Mathematics 2012 | Study Mode

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Question 21
A
3
B
4
C
5
D
7
Explanation
\(\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix}\) = \(\begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix}\)

10 - 3x = 15 - 20

-3x = 15 - 20 - 10

-3x = -15

x = 5

Correct option: C
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Question 22
A
-1
B
O
C
1
D
2
Explanation
Recall that a unit matrice is a diagonal matrix in which the elements in the leading diagonal is unity. Therefore,

I3 = \(\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\)

I3 = \(+1\begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} - 0\begin{vmatrix} 0 & 0 \\ 0 & 1 \end{vmatrix} + 0 \begin{vmatrix} 0 & 1 \\ 0 & 0 \end{vmatrix} \)

I3 = +1(1 - 0) - 0(0 - 0) + 0(0 - 0)

= 1(1)

= 1

Correct option: C
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Question 23
A
24o
B
30o
C
33o
D
36o
Explanation

Explanation not provided, please join discuss, your contributions are welcomed


Correct option: D
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Question 24
A
3.92cm3
B
2.13cm3
C
1.97cm3
D
1.62cm3
Explanation
Volume of cuboid = L x b x h

= 0.76cm x 2.6cm x 0.82cm

= 1.62cm3

Correct option: D
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Question 25
A
line parallel to 7x + 13y + 8 = 0
B
circle
C
semicircle
D
bisector of the line 7x + 13y + 8 = 0
Explanation

Explanation not provided, please join discuss, your contributions are welcomed


Correct option: A
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Question 26
A
\(\frac{1}{2}\)
B
\(\frac{2}{5}\)
C
\(-\frac{4}{7}\)
D
\(-\frac{2}{3}\)
Explanation
PQ = \(\frac{y_1 - y_0}{x_1 - x_0}\) = \(\frac{-3 - (-7)}{-2 - 5}\) = \(\frac{-3 + 7}{-2 - 5}\) = \(\frac{4}{-7}\)

Correct option: C
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Question 27
A
\(\sqrt{13}\)
B
\(3\sqrt{2}\)
C
\(\sqrt{26}\)
D
\(10\sqrt{5}\)
Explanation
P1 (4, 3), P2 (x, y)

y = 2x + 4 .....(1)

y = 7 - x .....(2)

Substitute (2) in (1)

7 - x = 2x + 4

7 - 4 = 2x + x

3 = 3x

x = 1

Substitute in eqn (2)

y = 7 - x

y = 7 - 1

y = 6

P2 (1, 6)

Distance between 2 points is given as

D = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

D = \(\sqrt{(1 - 4)^2 + (6 - 3)^2}\)

D = \(\sqrt{(-3)^2 + (3)^2}\)

D = \(\sqrt{9 + 9}\)

D = \(\sqrt{18}\)

D = \(\sqrt{9 \times 2}\)

D = \(3\sqrt{2}\)

Correct option: B
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Question 28
A
y = 2x - 3
B
y = 2x + 5
C
y = 3x - 2
D
y = 2x + 1
Explanation
\(\frac{y - y_1}{x + x_1}\) = \(\frac{y_2 - y_1}{x - x_1}\)

\(\frac{y - 1}{x + 2}\) = \(\frac{4 - 1}{-\frac{1}{2} + 2}\)

= \(\frac{y - 1}{x + 2}\) = \(\frac{3}{\frac{3}{2}}\)

y = 2x + 5

Correct option: B
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Question 29
A
\(\frac{1}{2}\)
B
\(\frac{\sqrt{2}}{2}\)
C
\(-\frac{\sqrt{2}}{2}\)
D
\(-\frac{1}{2}\)
Explanation

\(\theta\) = 135o

Cos 135o = Cos(90 + 45)o

= cos90ocos45o - sin90osin45o

= 0cos45o - (1 x \(\frac{\sqrt{2}}{2}\))

= \(-\frac{\sqrt{2}}{2}\)


Correct option: C
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Question 30
A
2x - \(\frac{1}{x^2}\)
B
2x + x2
C
2x - x2
D
2x + \(\frac{1}{x^2}\)
Explanation
y = x2 - \(\frac{1}{x}\)

y = x2 - x-1

\(\frac{\delta y}{\delta x}\) = 2x + x-2


\(\frac{\delta y}{\delta x}\) = 2x + \(\frac{1}{x^2}\)

Correct option: D

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