2006 - JAMB Mathematics Past Questions and Answers - page 5
41
THe cost of renovating a 6 m square room is N540. What is the cost of renovating a 9 m square room?
A
N1215
B
N720
C
N1620
D
N810
correct option: d
Cost of removing a 6m2 room = N540
Cost of renovating a 1m2 room = 540 / 6
Cost of removing a 9m2 room
= (540 / 6) * 9
= N810
Users' Answers & CommentsCost of renovating a 1m2 room = 540 / 6
Cost of removing a 9m2 room
= (540 / 6) * 9
= N810
42
The sum of the first n positive integers is
A
1/2 n(n-1)
B
n(n+1)
C
n(n-1)
D
1/2 n(n-1)
correct option: d
Let the positive integers be 1, 2, ,3, 4, .....n
∴ a = 1, d = 1 and n = n
Sn = n/2(2a + (n-1)d)
= n/2 (2 + n – 1)
= 1/2n(n + 1)
Users' Answers & Comments∴ a = 1, d = 1 and n = n
Sn = n/2(2a + (n-1)d)
= n/2 (2 + n – 1)
= 1/2n(n + 1)
43
If T = 2 π √1/g, make g the subject of the formula
A
(4π l2) / T
B
(4π2l) / T2
C
(4π2l2) / T2
D
(2π√l) / T
correct option: b
T = 2 π √1/g
T/2π = √1/g
(T/2π)2 = (√1/g)2
T2/4π2 = 1/g
T2 x g = 4π2 x l
G = (4π2 x l) / T2
Users' Answers & CommentsT/2π = √1/g
(T/2π)2 = (√1/g)2
T2/4π2 = 1/g
T2 x g = 4π2 x l
G = (4π2 x l) / T2
44
If y = x2 - x - 12, find the range of values of x for which y \( \geq \) 0
A
x < -3 0r x > 4
B
x \( \leq \) -3 or x \( \geq \) 4
C
-3 < x \( \geq \) 4
D
-3 \( \leq \) x \( \leq \) 4
correct option: c
y = x2 - x - 12
= (x - 4)(x - 3)
∴ x = 4 or x = -3
-3 < x < 4
But y \( \geq \) 0
∴ -3 < x \( \leq \) 4
Users' Answers & Comments= (x - 4)(x - 3)
∴ x = 4 or x = -3
-3 < x < 4
But y \( \geq \) 0
∴ -3 < x \( \leq \) 4
45
How many terms of the series 3, -6, +12, - 24, + ..... are needed to make a total of 1-28?
A
12
B
10
C
9
D
8
correct option: c
3, -6, +12, -24
a = 3, r = -2
\(8n = \frac{a(1-r^n)}{1-r}\\ ∴1-2^8 = \frac{3(1-(-2^{n-1}))}{1-(-2)}\\ 1-2^8 = \frac{3(1-(-2^{n-1}))}{3}\)
1-28 = 1-(-2)n-1
-28 = -2n-1
8 = n-1
n = 9
Users' Answers & Commentsa = 3, r = -2
\(8n = \frac{a(1-r^n)}{1-r}\\ ∴1-2^8 = \frac{3(1-(-2^{n-1}))}{1-(-2)}\\ 1-2^8 = \frac{3(1-(-2^{n-1}))}{3}\)
1-28 = 1-(-2)n-1
-28 = -2n-1
8 = n-1
n = 9
46
If tan \(\theta\) = \(\frac{5}{4}\) find sin2\(\theta\) - cos2\(\theta\)
A
\(\frac{9}{41}\)
B
\(\frac{5}{4}\)
C
1
D
\(\frac{9}{1}\)
correct option: a
(tan \(\theta\) = \(\frac{opp}{adj}\))
|AB|2 = 52 + 42 \(\to\) |AB|2 = 41
\(\to\) AB = \(\sqrt{41}\) sin2\(\theta\) - cos2\(\theta\)
\(\to\) \(\frac{5^2}{\sqrt{41}}\) - (\(\frac{4}{\sqrt{41}}^2\)) = \(\frac{25}{41}\) - \(\frac{16}{41}\)
= (\(\frac{9}{41}\))
Users' Answers & Comments|AB|2 = 52 + 42 \(\to\) |AB|2 = 41
\(\to\) AB = \(\sqrt{41}\) sin2\(\theta\) - cos2\(\theta\)
\(\to\) \(\frac{5^2}{\sqrt{41}}\) - (\(\frac{4}{\sqrt{41}}^2\)) = \(\frac{25}{41}\) - \(\frac{16}{41}\)
= (\(\frac{9}{41}\))
47
If the locus of the points which are equidistant from points P and Q meets line PQ at point N, then PN equals
A
2NQ
B
NQ
C
\(\frac{1}{4}\)NQ
D
\(\frac{1}{2}\)NQ
48
PQ and RS are two parallel lines. If the coordinates of P, Q, R, S are (1, q), (3, 2), (3, 4),(5, 2q) respectively, find the value of q
A
2
B
4
C
1
D
3
correct option: a
1 + q + 5 + 2q = 3 + 2 + 3 + 4
6 + 3q = 12 \(\to\) 3q = 12 - 6 = 6
q = 2
Users' Answers & Comments6 + 3q = 12 \(\to\) 3q = 12 - 6 = 6
q = 2
49
What is the locus of points equidistanct from the line ax + by + c = 0?
A
A line bx - ay + q = 0
B
a line ax - by + q = 0
C
A line ax + by + q = 0
D
a line bx + ay + q = 0
correct option: c
Users' Answers & Comments50
Find p, q for which \(\begin{pmatrix} 2p & 8 \ 3 & -5q \end{pmatrix}\)\(\begin{pmatrix} 1 \ 2\end{pmatrix}\)\(\begin{pmatrix}24 \ -17\end{pmatrix}\)
A
-4
B
45
C
4,2
D
2
correct option: d
2p x 2 + 8 x 1 = 24
\(\to\) 4p = 24 - 8 = 16, p = 4
3 x 1 + -5q x 2 = -17
\(\to\) -10q = -17 - 3
-10q = -20
q = 2
Users' Answers & Comments\(\to\) 4p = 24 - 8 = 16, p = 4
3 x 1 + -5q x 2 = -17
\(\to\) -10q = -17 - 3
-10q = -20
q = 2