2009 - JAMB Mathematics Past Questions and Answers - page 2
11
I.S∩T∩W=S II. S∪T∪W=S
III. T∩W=S
If S⊂T⊂W, which of the above statements are true?
III. T∩W=S
If S⊂T⊂W, which of the above statements are true?
A
I and II
B
I and III
C
II and III
D
I, II and III
correct option: d
S∩T∩W = S(This means that all the elements of s are in T and also in W.)
S∪T∪W = W (imply W is a universal set for S and T) T∩W = S imply all the elements of S are in T and W)
S ⊂ T ⊂ W
∴ I, II, and III
Users' Answers & CommentsS∪T∪W = W (imply W is a universal set for S and T) T∩W = S imply all the elements of S are in T and W)
S ⊂ T ⊂ W
∴ I, II, and III
12
If \(P=\sqrt{\frac{rs^3}{t}}\), express r in terms of p, s and t
A
\(\frac{p^2 t}{s^3}\)
B
\(\frac{p^3 t}{s^3}\)
C
\(\frac{p^3 t}{s^2}\)
D
\(\frac{p^ t}{s^3}\)
correct option: a
\(P=\sqrt{\frac{rs^3}{t}}\=
P^2 =\frac{rs^3}{t}\\ tp^2 = rs^3\\ r = \frac{p^2 t}{s^3}\)
Users' Answers & CommentsP^2 =\frac{rs^3}{t}\\ tp^2 = rs^3\\ r = \frac{p^2 t}{s^3}\)
13
A polynomial in x whose roots are 4/3 and -3/5 is
A
15x2 - 11x – 12
B
15x2 + 11x – 12
C
12x2 - x – 12
D
12x2 + 11x – 15
correct option: a
If 4/3 and -3/5 are roots of a polynomial
Imply x = 4/3 and - 3/5
3x = 4 and 5x = -3
∴3x-4 = 0 and 5x+3 = 0 are factors
(3x-4)(5x+3) = 0 product of the factors
15x2 + 9x – 20x – 12 = 0 By expansion
15x2 - 11x – 12 = 0
Users' Answers & CommentsImply x = 4/3 and - 3/5
3x = 4 and 5x = -3
∴3x-4 = 0 and 5x+3 = 0 are factors
(3x-4)(5x+3) = 0 product of the factors
15x2 + 9x – 20x – 12 = 0 By expansion
15x2 - 11x – 12 = 0
14
Which of the following equations represent the graph above?
A
y = 2+7x+4x2
B
y = 2-7x+4x2
C
y = 2+7x-4x2
D
y = 2-7x-4x2
correct option: d
x = -2 and x = 1/4
x = -2 and 4x = 1
x+2 and 4x-1
(x+2)(4x-1) = 0
4x2 - x + 8x -2 = 0
4x2 + 7x – 2 = 0 but y intercept is positive. Multiply the equation by -1
-4x2 - 7x + 2 = 0
∴y = 2 – 7x – 4x2
Users' Answers & Commentsx = -2 and 4x = 1
x+2 and 4x-1
(x+2)(4x-1) = 0
4x2 - x + 8x -2 = 0
4x2 + 7x – 2 = 0 but y intercept is positive. Multiply the equation by -1
-4x2 - 7x + 2 = 0
∴y = 2 – 7x – 4x2
15
W is directly proportional to U. If w = 5 when U = 3, find when W = 2/7
A
6/35
B
10/21
C
21/10
D
35/6
correct option: a
\(W ∝ U\\
W = KU\\
K = \frac{W}{U}\\
K = \frac{5}{3}\\
W = \frac{5}{3}U\\
\frac{2}{7} = \frac{5}{3}U\\
U = \frac{2}{7} \times \frac{3}{5}\\
U = \frac{6}{35}\)
Users' Answers & Comments16
Determine the value of x for which (x2 - 1) > 0
A
x < -1 or x > 1
B
-1 < x < 1
C
x > 0
D
x < -1
17
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 and x + 5 > 0
3x \(\leq\) 7 and x > -5
x \(\leq\) \(\frac{7}{3}\)
∴ Range -5 < x \(\leq\) \(\frac{7}{3}\)
Users' Answers & Comments3x \(\leq\) 7 and x > -5
x \(\leq\) \(\frac{7}{3}\)
∴ Range -5 < x \(\leq\) \(\frac{7}{3}\)
18
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
a = 5, d = 6, n = n
Sn = n/2(2a + (n-1)d)
= n/2(2(5) + (n-1)6)
= n/2(10 + 6n-6)
= n/2(6n+4)
= 6n2/2 + 4n/2
= 32 + 2n
= n(3n + 2)
Users' Answers & CommentsSn = n/2(2a + (n-1)d)
= n/2(2(5) + (n-1)6)
= n/2(10 + 6n-6)
= n/2(6n+4)
= 6n2/2 + 4n/2
= 32 + 2n
= n(3n + 2)
19
Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3,.....\)
A
10
B
9
C
10/9
D
9/10
correct option: a
\(a=1, r=\frac{9}{10}\\
S_n = \frac{a}{1-r}\\
S_n = \frac{1}{1-\frac{9}{10}}\\
=1\div \frac{1}{10}\\
=1\times \frac{10}{1}\\
10\)
Users' Answers & Comments20
If m * n = n - (m+2) for any real number m and n find he value of 3*(-5)
A
-6
B
-8
C
-10
D
-12