# Mathematics 2009 | Study Mode

Question 61
A
n(3n - 0.5)
B
n(3n + 2)
C
n(3n + 2.5)
D
n(3n + 5)
##### Explanation
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)

Question 62
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 < $$\frac{7}{3}$$
##### Explanation
3x - 7 $$\leq$$ 0 ; x + 5 > 0

3x $$\leq$$ 7 ; x > -5

= x $$\leq$$ $$\frac{7}{3}$$

-5 < x $$\leq$$ $$\frac{7}{3}$$

Question 63
A
10
B
9
C
$$\frac{10}{9}$$
D
$$\frac{9}{10}$$

Question 64
A
-6
B
-8
C
-10
D
-12
##### Explanation
If m x n = n

= n - (m + 2)

3 $$\ast$$ (-5) = -5 - (3 + 2)

= -5 - 5

= -10

Question 65
A
$$\frac{-5}{4}$$
B
$$\frac{-5}{6}$$
C
o
D
5

Question 66
A
-50
B
-22
C
22
D
50
##### Explanation
If Q = $$\begin{pmatrix} 9 & -2 \\ -7 & 4 \end{pmatrix}$$, then |Q| is

= 9 x 4 - (-2) x (-7)

= 36 - 14

= 22

Question 67
A
-5
B
-2
C
2
D
5
##### Explanation
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

Question 68
A
15o
B
30o
C
45o
D
60o
##### Explanation
x $$\leq$$ 90o (acute angle)

x2 = 3x

3x = 90o

x = $$\frac{90^o}{3}$$ = 30o

Question 69
A
12
B
10
C
9
D
8
##### Explanation
x + 150o = 180o (sum of angle on straight line)

x = 180o - 150o , x = 30o

number of sides (n) = $$\frac{360}{3}$$

= 12

Question 70
A
$$\frac{1}{\sqrt{2}}$$ cm2
B
1 cm2
C
$$\sqrt{2}$$cm2
D
2$$sqrt{2}$$cm2
##### Explanation
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

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