preferring
soft drink
Coca-Cola
Pepsi Cola
Pee cola
Fanta
Muscatella
Mirinda
Club cola
Sprite
6
5
8
3
5
4
6
3
a)
Draw a bar chart showing this
information using a scale of 2 cm
to 1 unit on the vertical axis
b)
How many pupils are in the class?
c)
What percentage of pupils in the
class prefer club cola.
Solution
b)
Number of pupils in class =
6+5+8+3+5+4+6+3 = 40 pupils
c)
Percentage of pupils who prefer
club cola =
.
THEORY FOR 1990
8
OBJECTIVE TEST B.E.C.E 1991
1.
P={1,2,3,8,10} and
Q= {8,1,
,3,2}. If P= Q, what is
the value
A. 1 B. 2 C. 3 D. 10
Solution
P=Q , elements in set P are the
same as the elements in set Q
,
=10.Ans. D.
2.
If Y = { house, tree} , V= { car,
house, tree}. Which of the
following is true of Y and V?
A. Y=V B. Y
Solution
Y is a subset of V written as
Y
, since the elements in set Y
can be found in set V. Ans. B.
3.
The following addition is done in
base ten. Find the missing addend.
2 3 4 5
+ 1 0 4 5
* * * *
----------------
5 1 1 0
---------------
A. 1300 B. 1720
C. 2765 D. 4065
Solution
Add 2345 to 1045 and subtract the
result from 5110.
2 3 4 5
+ 1 0 4 5
----------------
3 3 9 0
--------------
5 1 1 0
3 3 9 0
------------------
1 7 2 0
-----------------
Ans. B.
4.
Given that
find the least number that should
be multiply by 252 to make the
product a perfect square.
A.2 B. 3 C. 6 D. 7
Solution
7
The least integer is 7.
Ans. D
5.
Write 4687.02 in standard form.
A. 46.8702
10
3
B. 46.8702
Solution
4687.02 =
Ans. D.
6.
A boy spent
his pocket money
on transport and on sweets. what
fraction of his pocket money does
he spend on transport and sweets?
A.
Solution
Fraction spent on transport and
sweets =
Ans. D.
7.
Convert 11001
two
to a decimal
numeral.
A. 6 B. 7 C. 14 D. 25.2
Solution
11001
2
=(
Ans. D.
8.
The product of three numbers is
1197. Two of the numbers are 3
and 19. Find the third number.
A. 21 B. 54.4 C. 210 D. 544.
Solution
Let the third number be
9
9.
Find the G. C. F(H.C.F) of
.
A. 8 B. 9 C. 72 D. 648.
Solution
We pick the common numbers
with the least powers/exponents .
H.C.F = 2
3
x 3
2
= 8 x 9 = 72.
Ans. C.
Use the diagram below to answer
questions 10 to 12.
10.
Find the value of a.
A. 68
0
B. 75
0
C. 105
0
D. 124
0
Solution
a
0
+ 56
0
= 180
0
a= 180
0
56
0
a= 124
0
. Ans. D
11.
What is the value of b?
A. 68
0
B. 75
0
C. 105
0
D. 112
0
Solution
56
0
+56
0
+ b= 180
0
122
0
+b =
180
0
b= 180
0
-122
0
b = 68
0
.
Ans. A.
12. What is the value of c
0
?
A. 68
0
B. 75
0
C. 105
0
D. 124
0
Solution
56
0
+ c+19
0
= 180
0
b= 75
0
+c=180
0
c= 180
0
-75
0
c= 105
0
. Ans.C.
13.
Simplify
Solution
Ans. C.
14.
In the relation:
A. 18 B. 26 C. 32 D. 48.
Solution
Ans. B.
The marks obtained by 10 children
in a mental drill are
0,1,3,3,5,7,8,9,9,9. Use this
information to answer questions 15
to 18.
15.
What is the modal mark?
A. 3 B. 7 C. 8 D.9.
Solution
Modal mark( the most occurring
number) is 9. Ans. D.
16.
What is the median mark?
A. 3 B. 5 C. 6 D. 7.
Solution
0,1,3,3,5,7,8,9,9,9
Median (middle number) =
. Ans. C.
17.
Calculate the mean mark?
A. -54 B. 5.4 C. 10 D. 54.
Solution
Mean =
. Ans. B.
18.
What is the probability that a child
chosen at random is scored 3
marks?
A.
Solution
P( a child chosen scored a 3)
=
. Ans. C.
19.
A trader received a commission of
12
on sales made in a month.
His commission was 35,000.00.
find his total sales for the month.
A
10
.
Solution
Commission = commission rate x
total sales=
Let the total sales be x
.Ans. D.
20.
A map of a large town is drawn to
the scale of 1:100,000. What is the
distance in kilometres(km)
represented by a line segment 4 cm
long on the map?
A. 0.04km B. 0.4km
C. 4km D. 40km.
Solution
Actual distance = n x map distance
= 100,000 x 4 = 400,000cm
=
Ans. C.
21.
Adjoa and Ama share 600.00
between them in the ratio 3:2. Find
Adjoas share.
A. 200.00 B. 240.00
C. 300.00 D. 360.00.
Solution
Adjoas share =
Ans. D.
22. Simplify
Solution
.Ans. C.
23.
If
8 B. 10 C. 16 D. 20.
Solution
. Ans. A
24.
Find one- hundredth of 1.0756 .
A. 107.56 B. 10.756
C. 0.1756 D. 0.010756.
Solution
Ans. D.
25.
What is the rule of this mapping?
y 1 3 5 7 9
Solution
It is linear mapping, y
Ans. A.
26.
The circumference of a circular
track is 440m. Find the diameter of
this track. [Take
.
A. 70m B. 140m
C. 280m D. 691m.
Solution
Circumference =
Ans.B.
27.
If
(
) (
)
(
) (
) (
) (
)
Solution
*(
) (
)+
*(
) (
)+ (
)
(
) Ans. D.
28.
Which of the following would you
use to measure an angle?
A. Ruler B. A pair of compasses
C. A set square D. A protractor.
Solution
Ans. D.
11
29.
Express the ratio of 64cm to 48cm
in its simplest form.
A. 3:4 B. 4:3 C. 16:12 D. 12:16.
Solution
64:48 = 4:3. Ans. B.
In the diagram below, P
is an enlargement . Use
this information to answer
questions 30 and 31.
30.
What is the scale factor of this
enlargement?
A.-2 B.
Solution
Scale factor =
Ans. C.
31.
If |
| what is the length
of P
I
R
I
?
A. -7.2m B. -1.8m
C. 1.2m D. 1.8m
Solution
Scale factor =
Ans. D.
32.
Find the tangent of the angle
marked y in the diagram below.
A.
Solution
Using SOHCAHTOA
tan
Ans. D.
33.
Kojo paid 270,000.00 for a T.V
set after he has been given a
discount of 10%. Find the marked
price.
A. 300,000.00 B. 297,000.00
C. 280,000.00 D. 260,000.00.
Solution
New amount
=
Let the marked price be x
. Ans. A.
In a secondary school class, 23
pupils study Economics, 6 pupils
study both Government and
Economics. 48 pupils study either
Government or Economics or both.
Use this information to answer
questions 34 to 36.
34.
What is the total number of pupils
who study Government?
A. 17 B. 22 C. 24 D. 31
Solution
17+6+
,
25+6=31, 31 pupils study
Government. Ans. D.
12
35.
How many pupils study only
Government?
A. 17 B. 23 C. 24 D. 25
Solution
From the Venn diagram, 25 pupils
study only Government. Ans. D.
36.
How many pupils study only
Economics?
A. 17 B.23 C. 24 D. 25.
Solution
From the Venn diagram, 17 pupils
study only Economics. Ans. A.
37.
When a certain number is
subtracted from 10 and the result is
multiplied by 2, the final result is 4.
Find the number.
A. 8 B. 12 C. 16 D. 24.
Solution
Let the number be
Ans. A.
38.
From the diagram below, calculate
the bearing of point X from point
Y.
A. 035
0
B. 135
0
C. 045
0
D. 225
0
Solution
The bearing of point Y from point
X= 180
0
+045
0
=225
0
. Note:
bearing is measured in the
clockwise direction, starting from
the north. Ans. D.
39.
If 22% of the length of a rope is
55cm, find the full length of the
rope.
A. 12.1cm B. 25cm
C. 121cm D. 250cm.
Solution
Let the full length be
If 22= 55
100 =
if more , less divide
Ans. D.
40.
Which of the following best
describes the given construction?
A. Bisecting a line
B. Constructing the bisector of a
line segment
C. Constructing a perpendicular to
a line
D. Constructing a perpendicular
to a given line from a point outside
the line.
Solution
Ans. D
13
ESSAY QUESTIONS B.E.C.E 1991
a)
If X= { prime numbers less than
13}, and
Y= { odd numbers less than 13}
i) List the members of X and Y
ii) List the members of (X
Y) and
(X U Y)
b)
Three school children share some
oranges as follows:
AKwasi gets
of the total , and the
remainder is shared between Abena
and Jantuah in the ratio 3:2. If
Jantuah gets 24 oranges, how many
does Akwasi gets?
Solution
i) X = { 2,3,5,7,11} ,
Y = { 1,3,5,7,9,11}
ii) X
Y = {3,5,11}
XUY= {1,2,3,5,7,9,11}
b)
Let the total be
Akwasis share =
oranges
Q2
Using a ruler and a pair of
compasses only,
a)
Construct a triangle XYZ in which
| |
| |
| |
b) i) Construct the mediator of YX
ii) Draw a circle centre X and
radius of 5cm. Measure
| | A is the point of
intersection of the mediator and
circle in the triangular region XYZ.
Solution
Note: The mediator and the circle
meet at two places, but we are
interested only in the point of
intersection within the circle.
| |
Q3
a)
Solve the equation
b)
c)
i)
ii)
Solution
a)
(
)
(
*
b)
14
Note: addition is commutative,
thus
c) i)
[
] [
]
[
]
ii)
(
)
Q4
The following table shows the
distribution of voters in an election
for class prefects
Name
Number of votes
Acquaye
6
Borquaye
12
Commey
18
i) Draw a pie chart to illustrate the
information
ii) What fraction of the votes was cast
for Borquaye?
b)
The height in centimetres of 10
school children are as follows:
165, 165, 155, 159 174
154, 169, 155, 155, 150
i) Make a frequency table for the
data.
ii) Use your table to find the mode
and median of the distribution.
Solution
a)
Total number of votes = 6+12+18
= 36
Working out the angles
Acquaye =
ii)
Fraction of votes Borquaye had
=
.
b)
Height Tally
Frequency(f)
150
I
1
154
II
1
155
III
3
159
I
1
165
II
2
169
I
1
174
I
1
i)
The mode (height with highest
frequency) = 155 cm
Median = (middle height) =
.we keep adding the
frequencies from the top till we get 5 or
more,
157,
Note: we added the two middle height
since the sum of the frequency is even.
15
OBJECTIVE TEST B.E.C.E 1992
1.
Find the set of prime factors of 12.
A. {3} B. {2,3} C. {3,4} D. {2,6}
Solution
Factors of 12 = {1,2,3,4,6,12} ,
prime factors of 12 = {2,3}.
Ans. B.
2.
If P={ 7.11.13} and Q={9,11,13}.
Find PUQ.
A. {7} B. {9}
C. {7,9} D.{7,9,11,13}
Solution
PUQ= {7,9,11,13}. Ans. D.
3.
In the diagram, set Q has 30
members and set T has 25
members. Q n T has 10 members.
Find the number of members of
QUT.
A. 35 B. 45 C. 55 D. 65.
Solution
QUT= 20+10+15 = 45.
Ans. B.
4.
Find the value of
.
A. 5.0 B. 4.9 C. 2.5 D. 2.4.
Solution
=
.
Ans. C.
5.
Convert 39
ten
to base five numeral.
A. 100111 B. 1110
C. 234 D. 124.
Solution
Number Base Remainder
39
7
1
5
5
4
2
39
ten
=124
five
. Ans. D.
6.
Find the least whole number which
must be added to 207 to make it
divisible by 17.
A. 0 B. 3 C. 13 D. 14.
Solution
Ans. B.
7.
Simplify 2
(
)
Solution
2
(
) (
)
Ans. D.
8.
If 8.51
Solution
If 8.51
we move the
decimal point one place forward
to get the answer for
85.3
Ans. D.
9.
Express o.625 as a fraction in its
lowest term.
A.
Solution
0.625=
Ans. A.
10.
An amount of money is shared
between Kofi and Ama in the ratio
3:5. If Ama received 4,650.00,
what is Kofis share?
16
A.930.00 B. 1550.00
C.1743.75 D.2790.00.
Solution
Amas share=
the amount to be
shared
Kofis share = Amount to be
shared Amas share=
7440
.00. Ans. D.
11.
If $1.00 = 340.00, what was the
cedi value of an article which cost
$6.50.
A. 6,630.00 B. 2,380.00
C.2,210.00 D. 346.00.
Solution
1 = 340
650 =
, if more, less divide
.
Ans. C.
12.
Find the simple interest on
28,000.00 at 3
per annum for
6 months.
A.490.00 B.560.00
C.980.00 D.5,880.00.
Solution
Simple interest=
. Ans. A.
The bar chart shows the distance of
5 villages, P,Q,R and T from a
market town. Use it to answer
questions 13 and 14.
13.
Which village is farthest from the
market town?
A. P B.T C. R D. S.
Solution
The farthest village is the highest
bar, which is T. Ans. B.
14.
How much farther is village Q
than village R from the market
town?
A. 2km B. 3km C. 4km D. 5km.
Solution
Village Q is 10km from the market
town. Village R is 5km from the
market town.
Q is (10-5) =5km
farther than R. Ans. D.
15.
There are 20 beads in a box, some
are red and some are green. The
chance that one bead, taken at
random from the box is red is .
Find the number of red beads in the
box.
A. 16 B. 15 C. 10 D. 5.
Solution
P( selecting a red bead)
=
No. of red beads= 5. Ans. D.
16.
A bag contains 12 mangoes of
which 4 are not ripe. What is the
chance of picking at random a ripe
mango from the bag?
A.
.
17
Solution
P(picking a ripe mango)
=
Ans. C.
17.
Find the value of p
2
-6p+9 when
p= -2
A. -7 B. 13 C. 12 D. 25
Solution
P
2
-6p+9=(-2)
2
-6(-2)+9=
4- - 12+9=25. Ans. D.
18.
If
find the value of q in the
equation
A.-8 B. 1 C. 0 D. -1
Solution
.
Ans. C.
19.
Which of the following inequalities
is shown on the number line above,
where
is a real number?
A. P
Solution
Ans. D.
Use the mapping below to answer
questions 20 and 21.
{
}
{ y -1 1 5 7 9 12}
20.
find the value of
.
A. -7 B.5 C. 6 D. 10.
Solution
It is a linear mapping whose
general rule is
. Ans. D.
21.
Find the value of y.
A. 3 B. 1 C. -1 D. -3.
Solution
Ans. D.
22.
In the diagram below, find the
bearing of P from Q.
A.045
0
B. 090
0
C. 135
0
D. 180
0
Solution
The bearing of P from Q is 045
0
.
Ans. A.
23.
A polygon has 10 sides. Which of
the following gives the sum of its
interior angles.
A.
Solution
Sum of interior angles of a regular
polygon =
Ans. D.
The diagram shows the conversion
graph for miles and kilometres.
Use it to answer questions 24 and
25.
18
24.
Find in kilometres, the equivalent
of 4 miles.
A. 2.5 B. 3 C. 6.4 D. 6
Solution
From the graph 4 miles =6.4 km.
Ans. C.
25.
Express 4km in miles.
A. 6.4 B. 4 C. 3.5 D.6.
Solution
From the graph, 4km is equivalent
to 2.5. Ans. D.
The diagram below is a right
triangle. Use it to answer questions
26 and 27.
26.
Find |
|
A. 2.4cm B. 7cm
C. 13cm D. 17cm.
Solution
Using the Pythagoras theorem
| |
| |
| |
| |
| |
| |
.Ans. C.
27.
Find tan YXZ.
A.
Solution
From the SOHCAHTOA
Tan
.
Ans. D.
28.
The diagram shows two points P
and Q in the number plane. Find
the vector PQ.
A.
( )
(
) (
)
(
)
Solution
(
) (
) (
) Ans. B.
29.
Find the length of the vector
(
)
A. 7 B. 13 C. 17 D. 25.
Solution
Length of a vector is the same as
its magnitude
| |
. Ans. B.
30.
In the diagram below, square
P
I
Q
I
R
I
S
I
is an enlargement of
square PQRS is 4 cm
2
and the area
of square P
I
Q
I
R
I
S
I
is 9cm
2
. Find
the scale factor of the enlargement.
A.
19
Solution
Ans. C.
31.
The volume of a cube is 27cm
3
.
Find the area of its faces.
A. 3 cm
2
B. 6cm
2
C. 9cm
2
D. 18cm
2
Solution
Volume of cube = l
3
27=l
3
.
Each face of a cube is a square
and area of square =
= l
2
=3
2
=9 cm
2
. Ans. C.
32.
A cylinder is of height 3 cm and
radius of 2 cm. Find its curved
surface area.
A. 18
C
Solution
Curved surface area of a cylinder =
Ans. B.
33.
Find the area of the parallelogram
PQRS.
A. 20cm
2
B. 21 cm
2
C. 48 cm
2
D. 60 cm
2
Solution
Area of parallelogram = length of
base x perpendicular height =
12 x 4 = 48cm
2
. Ans. C.
34.
If
of a number is added to
of the
same number, the result is 8. Find
the number.
A. 3 B. 5 C. 15 D. 30.
Solution
Let
(
Ans. C.
35.
If 1:
is equivalent to
A. 4 B. 6.25 C. 24 D. 100.
Solution
(
*
.
Ans. A.
36.
Express
a percentage.
A. 0.375% B. 12
.
Solution
Ans. D.
37. Akosua buys 480 pineapples for
24,000.00. She sells all the
pineapples for 28,000.00. Find
her profit percent.
A. 13.9% B. 16.7%
C. 20% D.40%.
Solution
Profit = Selling price Cost price =
28,000 24,000 = 4,000.00
Profit percent =
Ans. B.
38.
How many edges has a cuboid?
20
A. four B. six C. eight D. twelve.
Solution
A cuboid has 12 edges. Ans. D.
The pie chart shows the
distribution of crops on a farm of
area 250 hectares. Use it to answer
questions 39 and 40.
39.
Find the area of the plot with corn.
A. 48.8ha B. 55.3 ha
C. 62.5ha D. 83.3ha.
Solution
Area for corn =
Ans. C.
40.
What fraction of the farm is planted
with the pepper?
A.
Solution
Angle representing pepper =
Ans. A.
21
ESSAY QUESTIONS- B.E.C.E 1992
1) a) Solve
Illustrate your result on the number
line.
b)
Find the truth set of the equation
c)
Factorize completely
d)
Make t the subject of the relation
Solution
a)
b)
{y:y =3} as truth set.
c)
d)
Q2
A landlady rented out her house for
240,000.00 for one year. During
the years, she paid 15% of the rent
as income tax. She also paid 25%
of the rent as property tax and
spent 10,000.00 on repairs.
Calculate
a)
the landladys total expenses.
b)
the remainder of the rent after the
landladys expenses.
c)
the percentage of the rent she spent
on repairs.
Solution
Rent=240,000.00
Expenditure
Income tax =
Property tax =
Repairs=10,000.00
Total expenses =
income tax+ property tax+
repairs =
36,000+60,000+10,000 =
106,000.00
b)
Remainder of rent after expenses =
240,000
106,000 = 134,000.00
c)
Percentage of rent spent on repairs
=
Q3
a)
Using a scale of 2 cm to 1 unit on
both axes, draw two perpendicular
lines Ox and Oy on a graph sheet.
b)
On this graph sheet, mark the x-
axis from -5 to 5 and the y-axis
from -6 to 6.
c)
Plot on the same graph sheet the
points A(1,1), B(4,3) and C(2,5).
Join the points A,B and C to form a
triangle.
d)
Using the y-axis as the mirror line,
draw the image of the triangle ABC
such that
.
e)
Using the x-axis as the mirror line,
draw the image of triangle ABC
such that
Write down
the coordinates of
Solution
d)
Reflection using y-axis as the
mirror line
22
e)
Reflection using the x-axis as the
mirror line (
Plot
on the graph sheet and
join them to form triangle
Plot also
on
the graph sheet and join them to
form a triangle.
Solution
Q4
The table below gives the
frequency distribution of marks
obtained in a class test by a group
of 64 pupils.
Marks
(out of ten)
Frequency
2
3
4
5
6
7
8
9
9
14
13
10
5
8
2
3
a)
Draw a bar chart for the
distribution
b)
A pupil is chosen at random from
the class, what is the probability
that the pupil obtained 7 marks
Solution
b)
Probability( selecting a student
who obtained 7)
=
Q5
Using a ruler and a pair of
compasses only,
a)
Draw |
|
b)
Construct a perpendicular to PQ at
Q.
c)
Construct <QPS =60
0
at the point P
on PQ such that |
|=6.5 cm.
d)
Construct a line parallel to PQ
through S. Let the perpendicular
through Q and parallel through S
meet at R. Measure |
|
23
Solution
Steps involved in constructing the
figure.
a)
PS= 9cm
b)
Construct 90
0
angle at Q on line PQ
c)
Construct 60
0
at P such that <QPS
= 60
0
Measure 6.5 cm and step at P
and make an arc on the 60
0
line to
get point S.
d)
To construct a line parallel to PQ,
measure QR and put the tip of the
compass at Q and make an arc at
point S. Make similar arcs above
line PQ by putting the tip of the
compass on line PQ. Draw a line to
pass onto of the arcs draw and
name the point intersection of the
parallel line to PQ RS. The
perpendicular at Q meet at
R.|
|
24
OBJECTIVE TEST-B.E.C.E 1993
1.
Expand
Solution
Ans. D.
2.
Find the missing number in the
following binary operation.
1100110
-
*******
111011
A. 11101 B. 101001
C. 100011 D. 101011.
Solution
1100110
- 111011
---------
101011
---------
Ans. D.
3.
If
{
}
A.{15} B. {13,15} C. {11,13,15}
D. {9,11,14,15}
Solution
Numbers greater than or equal to
13 from the set are {13,15} .
Ans. B.
4.
Which of these has the least
number of lines of symmetry?
A. An equilateral triangle
B. A rectangle C.A square
D. A circle.
Solution
A rectangle has only 2 lines of
symmetry which is the least out of
the four listed. Ans. B.
5.
Find 2
of 2000.00
A. 40.00
B. 50.00
C. 100.00 D. 800.00
Solution
2
. Ans. B.
6.
Find the highest common
factor(H.C.F) of 18,36 and 120.
A.
Solution
18=
H.C.F = 2
. Ans. C.
7.
Arrange the fraction
in
ascending order.
Solution
in
ascending order. Ans. C.
8.
Make "b" the subject of the
relation:
Solution
.Ans. D.
9.
A man has three children whose
ages are 9years, 12years and
24years. Find the ratio of their
ages.
A. 1:2:3 B. 1:2:4
C. 2:3:6 D. 3:4:8
Solution
9:12:24 =3:4:8. Ans. D.
10.
Ten students in Kwamekrom J.S.S
took 9 days to weed the school
25
compound. How long would 15
students take to weed the same
compound if they worked at the
same rate?
A. 5days B. 6days C. 13
days
D. 14days.
Solution
10 = 9
15 =
.
Ans. B.
11.
Which of the following
inequalities is/are true?
I
. A. I only B. II only C.
III only D. I and II only.
Solution
Convert each set to a common
denominator
,false
Ans. A.
12.
Find the image in the mapping
below
3 5 7 ?
A. p
2
+2 B. P
2
+1 C. 2p+1 D. p+2
Solution
It is a linear mapping
. Ans.C.
13.
A car travelled a distance of 50km
in an hour. What distance did it
travel in 30 minutes at the same
speed.
A. 1,500km B. 100km
C. 80km D. 25km
Solution
50km = 1hour
Ans. D.
14.
In an enlargement the area of the
object was multiplied by 144 to get
the area of the image. Find the
scale factor of the enlargement.
A. 12 B. 36 C. 48 D. 144
Solution
Area of image = 144x
. Ans. A.
15.
Mr Yevu saved 2,500.00 at a
simple interest rate of 25% per
annum for 4 years. Calculate the
interest he earned on his savings.
A.625.00 B.2,500.00
C.3,125.00 D. 5,000.00.
Solution
Simple interest=
. Ans.B.
The table below gives the number
of goals scored by a football team
in a league season.
Use it to answer question 16 to 18.
16.
Find the total number of goals
scored by the team.
A. 41 B. 40 C. 20 D. 19.
Solution
Number of
goals scored
in a match
0
1 2 3
4
5
Frequency
1
7 6 4
1
1
26
Total no. of goals = no. of goals
per match times no. of matches
played. Ans. B.
17.
What is the mean number of goals
scored by the team?
A.1 B.6 C. 4 D.2
Solution
Number of
goals scored in
a match(
Frequency
(f)
f
0
1
2
3
4
5
1
7
6
4
1
1
0
7
12
12
4
5
Mean =
goals.
Ans. D.
18.
What is the total number of
matches played in the league
season?
A. 6 B. 15 C. 19 D. 20.
Solution
Total number of
matches=1+7+6+1+1=20. Ans.D
19.
The probability of obtaining a head
when a coin is tossed is
. What is
the probability of obtaining a tail?
A. 1 B.
Solution
Sample space for tossing a coin
once {H,T}, P(obtaining a tail)
=
. Because P(H)+P(T)=1.
Ans. B.
20.
Given that
(
)
(
)
(
) (
)
(
) (
)
Solution
(
) (
)
(
) (
) (
).Ans. A.
21.
Find in base ten, the value of the 4
in 143
5
.
A. 5 B. 40 C. 25 D. 20
Solution
143
5
=(
The
value of the 4 is20. Ans. D.
22.
If the interior angle of a regular
polygon is 120
0
, how many sides
does it have?
A. 5 B.6 C. 7 D.8
Solution
Interior angle of a regular polygon
=
.Ans. B.
23.
Simplify
(
) (
)
Solution
(
) (
)
(
* (
*
Ans. C.
24.
Find the solution set of
{ }
{ }
{
}
27
{
}
Solution
Ans. D.
25.
In the diagram below,|
|
| |
| | | |
Calculate the size of the angle
marked
Solution
DEC is an equilateral
<DEC = 60
0
, <AEC + < DEC =
180
0
.
<AEC = 180
0
60
0
= 120
0
,
AEC
is an isosceles
<EAC = <ACE =
Ans. C.
26.
Five times a number is four more
than the number. Find the number.
A.
Solution
.
Ans. B.
27.
A basket contains 450 oranges. If
each orange cost 15.00, find the
cost of the oranges.
A. 30.00 B. 435.00
C. 465.00 D. 6,750.00
Solution
Total cost of the 450 oranges = 450
x the price of one orange= 450 x 15
=6,750.00. Ans.D.
28.
A bottle of soft drink cost 200.00.
The commission paid on one bottle
is 2% of the cost price. Find the
commission on 24 bottles of the
soft drink.
A. 96.00 B. 296.00 C.400.00
D. 4,704.00
Solution
Total cost of 24 bottles =
. Ans. A.
29.
If
is equivalent to
A. 1 B. 2 C. 4 D. 5
Solution
. Ans. B.
30.
Write 39.9748km, correct to three
significant figures.
A. 39.9km B. 39.975km C. 40km
D.40.0km
Solution
39.9748km = 40.0 km. Ans. D.
31.
Find
.
Solution
28
Ans. C.
32.
The bearing of Aboku from Bebeka
is 055
0
. What is the bearing of
Bebeka from Aboku?
A. 235
0
B. 055
0
C. 125
0
D. 305
0
Solution
The bearing of Bebeka from Aboku
is back bearing given as
Ans. A.
33.
The diagram above shows the
construction of:
A. the perpendicular bisector of
the line.
B. an angle of 45
0
at A
C. an angle of 45
0
at the point B.
D.an angle of 90
0
at the point O.
Solution
Ans. D.
34.
The dimension of the rectangle are
given in base two. Find its
perimeter.
A. 100
two
cm B. 1001
two
cm
C. 110
two
cm D. 1010
two
cm
Solution
Perimeter of rectangle = 2L+2W=
2(11)+2(10) = 22+20 =
2 2
+ 2 0
------
1010
-------
Ans. D.
35.
The area of the circle, centre O is
120cm
2
. Angle AOB is 60
0
. Find
the area of the sector AOB.
A. 2 cm
2
B. 3cm
2
C. 6 cm
2
D. 20cm
2
Solution
Area of sector =
=20cm
2
.
Ans. D.
36.
In the diagram below, ABCD is a
parallelogram, BC and AF are
straight lines, angle ABC=110
0
and angle DEF= 40
0
. Find the
angle marked
Solution
Note: <ADC= <ABC = 110
0
,
consider
DEF
Ans. A.
37.
In the diagram below,
AC
Angle CBT is 40
0
and
angle DET is 140
0
. Find the angle
marked
29
A. 320
0
B. 280
0
C. 220
0
D. 100
0
Solution
<GTE = <TEF = 40
0
, alternate
angles
<CBT = <BTG = 40
0
, alternate
angles
40
0
+40
0
+
=360
0
,
angles around a point.
80
0
+
=360
0
=360
0
-80
0
=280
0
.Ans. B.
38.
In the diagram below, the angle of
elevation of K from M is
A. 17
0
B. 73
0
C. 90
0
D. 107
0
Solution
Angle of elevation is the angle
between the eye level and the
horizontal which is angle GMK.
73
0
+90
0
+ <GMK=180
0
163
0
+<GMK =180
0
GMK=180
0
- 163
0
=17
0
.
Ans. A.
39.
In the diagram below, ACD is an
isosceles triangle in which |
|
| | is parallel to BE.
Find the value of angle marked
A. 055
0
B. 62.5
0
C. 110
0
D. 117.5
0
Solution
Let <ADC= <DCA = y
since
triangle ACD is an isosceles
.
Ans. D.
40.
Three girls Ama, Adjoa and Abena
measured the length of sides of 3
right angled triangles as follows.
Amas measurement were 50mm,
40mm 50mm, Adjoas
measurement were 20mm, 30mm
40mm, Abenas measurement were
20mm, 30mm, 40mm. Whose
measurement was/were correct.
A. Amas only B. Adjoas only
C. Adjoas and Abenas
D. Amas and Adjoas.
Solution
The set of Pythagorean triple are
50,120 and 130.
Note: Pythagorean triples are three
set of numbers which obeys the
Pythagoras theorem
Ans. B.
30
ESSAY QUESTIONS- B.E.C.E 1993
1)
a)
Simplify
b) Solve 5(a-5)
c)
If r =
(
) (
)
calculate
Solution
b)
10(a-5) 1( 2a+6) = 8
(
) (
)
*(
) (
)+ (
)
(
)
Q2 Using a ruler and a pair of
compasses only,
a)
Construct a triangle ABC such that
| |
b)
i)
Bisect the angle ACB to meet
| | at D.
ii)
What type of triangle is CDA?
c)
Calculate the area of triangle ABC.
Solution
a)
| |
b)
Triangle CDA is an isosceles
triangle since |
| | |
c)
Area of triangle ABC =
| | | |
Q3
Olu bought a radio for
After one year the radio was
valued at 75% of the cost price.
a)
What was the value of the radio
after one year.
b)
If he sold the radio for 55,700.00,
calculate his profit or loss over the
cost price.
Solution
a)
Cost price =65,000.00
Value of the radio after one year
=
b)
If it was sold for 55,700.00. Note
the value of the radio after one year
is the new cost price =48750.00
profit = selling price cost price =
55,700-48,750 =6,950.00
Q4
a)
Using a scale of 2 cm to 1 unit on
both axes, draw two perpendicular
lines Ox and Oy on a graph sheet.
31
b)
On this graph sheet, mark the x-
axis from -5 to 5 and the y axis
from -6 to 6.
c)
Plot on the same graph sheet the
points A(-2,4) and B(4,-5). Join the
points A and B with the help of a
ruler.
d)
Using the graph, find;
i) The gradient (or slope) of line AB,
ii) The value of x when y = 0
iii) The value of y when x = 2
e)
Plot on the same graph sheet, the
points C(-3,-1) and D(3,3). Join the
points C and D. with the help of a
protractor, measure the angle
between the lines AB and CD.
What gradient of the line CD?
Solution
d) i) gradient between two points =
--
ii) when
iii)
e)
Q5
The ages of 20 school children are
recorded as follows.
13 9 15 17 13
9 11 9 11 15
17 15 11 9 9
11 15 11 11 11
a)
Make a frequency table for the data
using the ages 9, 11 ,13 ,...
b) Use your table to calculate the
mean age( correct to the nearest
whole number).
Solution
a)
Age(
Tally Frequency
(f)
9
11
13
15
17
IIII
IIII11
11
11II
II
5
7
2
4
2
45
77
26
60
34
b)
Mean=
to the nearest whole
number)
32
OBJECTIVE TEST B.E.C.E 1994
1.
Which of the following is the set of
factors of 12?
A. {12,6,4,3,2,1} B. {12,6,4,3,2}
C. { 12,6,4,2} D. {6,4,2,1}
Solution
Factors of 12 = { 1,2,3,4,6,12}.
Note: 1 is factor of every number
and every number is a factor of
itself. Ans. A.
2.
Which of the following describes
the relationship between sets A and
B in the Venn diagram below.
A. A
B
B. A
B=5
C. A
B=
D. AUB={1,2,3,4,5,6,7}
Solution
A and B are disjoint and have no
elements in common. A
B=
Ans. C.
3.
Mark is 30 years old. Yaw is half
as old as Mark. Paul is 10 years
older than Yaw. How old is Paul?
A. 30 years B. 25 years
C. 20 years D. 15 years.
Solution
Mark= 30 yrs, Yaw=
Marks =
,Pauls age =10+
Yaws age = 10+15= 25 years.
Ans. B.
4.
How many lines of symmetry does
a rectangle have?
A. 1 B. 2 C. 3 D. 4
Solution
A rectangle has 2 lines of
symmetry. Ans. B.
5.
Which of the following is not a
prime number?
A.3 B. 5 C. 7 D. 9
Solution
A Prime number is a number
which have only two factors, 1
and the number itself. 9 is not a
prime number. Ans. D.
6.
If
{ } find the truth set
of
.{1,2} B.{2,3}
C. {1,2,3} D. {3}
Solution
numbers
less than 3 are 1,2.
Ans. A.
7.
In how many years will 5000.00
yield a simple interest of 1,000.00
at a rate of 5% per annum?
A. 4 years B. 5 years
C. 10 years D. 25 years.
Solution
Simple interest =
Ans. A.
8.
Make "m" the subject in the
relation
Solution
33
Ans.D
9.
What property of arithmetic
operation is illustrated by
a
A. Addition B. Associative
C. Commutative D. Distributive
Solution
It is the distributive property.
Ans. D.
10.
Simplify
30 B. 63 C. 225 D. 240
Solution
Note:
Ans. C.
11.
If
Solution
Ans. D.
12.
Calculate the size of an exterior
angle of a regular pentagon?
A.
Solution
Exterior angle of a polygon=
Ans. A.
13.
Factorise
{ }{ }
{ }{ }
{ }{ }
{ }{ }
Solution
Ans. B.
14.
Kwame, Atsu and Kojo shared a
profit of 50,000.00 in the ratio
1:4:3 respectively. How much did
Atsu get?
A.62,000.00 125,000.00
C.187,500.00 D.25,000.00
Solution
Atsus share=
.Ans.D.
15.
Use the identity a
2
-b
2
= (a+b)(a-b)
to evaluate
Solution
Ans.B
16.
What is the probability of obtaining
a prime number when a fair die is
thrown once? A.
Solution
Sample space for throwing a die
once ={1,2,3,4,5,6} Prime numbers
within the sample space = { 2,3,5}.
P(obtaining a prime number)=
Ans.B.
17.
The following are the scores
obtained by girls in a beauty
contest: 12,16,19,17, 8,11,19. What
is the probability of obtaining a
score of 19?
A.
Solution
P(that a score is 19)
=
.
Ans. C.
18.
Express 25 as a percentage of 75.
A. 300% B. 100%
C. 50% D. 33.3%
Solution
Ans. D
19.
Find the value of M given that
M=(
.
A.
Solution
.
Ans. C
34
20.
Express 0.0043216 in standard
form.
A.4.3216
B
C
D
Solution
0.004216 = 4.3216
.Ans. B.
21.
Given that
.
A. 28 B. 8 C. -7 D. -28
Solution
(2a+b)(a-2b) =
.
Ans. D.
22.
Which of the following is
illustrated on the number line.
A.
.
Solution
x is greater than or equal to -1 and
less than . Ans. B.
23.
In the diagram above, A is the
centre of the circle with radius 20
cm. If angle BAC is 90
0
, find the
perimeter of the shaded sector.
[Take
A. 71.4 cm B. 31.8cm
C. 40.0cm D. 51.4cm
Solution
Perimeter of sector =
*
+
Ans. A.
24.
In triangle ABC, |
| | |
| |
| |
A.
3 cm B. 4cm C. 9cm D. 33cm.
Solution
In triangle BCD,
| |
| | | |
| | | |
| |
| |
| |
| |
| |
Ans. A.
25.
Write 35,632.00, correct to the
nearest thousand cedis.
35
A. 40,000.00 B.36,000.00
C. 35,600.00 D. 35,000.00
Solution
35,632=36,000 to the nearest
thousand. Ans. B.
26.
Solve for
A. 12 B. 2
Solution
Ans. A.
27.
Evaluate (
Solution
(
)
.
Ans.A.
28.
A boy walked 7 km in a bearing
060
0
. Which of the following
diagrams shows his direction.
Solution
Ans. C, since bearing is done in
the clockwise direction
starting from the north.
29.
In the following diagram, G
I
OH
I
is
an enlargement of triangle GOH
with scale factor k. If |
|
| |
|
| what is
the value of k.
.
Solution
K=
, Note: the answer is negative
because the object and the image
are on opposite sides of the centre
of the enlargement.
Ans. B.
30.
If
A. Five B. Eight C. Seven D. Six
Solution
.
Ans. A.
31.
How many faces has a cuboid?
A. 6 B. 8 C. 12 D. 16
Solution
A cuboid has 6 faces.
Ans. A.
32.
Which of the following is a factor
of the expression
?
A. c-d B. a-2b C. a+b D. a+2b.
Solution
.
Ans. B.
33.
Three boys weeded a piece of land
in 4 hours. How long would it take
18 boys to weed the same piece of
land weeding at the same rate?
A.
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- Robert Akumbobe (Author), 2015, Mathematics for Junior High Schools in West Africa, Munich, GRIN Verlag, https://www.grin.com/document/303413
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