# Mathematics 2009 | Study Mode

Question 21
A
-5/4
B
-5/6
C
zero
D
5
##### Explanation
mn = m + n + mn
for inverse -5-1 x -5 = e
-5-1 + -5 + (-5-1)(-5) = 0
-5 + (-5-1(-5)) = 5
-5-1.(1 + -5) = 5
-5-1(-4) = 5
-5-1 = -5/4

Question 22
A
-50
B
-22
C
22
D
50
##### Explanation
Q = $$\left[ \begin{array}{ccc} 9 & -2 \\ -7 & 4 \\ \end{array} \right]$$
|Q| = 9x4 - (-2x7)
= 36 - 14
= 22

Question 23
A
-5
B
-2
C
2
D
5
##### Explanation
$$P=\left[\begin{array}{cc}x+3 & x+2\\ x+1 & x-1\end{array}\right]$$ evaluate x if |P| = -10
(x+3)(x-1) - {(x+1)(x+2)} = -10
x2 - x + 3x - 3 - {x2 + 2x + x + 2} = -10
x2 + 2x - 3 - {x2 + 3x + 2} = -10
-x - 5 = -10
-5 + 10 = x
5 = x
x = 5

Question 24
A
15o
B
30o
C
45o
D
60o
##### Explanation
y = x, Gradient (m1) = 1
y = 3x gradient (m2) = 3
$$tan\theta = \frac{m_2 - m_1}{1+m_2 m_1}\\ tan\theta = \frac{\sqrt{3}-1}{1+\sqrt{3}\times 1}\\ =\frac{1.73 -1 }{1+1.73}= \frac{0.73}{2.73}=0.268$$
= Tan-1 (0.268)
= 15o

Question 25
A
12
B
10
C
9
D
8
##### Explanation
Sum of interior angles of a polygon = each interior x n
(n-2)180 = 150 x n
180n - 360 = 150n
180n-150n = 360
30n = 360
n = 360/30
n = 12 sides

Question 26
A
47o
B
52o
C
56o
D
99o
##### Explanation
In TYX
XY = TY y =47o base s of ISC
But y+x+34+47 = 180 interior
opposite s are supplementary
47 + x + 34 + 47 = 180
x + 128= 180
x = 180- 128
x = 52o

Question 27
A
1/2 cm2
B
1 cm2
C
2 cm2
D
22 cm2
X2 + x2 = 22
2x2 = 4
x2 = 4/2
x2 = 2
x = +/-2
Area of = 1/2bh
= 1/2 x 2 x 2
= 2/2
= 1 cm2

Question 28
A
7cm
B
9cm
C
12cm
D
24cm
##### Explanation
x2 + 52 = 132
x2 + 25 = 169
x2 = 144

x = 144

= 12
Length of the chord AB = 2x
2*12= 24cm

Question 29
A
7.00 cm
B
3.50 cm
C
3.00 cm
D
1.75 cm
##### Explanation
 154 = 4 x 22 x r2 7

 154x7 = r2 4x22

49/4 = r

 7 = r 2

r = 3.50

Question 30
A
x + y = 0
B
x - y = 0
C
x + y + k = 0
D
x - y - k = 0
##### Explanation
Locus of a particle which moves in the first quadrant so that it is equidistant from the lines
X = 0 and Y = 0 and x = 0 and y = 0 are the x and y axes is the lines bisecting the angle between x and y axes

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