Correct Answer: A. 8

Explanation

y \(\alpha\) \sqrt{x + 1}\), y = k\sqrt{x + 1}\)

6 = k\(\sqrt{3 + 1}\)

6 = k\(\sqrt{4}\)

6 = 2k

k = \(\frac{6}{2}\) = 3

y = \(\sqrt{(x + 1)}\)

9 = 3\(\sqrt{(x + 1)}\)(divide both side by 3)

\(\frac{9}{3}\) = \(\frac{3\sqrt{x + 1}}{3}\)

3 = \(\sqrt{x + 1}\)(square both sides)

9 = x + 1

x = 9 - 1

x = 8

Explanation

(a)

Let O(x, y) be the centre of the circle. O is the midpoint of the two points with given coordinates.

\(x = \frac{2 + 6}{2} = \frac{8}{2} = 4\)

\(y = \frac{1 + 7}{2} = \frac{8}{2} = 4\)

The centre is (4, 4).

(b) Radius of circle = \(\sqrt{(4 - 1)^{2} + (4 - 2)^{2}}\)

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

= \(\sqrt{13} units\).

Equation of the circle : \((x - 4)^{2} + (y - 4)^{2} = (\sqrt{13})^{2}\)

\((x^{2} - 8x + 16) + (y^{2} - 8y + 16) = 13\)

\(x^{2} + y^{2} - 8x - 8y + 32 - 13 = 0\)

\(x^{2} + y^{2} - 8x - 8y + 19 = 0\)

Correct Answer: B. 102°

Correct Answer: C. 3

Correct Answer: C. 3

Correct Answer: (b)2:3

Explanation

(a) a=8;l=52;n=?

\(S_n=\frac{n}{2}(a+l)=286\)

\(=\frac{n}{2}(-8+52)=286\)

\(=\frac{n}{2}(44)=286\)

=22n=286

\(∴n=\frac{286}{22}=13\)

(b) l = a + (n - 1)d = 52

= -8 + (13 - 1)d = 52

= -8 + 12d = 52

= 12d = 52 + 8

= 12d = 60

\(∴d=\frac{60}{12}=5\)

Correct Answer: A. 1001 101

Explanation

\(\begin{array}{c|c} 2 & 77 \\ \hline 2 & 38 R1 \\ 2 & 19 R0 \\ 2 & 9 R1 \\ 2 & 4 R1 \\ 2 & 2 R0 \\ 2 & 1 R0 \\ & 0 R1\end{array}\)

77_ten = 1001101_two

Explanation

(a)

\(\bar{x} = \frac{\sum fx}{\sum f}\)

= \(\frac{1835}{80}\)

\(\approxeq 22.9yrs\)

(b)(i)

(ii) Modal age = \(\frac{20 + 24}{2} = 22\)

(c) P(picking from the modal class) = \(\frac{25}{80}\)

= \(\frac{5}{16}\).

(a)

\(\bar{x} = \frac{\sum fx}{\sum f}\)

= \(\frac{1835}{80}\)

\(\approxeq 22.9yrs\)

(b)(i)

(ii) Modal age = \(\frac{20 + 24}{2} = 22\)

(c) P(picking from the modal class) = \(\frac{25}{80}\)

= \(\frac{5}{16}\).

Correct Answer: A. x=2 or -5

Explanation

10