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No expanded working has been attached for this question yet. The verified answer is Option D.

P \(\cap\) Q = {f, e} = 2

Let the number be x. \(\sqrt{x} = 2k \implies x = (2k)^2\) = \(4k^2\) \(\frac{1}{2} \times 4k^2 = 2k^2\)

\(cos45^o \times cos30^o - sin45^o \times sin30^o\) \(\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}}\times \frac{1}{2}\) \(\frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}; = \frac{\sqrt{3}-1}{2\sqrt{2}} = \frac{\sqrt{6}-\sqrt{2}}{4}\)

Volume of a cone = \(\frac{\pi r^2 h}{3}\) r = 2h. V = \(\frac{\pi \times (2h)^2 \times h}{3}\) = \(\frac{4}{3} \pi h^3\)

No expanded working has been attached for this question yet. The verified answer is Option C.

To calculate the circumference of a circle, use the formula C = \pid, where "C" is the circumference, "d" is the diameter, and \pi is 3.14 Or The ratio of the circumference to the diameter of a circle is the mathematical constant \pi (pi), which is approximately 3.14.

- If two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides. Given: Heights of cylinder --> 21 : 7 or 3 : 1 = \(\frac{3}{1}\) = 3 times height enlargement Volume / Capacity of larger cylinder = 3\(^3\) \(\times\) 250g = 27 \(\times\) 250g = 6,750 or 6.75kg

(a) Items Percentage(%) Degree in pie chart Pension 5 \(\frac{5}{100} \times 360^\circ = 18^\circ\) Income tax 25 \(\frac{25}{100} \times 360^\circ = 90^\circ\) Food 40 \(\frac{40}{100} \times 360^\circ = 144^\circ\) Transport 10 \(\frac{10}{100} \times 360^\circ = 36^\circ\) Rent 12.5 \(\frac{12.5}{100} \times 360^\circ = 45^\circ\) Others 7.5 \(\frac{7.5}{100} \times 360^\circ = 27^\circ\) 100 360^\circ A pie- chart showing the monthly contributions and expenditure pattern of an employee in 1999. (b)(i) \(360^\circ = N10,800.00\) \(\text{Pension} - 18^\circ = \frac{18}{360} \times N10,800\) = \(N540\) (ii) \(360^\circ = N10,800.00\) \(\text{Income tax} - 90^\circ = \frac{90}{360} \times N10,800\) = \(N2700\) (c) The percentage sum of pension and income tax = (5 + 25)% = 30% Take home pay = 100% - 30% = 70% = \(\frac{70}{100} \times N10,800\) = \(N7560\)

(a)(i) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 2, 5, 7} A' = U - A = {3, 4, 6, 8, 9, 10} (ii) \(A \cap B = {1, 2, 5, 7} \cap {1, 3, 6, 7} = {1, 7}\) \((A \cap B)' = {2, 3, 4, 5, 6, 8, 9, 10}\) (iii) \(A \cup B = {1, 2, 5, 7} \cup {1, 3, 6, 7}\) = \({1, 2, 3, 5, 6, 7}\) \((A \cup B)' = {4, 8, 9,10}\) (iv) {1, 3, 6}, {1, 3, 7}, {1, 6, 7} and {3, 6, 7}. (b) The nth term of the sequence is given as \(U_{n} = \frac{n + 1}{n(n + 2)}, n = 1, 2,3\) For the 15th term, \(U_{15} = \frac{16}{15 \times 17}\) (c)(i) \(T_{n} = a + (n - 1)d\) \(T_{n} = 3 + (n - 1)4 = 3 + 4n - 4\) = \(4n - 1\) (ii) \(4n - 1 > 100\) \(4n > 100 + 1 \implies 4n > 101\) \(n > 25.25\) The least term greater than 100 = 26th term.

The given line is 2y + 8x - 17 = 0. Rewrite in slope form: 2y = -8x + 17 y = -4x + \(\frac{17}{2}\) Slope = −4. The line through points \((-1, -p)\) and \((-2p, 2)\) must have the same slope (parallel lines). Slope = \(\frac{2 - (-p)}{-2p - (-1)} = \frac{2 + p}{1 - 2p}\) \(\frac{2 + p}{1 - 2p} = -4\) Cross-multiply: 2 + p = -4(1 - 2p) 2 + p = -4 + 8p 2 + 4 = 8p - p 6 = 7p p = \(\frac{6}{7}\)

Hint: Represent the question in a venn diagram, such that n(B ∩ M) = x n(B) only = 125-x n(M) only = 110-x => 125-x + 110-x + x = 220 => x = 15. n(B) only = 125 - 15 = 110

52.4 - 5.7 - 3.45 - 1.75 = 52.4 - (5.7 + 3.45 + 1.75) = 52.4 - 10.90 = 41.5

\((\sqrt{0.7} + \sqrt{70})^{2}\) = \((\sqrt{0.7} + \sqrt{70})(\sqrt{0.7} + \sqrt{70})\) = \(0.7 + 2\sqrt{0.7 \times 70} + 70\) = \(0.7 + 14 + 70 \) = 84.7

\(\frac{0.21 \times 0.072 \times 0.00054}{0.006 \times 1.68 \times 0.063}\) = \(\frac{9 \times 10^{-10}}{7 \times 10^{-8}}\) = \(1.2857 \times 10^{-2}\) = \(0.012857 \approxeq 0.01286\) (to 4 s.f)