# Mathematics 2008 | Study Mode

Question 11
A
30
B
40
C
50
D
60
##### Explanation
n(M) only = 30-10 = 20
n(E) only = 20-10 = 10
n(ME) = 10
ME = 20+10+10
= 40

Question 12
A
$$\frac{9L^2}{16M^2}P$$
B
$$\frac{3L}{4M\sqrt{P}}$$
C
$$\frac{\sqrt{3L}}{4MP}$$
D
$$\frac{3L^2}{16M^2}P$$
##### Explanation
$$L=\frac{4}{3}M\sqrt{PQ}\\ =\frac{3}{4M} \times L = \sqrt{PQ}\\ =\left(\frac{3L}{4M}\right)^2=(\sqrt{PQ})^2\\ =\frac{9L^2}{16M^2}=PQ\\ =Q=\frac{9L^2}{16M^2 P}$$

Question 13
A
4
B
5
C
6
D
7
##### Explanation
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

Question 14
A
(x+5y)(7x+y)
B
(x+5y)(7x-y)
C
(x-5y)(7x+y)
D
(x-5y)(7x-y)
##### Explanation
(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)

Question 15
A
30
B
21
C
16
D
12
(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

Question 16
A
+/-16
B
+/-8
C
+/-4
D
+/-2
##### Explanation
P 1/q
P = k/q
K = q2P
= 428
P = 128/q
32 = 128/q
q2 = 128/32
q2 = 4
q = 4 = +/-2

Question 17
A
-4 $$\leq$$ x $$\leq$$ 7
B
-7 $$\leq$$ x $$\leq$$ 4
C
x $$\geq$$ -7
D
-7 $$\leq$$ x $$\leq$$ 6
##### Explanation
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

Question 18
A
x 2, x 3
B
x 3, x 2
C
x -2, x -3
D
x -3, x 2
##### Explanation
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

Question 19
A
12
B
4
C
-12
D
-24
##### Explanation
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

Question 20
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
##### Explanation
X * Y = 2X - 3Y + 2
2*3 = 2(2) - 3(3) + 2
=4-9+2
= -3
But -3 does not belong to positive integer

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