2009 - JAMB Mathematics Past Questions and Answers - page 7
61
The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35,... is
A
n(3n - 0.5)
B
n(3n + 2)
C
n(3n + 2.5)
D
n(3n + 5)
correct option: b
Tn = \(\frac{1}{2}\)n(2a + (n - 1)d)
= \(\frac{1}{2}\)n(2 x 5 + (n - 1) 6
= \(\frac{1}{2}\)n(10 + 6n - 6)
= n\(\frac{1}{2}\)(6n + 4)
= n(3n + 2)
Users' Answers & Comments= \(\frac{1}{2}\)n(2 x 5 + (n - 1) 6
= \(\frac{1}{2}\)n(10 + 6n - 6)
= n\(\frac{1}{2}\)(6n + 4)
= n(3n + 2)
62
Find the range of values of x for which 3x - 7 \(\leq\) 0 and x + 5 > 0
A
-5 < x < \(\frac{7}{3}\)
B
-5 \(\leq\) x \(\leq\) \(\frac{7}{3}\)
C
-5 < x \(\leq\) \(\frac{7}{3}\)
D
-5 \(\leq\) x < \(\frac{7}{3}\)
correct option: c
3x - 7 \(\leq\) 0 ; x + 5 > 0
3x \(\leq\) 7 ; x > -5
= x \(\leq\) \(\frac{7}{3}\)
-5 < x \(\leq\) \(\frac{7}{3}\)
Users' Answers & Comments3x \(\leq\) 7 ; x > -5
= x \(\leq\) \(\frac{7}{3}\)
-5 < x \(\leq\) \(\frac{7}{3}\)
63
Find the infinity, the sum of the sequence 1, \(\frac{9}{10}\), (\(\frac{9}{10}\))2, (\(\frac{9}{10}\))3,...
A
10
B
9
C
\(\frac{10}{9}\)
D
\(\frac{9}{10}\)
correct option: b
Users' Answers & Comments64
If m \(\ast\) n = n-(m + 2) for any real numbers m and n, find the value of 3 \(\ast\) (-5)
A
-6
B
-8
C
-10
D
-12
correct option: c
If m x n = n
= n - (m + 2)
3 \(\ast\) (-5) = -5 - (3 + 2)
= -5 - 5
= -10
Users' Answers & Comments= n - (m + 2)
3 \(\ast\) (-5) = -5 - (3 + 2)
= -5 - 5
= -10
65
A binary operation \(plus\) defined on the set of integers is such that m \(plus\) n = n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0.
A
\(\frac{-5}{4}\)
B
\(\frac{-5}{6}\)
C
o
D
5
correct option: d
Users' Answers & Comments66
If Q = \(\begin{pmatrix} 9 & -2 \ -7 & 4 \end{pmatrix}\), then |Q| is
A
-50
B
-22
C
22
D
50
correct option: c
If Q = \(\begin{pmatrix} 9 & -2 \ -7 & 4 \end{pmatrix}\), then |Q| is
= 9 x 4 - (-2) x (-7)
= 36 - 14
= 22
Users' Answers & Comments= 9 x 4 - (-2) x (-7)
= 36 - 14
= 22
67
If p = \(\begin{pmatrix} x + 3 & x + 2 \ x + 1 & x - 1 \end{pmatrix}\) evaluate x if |p| = -10
A
-5
B
-2
C
2
D
5
correct option: d
If p = \(\begin{pmatrix} x + 3 & x + 2 \ x + 1 & x - 1 \end{pmatrix}\) evaluate x if |p| = -10
|P| = (x + 3)(x - 1) - (x + 2)(x + 1)
x2 + 2x - 3 - (x2 + 3x + 2)
x2 + 2x - 3 - x2 - 3x - 2
-x - 5 = -10
-x = -10 + 5
x = 5
Users' Answers & Comments|P| = (x + 3)(x - 1) - (x + 2)(x + 1)
x2 + 2x - 3 - (x2 + 3x + 2)
x2 + 2x - 3 - x2 - 3x - 2
-x - 5 = -10
-x = -10 + 5
x = 5
68
Find the acute angle between the straight lines y = x and y = \(\sqrt{3x}\)
A
15o
B
30o
C
45o
D
60o
correct option: b
x \(\leq\) 90o (acute angle)
x2 = 3x
3x = 90o
x = \(\frac{90^o}{3}\) = 30o
Users' Answers & Commentsx2 = 3x
3x = 90o
x = \(\frac{90^o}{3}\) = 30o
69
A rectangular polygon has 150o as the size of each interior angle. How many sides does it has?
A
12
B
10
C
9
D
8
correct option: a
x + 150o = 180o (sum of angle on straight line)
x = 180o - 150o , x = 30o
number of sides (n) = \(\frac{360}{3}\)
= 12
Users' Answers & Commentsx = 180o - 150o , x = 30o
number of sides (n) = \(\frac{360}{3}\)
= 12
70
If the hypotenuse of a right-angled isosceles triangle is 2cm , what is the area of the triangle?
A
\(\frac{1}{\sqrt{2}}\) cm2
B
1 cm2
C
\(\sqrt{2}\)cm2
D
2\(sqrt{2}\)cm2
correct option: b
sin45o = \(\frac{y}{2}\)
y = 2 sin45o
y = 2 (\(\frac{1}{\sqrt{2}}\))
y = \(\frac{2}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)
y = \(\frac{2\sqrt{2}}{2}\)
y = \(\sqrt{2}\)
Since it is an isosceles triangle
x = \(\sqrt{2}\)
Area of \(\Delta\) = \(\frac{1}{2}\)bh
= \(\frac{1}{2}\) x \(\sqrt{2}\) x \(\sqrt{2}\)
= \(\frac{1}{2}\) x 2
= 1 cm2
Users' Answers & Commentsy = 2 sin45o
y = 2 (\(\frac{1}{\sqrt{2}}\))
y = \(\frac{2}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)
y = \(\frac{2\sqrt{2}}{2}\)
y = \(\sqrt{2}\)
Since it is an isosceles triangle
x = \(\sqrt{2}\)
Area of \(\Delta\) = \(\frac{1}{2}\)bh
= \(\frac{1}{2}\) x \(\sqrt{2}\) x \(\sqrt{2}\)
= \(\frac{1}{2}\) x 2
= 1 cm2