1994 - JAMB Mathematics Past Questions and Answers - page 3
21
\(\begin{array}{c|c} \oplus mod 10 & 2 & 4 & 6 & 8 \ \hline 2 & 4 & 8 & 2 & 6 \4 & 8 & 6 & 4 & 2\ 4 & 8 & 6 & 4 & 2\ 6 & 2 & 4 & 6 & 8\ 8 & 6 & 2 & 8 & 4\end{array}\)
The multiplication table above has modulo 10 on the set S = (2, 4, 6, 8). Find the inverse of 2
The multiplication table above has modulo 10 on the set S = (2, 4, 6, 8). Find the inverse of 2
A
2
B
4
C
6
D
8
correct option: a
The inverse of 2 is 6 since 2 x 6 = 12; under mod 10
12 = 2 which is also the value required
Users' Answers & Comments12 = 2 which is also the value required
22
Solve for x and y \(\begin{pmatrix} 1 & 1 \ 3 & y \end{pmatrix}\)\(\begin{pmatrix} x \ 1 \end{pmatrix}\) = \(\begin{pmatrix} 4 \ 1\end{pmatrix}\)
A
x = 3, y = 8
B
x = 3, y = -8
C
x = -8, y = 3
D
x = 8, y = -3
correct option: b
\(\begin{pmatrix} 1 & 1 \ 3 & y \end{pmatrix}\)\(\begin{pmatrix} x \ 1 \end{pmatrix}\) = \(\begin{pmatrix} 4 \ 1\end{pmatrix}\) = x + 1 = 4
x = 4 - 1
= 3
3x + y =1
3(3) = y = 1
= 9 + y = 1
y = 1 - 9
= -8
Users' Answers & Commentsx = 4 - 1
= 3
3x + y =1
3(3) = y = 1
= 9 + y = 1
y = 1 - 9
= -8
23
The determination of the matrix \(\begin{pmatrix} 1 & 3 & 3 \ 4 & 5 & 6\ 2 & 0 & 1 \end{pmatrix}\) is
A
-67
B
-57
C
-3
D
3
correct option: d
4 x 2 = -8 upward arrows = +ve
2 x 5 x 3 = 30
0 x 6 = \(\frac{0}{22}\) downward arrows = -ve
-1(1 x 5x - 1) = 5 - (2 x 6 x 2) = -24
= -(4 x 0 x 1)
= \(\frac{0}{-19}\)
therefore 22 - 19 = 3
Users' Answers & Comments2 x 5 x 3 = 30
0 x 6 = \(\frac{0}{22}\) downward arrows = -ve
-1(1 x 5x - 1) = 5 - (2 x 6 x 2) = -24
= -(4 x 0 x 1)
= \(\frac{0}{-19}\)
therefore 22 - 19 = 3
24
\(\begin{array}{c|c} \text{Age in years} & 10 & 11 & 12 \ \hline \text{Number of pupils} & 6 & 27 & 7\end{array}\)
The table above shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?
The table above shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?
A
\(\frac{27}{40}\)
B
\(\frac{17}{20}\)
C
\(\frac{33}{40}\)
D
\(\frac{3}{20}\)
correct option: b
Users' Answers & Comments25
If three angles of a quadrilateral are (3y - x - z)o, 3xo, (2z - 2y - x)o find the fourth angle in terms of x, y and z
A
(360 - x- y - z)o
B
(360 + x + y - z)o
C
(180 - x + y + z)o
D
(180 - x + y + z)o
correct option: a
The sum of angles of a quadrilateral is 360o
∴ (3y - x - z)o + 3xo + (2z - 2y - x)o + po = 360o
Where P is the fourth angle
3y - x - z + 3x + 2z - 2y - x + p = 360o
p = 360 - (x + y + z)
∴ p = (360 - x - y - z)o
Users' Answers & Comments∴ (3y - x - z)o + 3xo + (2z - 2y - x)o + po = 360o
Where P is the fourth angle
3y - x - z + 3x + 2z - 2y - x + p = 360o
p = 360 - (x + y + z)
∴ p = (360 - x - y - z)o
26
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 box volume of wood in the box is
A
11 520cm3
B
36 000cm3
C
38 200cm3
D
47 520cm3
correct option: a
Internal dimension are 50cm, 36cm and 20cm
internal volume = 50 x 36 x 20cm3
1000 x 36cm3
= 36000cm3
External dimension are 54cm x 40cm x 22cm
= 2160cm2 x 22cm = 47520cm3
Volume of wood = Ext. volume - Int. volume
= 47,520cm3 - 36,000cm3
= 11,520cm3
Users' Answers & Commentsinternal volume = 50 x 36 x 20cm3
1000 x 36cm3
= 36000cm3
External dimension are 54cm x 40cm x 22cm
= 2160cm2 x 22cm = 47520cm3
Volume of wood = Ext. volume - Int. volume
= 47,520cm3 - 36,000cm3
= 11,520cm3
27
Calculate the perimeter, in cm, of a sector of a circle of radius 8cm and angle 45o
A
2\(\pi\)
B
8 + 2\(\pi\)
C
16 + 2\(\pi\)
D
16 + 16\(\pi\)
correct option: c
Perimeter = OP + OQ + PQ
= 8 + 8 + PQ
length PQ = \(\frac{\theta}{360 \times 2\pi r}\)
= \(\frac{45}{360}\) x 2 x \(\pi\) x 8
= 2\(\pi\)
Perimeter of sector 2r + L
Where l = length of arc and r = radius
∴ P = 2(8) + 2\(\pi\)
= 16 + 2\(\pi\)
Users' Answers & Comments= 8 + 8 + PQ
length PQ = \(\frac{\theta}{360 \times 2\pi r}\)
= \(\frac{45}{360}\) x 2 x \(\pi\) x 8
= 2\(\pi\)
Perimeter of sector 2r + L
Where l = length of arc and r = radius
∴ P = 2(8) + 2\(\pi\)
= 16 + 2\(\pi\)
28
What is the locus of a point P which moves on one side of a straight line XY, so that the angle XPY is always equal to 90o?
A
the perpendicular bisector of XY
B
a right-angled triangle
C
a circle
D
a semi circle
correct option: d
Since XY is a fixed line and
XPY = 90o P is on one side of XY
P1P2P3......Pn are all possible cases where
XPY = 90o the only possible tendency is a semicircle because angles in semicircle equals 90o
Users' Answers & CommentsXPY = 90o P is on one side of XY
P1P2P3......Pn are all possible cases where
XPY = 90o the only possible tendency is a semicircle because angles in semicircle equals 90o
29
If M(4, q) is the mid-point of the line joining L(p, -2) and N(q, p). Find the values of p and q
A
P = 2, q = 4
B
p = 3, q = 1
C
p = 5, q = 3
D
p = 6, q = 2
correct option: d
\(\frac{p + q}{2}\) = 4
p + q = 8 ....(i)
\(\frac{p - 2}{2}\) = q
p - 2q 2 ....(ii)
q = 2, p = 6
3q = 6
Users' Answers & Commentsp + q = 8 ....(i)
\(\frac{p - 2}{2}\) = q
p - 2q 2 ....(ii)
q = 2, p = 6
3q = 6
30
The angle of depression of a boat from the top of a cliff 10m high is 30. How far is the boat from the foot of the cliff?
A
\(\frac{5√3m}{3}\)
B
5√3m
C
10√3m
D
\(\frac{10√3m}{3}\)
correct option: c
RQP = 90o
PQS = 30o but
RQS = 90o = \(\frac{RS}{10}\)
RS = 10 tan 60o
RS = 10 tan 60o
RS = 10√3m
Users' Answers & CommentsPQS = 30o but
RQS = 90o = \(\frac{RS}{10}\)
RS = 10 tan 60o
RS = 10 tan 60o
RS = 10√3m