2008 - JAMB Mathematics Past Questions and Answers - page 2
11
A book seller sells Mathematics and English books. If 30 customers buy Mathematics books, 20 customers buy English books and 10 customers buy the two books, How many customers has he altogether.
A
30
B
40
C
50
D
60
correct option: b
n(M) only = 30-10 = 20
n(E) only = 20-10 = 10
n(M∩E) = 10
∴M∪E = 20+10+10
= 40
Users' Answers & Commentsn(E) only = 20-10 = 10
n(M∩E) = 10
∴M∪E = 20+10+10
= 40
12
Make Q the subject of formula when \(L=\frac{4}{3}M\sqrt{PQ}\)
A
\(\frac{9L^2}{16M^2}P\)
B
\(\frac{3L}{4M\sqrt{P}}\)
C
\(\frac{\sqrt{3L}}{4MP}\)
D
\(\frac{3L^2}{16M^2}P\)
correct option: a
\(L=\frac{4}{3}M\sqrt{PQ}\\
=\frac{3}{4M} \times L = \sqrt{PQ}\\
=\left(\frac{3L}{4M}\right)^2=(\sqrt{PQ})^2\\
=\frac{9L^2}{16M^2}=PQ\\
=Q=\frac{9L^2}{16M^2 P}\)
Users' Answers & Comments13
If 2x2 - kx - 12 is divisible by x-4, Find the value of k.
A
4
B
5
C
6
D
7
correct option: b
2x2 - kx - 12 is divisible by x-4
implies x is a factor ∴ x = 4
f(4) implies 2(4)2 - k(4) - 12 = 0
32 - 4k - 12 = 0
-4k + 20 = 0
-4k = -20
k = 5
Users' Answers & Commentsimplies x is a factor ∴ x = 4
f(4) implies 2(4)2 - k(4) - 12 = 0
32 - 4k - 12 = 0
-4k + 20 = 0
-4k = -20
k = 5
14
Factorize complete;y (4x+3y)2 - (3x-2y)2
A
(x+5y)(7x+y)
B
(x+5y)(7x-y)
C
(x-5y)(7x+y)
D
(x-5y)(7x-y)
correct option: a
(4x+3y)2 - (3x-2y)2
(4x+3y+3x-2y)(4x+3y-(3x-2y))
(4x+3y+3x-2y)(4x+3y-3x+2y)
(x+5y)(7x+y)
Users' Answers & Comments(4x+3y+3x-2y)(4x+3y-(3x-2y))
(4x+3y+3x-2y)(4x+3y-3x+2y)
(x+5y)(7x+y)
15
If x - 3 is directly proportional to the square of y and x = 5 when y =2, find x when y = 6.
A
30
B
21
C
16
D
12
correct option: b
(x – 3) ∝ y2
X-3 = Ky2
K = X-3 / y2
= 5-2/22
= 2/4
= 1/2
∴X-3 = 1/2y2
X-3 = 1/2(6)2
X-3 = 1/2 x 30/1
X-3 = 18
X = 21
Users' Answers & CommentsX-3 = Ky2
K = X-3 / y2
= 5-2/22
= 2/4
= 1/2
∴X-3 = 1/2y2
X-3 = 1/2(6)2
X-3 = 1/2 x 30/1
X-3 = 18
X = 21
16
If p = varies inversely as the square of q and p=8 when q=4, find when p=32
A
+/-16
B
+/-8
C
+/-4
D
+/-2
correct option: d
P ∝ 1/q
P = k/q
K = q2P
= 428
∴P = 128/q
32 = 128/q
q2 = 128/32
q2 = 4
q = √4 = +/-2
Users' Answers & CommentsP = k/q
K = q2P
= 428
∴P = 128/q
32 = 128/q
q2 = 128/32
q2 = 4
q = √4 = +/-2
17
Find the range of values of x which satisfy the inequalities 4x - 7 \(\leq\) 3x and 3x - 4 \(\leq\) 4x
A
-4 \(\leq\) x \(\leq\) 7
B
-7 \(\leq\) x \(\leq\) 4
C
x \(\geq\) -7
D
-7 \(\leq\) x \(\leq\) 6
correct option: a
4X - 7 \(\leq\) 3X and 3X - 4 \(\leq\) 4X
4X - 3X \(\leq\) 7 and 3X - 4X \(\leq\) 4
X \(\leq\) 7 and -X \(\leq\) 4 = X \(\geq\) -4
Range -4 \(\leq\) x \(\leq\) 7
Users' Answers & Comments4X - 3X \(\leq\) 7 and 3X - 4X \(\leq\) 4
X \(\leq\) 7 and -X \(\leq\) 4 = X \(\geq\) -4
Range -4 \(\leq\) x \(\leq\) 7
18
Solve the quadratic inequalities x2 - 5x + 6 ≥0
A
x ≤ 2, x ≥ 3
B
x ≤ 3, x ≥ 2
C
x ≤ -2, x ≥ -3
D
x ≤-3, x ≥ 2
correct option: a
x2 - 5x + 6 = 0
(X-2)(X-3) = 0
X-2 = 0 implies X = 2
X-3 = 0 implies X = 3
∴ x ≤ 2, x ≥ 3
Users' Answers & Comments(X-2)(X-3) = 0
X-2 = 0 implies X = 2
X-3 = 0 implies X = 3
∴ x ≤ 2, x ≥ 3
19
The fifth term of an A.P is 24 and the eleventh term is 96. Find the first term.
A
12
B
4
C
-12
D
-24
correct option: d
U5 = 24, n = 5 and U11 = 96, n = 11
Un = a + (n-1)d
24 = a + (5-1)d imply 24 = a+4d .....eqn1
96 = a + (11-1)d imply 96 = a+10d ...eqn2
eqn1 - eqn2 -72 = -6d
d = 72/6 = 12
but 24 = a+4d
24 = a + 4(12)
24 = a + 48
a = 24-48
a = -24
Users' Answers & CommentsUn = a + (n-1)d
24 = a + (5-1)d imply 24 = a+4d .....eqn1
96 = a + (11-1)d imply 96 = a+10d ...eqn2
eqn1 - eqn2 -72 = -6d
d = 72/6 = 12
but 24 = a+4d
24 = a + 4(12)
24 = a + 48
a = 24-48
a = -24
20
A binary operation * is defined on the set of positive integers is such x*y = 2x-3y+2 for all positive integers x and y. The binary operation is
A
commutative and close on the set of positive integers
B
neither commutative nor closed on the set of ppositive integers
C
commutative but not closed on the set of positive integers
D
not cummutative but closed on the set of positive integers
correct option: b
X * Y = 2X - 3Y + 2
2*3 = 2(2) - 3(3) + 2
=4-9+2
= -3
But -3 does not belong to positive integer
Users' Answers & Comments2*3 = 2(2) - 3(3) + 2
=4-9+2
= -3
But -3 does not belong to positive integer