# Mathematics 2008 | Study Mode

Question 61
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

4x - 3x $$\leq$$ 7

x $$\leq$$ 7

ii. 3x - 4 $$\leq$$ 4x

3x - 4x $$\leq$$ 4

-x $$\leq$$ -4

-4 $$\leq$$ x $$\leq$$ 7

Question 62
A
x $$\leq$$ 2, x $$\geq$$ 3
B
x $$\leq$$ 3, x $$\geq$$ 2
C
x $$\leq$$ -2, x $$\geq$$ -3
D
x $$\leq$$ -3,x $$\geq$$ 2
##### Explanation
x2 - 5x + 6 $$\geq$$ 0

x2 - 2x - 3x + 6 $$\geq$$ 0

x(x - 2) - 3(x - 2) $$\geq$$ 0

(x - 2) (x - 3) $$\geq$$ 0

x $$\geq$$ 2 or $$\geq$$ 3

x $$\leq$$ 2 $$\geq$$

Question 63
A
12
B
4
C
-12
D
-24
##### Explanation
In = a + (n - 1)d

24 = a + (5 - 1)d

24 = a + 4d.......(i)

96 = a + (11 - 1)d

96 = a + 10d.......(ii)

a = 24 - 4d.......(iii)

96 = 24 - 4d + 10d

96 = 24 + 6d

96 - 24 = 6d

72 = 6d

d = $$\frac{72}{6}$$

d = 12

a = 24 - 4d

a = 24 - 4 x 12

a = 24 - 48

a = -24

Question 64
A
commutative and closed on the set of positive integers
B
neither commutative nor closed on the set of positive integers
C
commutative but not closed on the set of positive integers
D
not commutative but closed on the set of positive integers
##### Explanation
a $$\ast$$ b = b $$\ast$$ a

x $$\ast$$ y = y $$\ast$$ x

2x - 3y + 2 $$\neq$$ 2y - 3y - 3x + 2

2 $$\ast$$ 3 = 2(2) -3(3) + 2

= 4 - 9 + 2

= -3

1 $$\ast$$ 2 = 2(1) - 3(2) + 2

= 2 - 6 + 2

= 2 - 6 + 2

= -2

Question 65
A
1
B
o
C
-$$\frac{1}{2}$$
D
-1
##### Explanation
m $$\Delta$$ n = m + n + mn

m $$\Delta$$ e = e $$\Delta$$ m = m

m $$\Delta$$ e = m

m + e + me = m

e + me = m - m

e + me = 0

e(1 + m) = 0

e = $$\frac{0}{1 + m}$$ = 0

Question 66
A
-3, -2
B
-5, -3
C
-2, -5
D
-3, -5
##### Explanation

$$\begin{pmatrix} 1 & 0 \\ -1 & -1\\ 2 & 2 \end{pmatrix}$$ + $$\begin{pmatrix} x & 1 \\ -1 & 0\\ y & -2 \end{pmatrix}$$ = $$\begin{pmatrix} -2 & 1 \\ -2 & -1\\ -3 & 0 \end{pmatrix}$$

therefore, (x, y) = (-3, -5) respectively

Question 67
A
-$$\frac{1}{8}$$
B
$$\frac{3}{8}$$
C
$$\frac{5}{8}$$
D
$$\frac{1}{4}$$
##### Explanation
-2p + r = 1.......(i)

2p + 3r = 0.......(ii)

r - 1 + 2p ........(iii)

2p + 3(1 + 2p) = 0

2p + 3(1 + 2p) = 0

2p + 3 + 6p = 0

3 - 8p = 0 $$\to$$ 8p = 3

p = $$\frac{3}{8}$$

6 = 1 - 2 $$\frac{3}{8}$$

= 1 - $$\frac{6}{8}$$

$$\frac{8 - 6}{8}$$ = $$\frac{2}{8}$$

= $$\frac{1}{4}$$

Question 68
A
30o
B
45o
C
60o
D
90o
##### Explanation
Equilateral are equal in sides and angle

180o = 60o + 60o + 60o

$$\theta$$ = 60o

Question 69
A
44 000 litres
B
4400 litres
C
440 litres
D
44 litres
##### Explanation
r = 1

h = 14

$$\pi$$ = $$\frac{22}{7}$$

A = $$\pi$$r2h

A = $$\frac{22}{7}$$ x 12 x 14

A = 44m2

A = 44 x 10 litres

A = 440 litres

Question 70
A
(2, 5)
B
(5, 2)
C
(1, 0)
D
(0,1)
##### Explanation
let (6, 2) be represented as (x1, y1) and (4, 2) be (x2, y2)

p(6, 2) R(4, 2)

m.p = ($$\frac{x_1 + x_2}{2}$$) ($$\frac{y_1 + y_2}{2}$$)

= ($$\frac{6 + 4}{2}$$ , $$\frac{2 + 2}{2}$$)

= ($$\frac{10}{2}$$,$$\frac{4}{2}$$)

= (5, 2)

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