1999 - JAMB Mathematics Past Questions and Answers - page 2
11
The sum of two numbers is twice their difference. If the difference of the numbers is P, find the larger of the two numbers
A
p/2
B
3p/2
C
5p/2
D
3p
correct option: b
Let the numbers be x and y
x+y = 2p.....(i)
x-y = p......(ii)
2x = 3p
x = 3p/2
Users' Answers & Commentsx+y = 2p.....(i)
x-y = p......(ii)
2x = 3p
x = 3p/2
12
A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation.
A
2/3
B
1/2
C
-1/2
D
-2/3
correct option: a
a*a-1 = aa-1 + a + a-1 = e
if e = 0
2.2-1 + 2 + 2-1 = 0
3.2-1 + 2 = 0
= 2-1 = -\(\frac{2}{3}\)
Users' Answers & Commentsif e = 0
2.2-1 + 2 + 2-1 = 0
3.2-1 + 2 = 0
= 2-1 = -\(\frac{2}{3}\)
13
Factorize completely X2+2XY+Y2+3X+3Y-18
A
(x+y+6)(x+y-3)
B
(x-y-6)(x-y+3)
C
(x-y+6)(x-y-3)
D
(x+y-6)(x+y+3)
correct option: a
Users' Answers & Comments14
Three consecutive positive integers k, l and m are such that l2 = 3(k+m). Find the value of m
A
4
B
5
C
6
D
7
15
Express \(\frac{1}{X^{3}-1}\) in partial fractions
A
1/3{(1/x-1)-(x-2/x2-x+1)}
B
1/3{(1/x-1)-(x+2/x2+x+1)}
C
1/3{(1/x-1)-(x-2/x2+x+1)}
D
1/3{(1/x-1)-(x-2/x2-x-1)}
correct option: b
Users' Answers & Comments16
The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.
A
8/5
B
8/3
C
72/25
D
56/9
correct option: c
Le the common ratio be r so that the first term is 2r.
Sum, s = a/(1-r)
ie. 8 = 2r/(1-r)
8(1-r) = 2r, r = 8/5.
Sn = a(1-rn)/(1-r)
Solve further to get 72/25
Users' Answers & CommentsSum, s = a/(1-r)
ie. 8 = 2r/(1-r)
8(1-r) = 2r, r = 8/5.
Sn = a(1-rn)/(1-r)
Solve further to get 72/25
18
Find a positive value of ã if the coordinate of the centre of a circle X2+y2-2ãx+4y-ã = 0 is (ã,-2) and the radius is 4 units.
A
1
B
2
C
3
D
4
correct option: c
Users' Answers & Comments19
A man 1.7m tall observes a bird on top of a tree at an angle of 300. if the distance between the man's head and the bird is 25m, what is the height of the tree?
A
26.7m
B
14.2m
C
\(1.7+(25\frac{\sqrt{3}}{3}m\)
D
\(1.7+(25\frac{\sqrt{2}}{2}m\)
correct option: c
Hint: Make a sketch forming a right angled triangle. Let X = height required. Such that x/25 = tan 30.
Users' Answers & Comments20
In ∆MNO, MN = 6 units, MO = 4 units and NO = 12 units. If the bisector of and M meets NO at P, calculate NP.
A
4.8 units
B
7.2 units
C
8.0 units
D
18.0 units