\(\begin{pmatrix} 4 & 1 \\ -2 & 9 \end{pmatrix}\)
\(\begin{pmatrix} -4 & 1 \\ 2 & 9 \end{pmatrix}\)
\(\begin{pmatrix} -4 & 3 \\ -2 & 13 \end{pmatrix}\)
\(\begin{pmatrix} -4 & 3 \\ -2 & 9 \end{pmatrix}\)
Correct answer is D
\(\begin{pmatrix} 1 & -2 \\ 3 & 4 \end{pmatrix} \(\begin{pmatrix} -2 & 3 \\ 1 & 0 \end{pmatrix}\)
= \(\begin{pmatrix} (1 \times -2) + (-2 \times 1) & (1 \times 3) + (-2 \times 0) \\ (3 \times -2) + (4 \times 1) & (3 \times 3) + (4 \times 0) \end{pmatrix}\)
= \(\begin{pmatrix} -4 & 3 \\ -2 & 9 \end{pmatrix}\)
Express \(\frac{7\pi}{6}\) radians in degrees.
315°
210°
105°
75°
Correct answer is B
\(\pi = 180°\)
\(\frac{7\pi}{6} = \frac{7 \times 180}{6} \)
= \(210°\)
A rectangle has a perimeter of 24m. If its area is to be maximum, find its dimension.
12, 12
6, 6
4, 8
9, 3
Correct answer is B
\(Perimeter = 2(l + b) = 24\)
\(l + b = 12 \implies l = 12 - b\)
\(Area = (12 - b) \times b = 12b - b^{2}\)
\(\frac{\mathrm d A}{\mathrm d b} = 12 - 2b = 0\) (at maximum)
\(2b = 12 \implies b = 6\)
\(l = 12 - 6 = 6m\)
Evaluate \(\int_{1}^{2} (2 + 2x - 3x^{2}) \mathrm {d} x\).
-2
2
8
10
Correct answer is A
\(\int_{1}^{2} (2 + 2x - 3x^{2}) \mathrm {d} x\)
= \((2x + x^{2} - x^{3})|_{1}^{2}\)
= \((2(2) + 2^{2} - 2^{3}) - (2(1) + 1^{2} - 1^{3})\)
= \(0 - 2 = -2\)
What is the coordinate of the centre of the circle \(5x^{2} + 5y^{2} - 15x + 25y - 3 = 0\)?
\((\frac{15}{2}, -\frac{25}{2})\)
\((\frac{3}{2}, -\frac{5}{2})\)
\((-\frac{3}{2}, \frac{5}{2})\)
\((-\frac{15}{2}, \frac{25}{2})\)
Correct answer is B
Equation for a circle: \((x - a)^{2} + (y - b)^{2} = r^{2}\)
Expanding, we have:
\(x^{2} - 2ax + a^{2} + y^{2} - 2by + b^{2} = r^{2}\)
Given: \(5x^{2} + 5y^{2} - 15x + 25y - 3 = 0\)
Divide through by 5,
\(= x^{2} + y^{2} - 3x + 5y - \frac{3}{5} = 0\)
Comparing, we have
\(- 2a = -3; a = \frac{3}{2}\)
\(-2b = 5; b = -\frac{5}{2}\)