Explanation

(b) A = {0, 1, 2, 3, 4, 5, 6, 7}

B = {4, 6, 8, 10, 12}

C = {2, 3, 5, 7}

U = {0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(i) \(B \cup C = {2, 3, 4, 5, 6, 7, 8, 10, 12}\)

\((B \cup C)' = {0, 1, 9, 11}\)

(ii) \(A' = {8, 9, 10, 11, 12}\)

\(A' \cap B \cap C = { }\)

Correct Answer: C. 7

Explanation

\(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2}; \frac{15}{2} - \left(\frac{5}{2}+\frac{3}{1}\right)\div \frac{33}{2}\\

\frac{15}{2} - \left(\frac{5+6}{2}\right)\div \frac{33}{2}; \frac{15}{2} - \frac{11}{2} \div \frac{33}{2}\\

\(\frac{11}{2}\) ÷ \(\frac{33}{2}\) = \(\frac{11}{2}\) * \(\frac{2}{33}\)

= \(\frac{11}{33}\) or \(\frac{1}{3}\) (when simplified)

\(\frac{15}{2}\) - \(\frac{1}{3}\) = \(\frac{43}{6}\)

7.166

The nearest whole number is 7

Correct Answer: D. 2/3

Explanation

\((\frac{16}{81})^{\frac{1}{4}}\)

= \(((\frac{2}{3})^{4})^{\frac{1}{4}}\)

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

Correct Answer: B. a + b

Correct Answer: A. 10

Explanation

n(PuQ) = n(p) + n(q) - n(PnQ)

40 = 20 + 30 - n(PnQ)

n(PnQ) = 50 - 40 = 10

Correct Answer: A. 10.5

Explanation

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an even amount of numbers in the set meaning there are two middle numbers- 8 and 13. In order to find the median we take the average of 8 and 13: 8+13/2=10.5

Correct Answer: C. 55°

Explanation

?SOR = ?ORQ alternate angle.

Also ?OQR = ?OQR (Base angle of isosceles)

?QOR = 108

Correct Answer: C. \(\frac{1}{2}\)

Explanation

\(f(x) = \frac{4}{x} - 1\). Let y = f(x)

\(y = \frac{4 - x}{x} \implies xy + x = 4\)

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

\(f^{-1}(7) = \frac{4}{7 + 1} = \frac{1}{2}\)

Correct Answer: (a) 746.431

Correct Answer: B. sinx + x cosx