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set = 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 multiples of 3 = 6, 9, 12, 15 multiples of 4 = 4, 8, 12 Prob(multiples of 3 or 4) = Prob(multiple of 3) + pro(multiple of 4) - pro(3 ∩ 4) = \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12} - \frac{1}{2}\) = \(\frac{4 + 3 - 1}{12}\) = \(\frac{1}{2}\)

Volume of cylinder = \(\pi r^2 h\) = \(\frac{22}{7} \times 14^2\) x 14 x 18 = 22 x 28 x 18 = 11088cm3 1000cm3 = \(\frac{1}{1000}\) x 11088cm3 = 11.088 = 11

Each interior angle = \(\frac{360^o}{n}\) 45o = \(\frac{360^o}{n}\) 45on = 360o n = \(\frac{360^o}{45}\) = 8

The bearing S 20^\circ W is equivalent to a bearing of 200^\circ. Moving clockwise 90^\circ ⇒ 200^\circ + 90^\circ = 290^\circ This is equivalent to N 70^\circ W.

A prism has 3 rectangular faces and 2 triangular faces and 2 rectangular faces = 10(3 + 4 + 5) = 120 Area of triangular faces = \(\sqrt{s(s - a) (s - b) (s - c)}\) where s = \(\frac{a + b + c}{2}\) = \(\frac{3 + 4 + 5}{2}\) = \(\frac{12}{2}\) = 6 Area of \(\bigtriangleup\) = \(\sqrt{6(6 - 30(6 - 4)(6 - 5)}\) = \(\sqrt{6 \times 3 \times 2 \times 1}\) = 6 Area of triangle faces = 2 x 6 = 12cm2 Total surface area = Area of rectangular face + Area of \(\bigtriangleup\) = 120 + 12 = 132cm2

x = \(\frac{1}{2}\) and x = \(\frac{-2}{3}\) expand (x - \(\frac{1}{2}\))(x + \(\frac{2}{3}\)) = 0 x(x + \(\frac{2}{3}\)) - \(\frac{1}{2}(x + \frac{2}{3}\)) = 0 x2 + \(\frac{4x - 3x}{6} - \frac{2}{6} = 0\) \(x^2 + \frac{x}{6} - 2 = 0\) 6x2 + x - 2 = 0

\(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) = \(\frac{\log 27\frac{1}{2}}{81\frac{1}{2}}\) = \(\frac{\log 3\frac{1}{2}}{\log 3^2}\) \(\frac{\frac{3}{2} \log 3}{2 \log 3} = \frac{3}{2} \div \frac{2}{1}\) = \(\frac{3}{2} \times \frac{1}{2}\) = \(\frac{3}{4}\)

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

Perimeter of sector = 2r + \(\frac{\theta}{360^o} \times 2\pi r\) \(\pi + 8 = 2 \times 4 + \frac{\theta}{3360^o} \times 2 \pi \times 4\) \(\pi + 8 + \frac{\theta}{360^o} \times 8 \pi\) P + 8 - 8 = \(\frac{\theta \pi}{456o}\) \(\pi = \frac{\theta \pi}{45^o}\) \(\theta \pi = 45^o\)

Error = 1.80m - 1.75m = 0.05m %error = \(\frac{\text{error}}{\text{true measurement}}\) x 100% %error = \(\frac{ 0.05}{ 1.75}\times100\) %error = \(\frac{20}{7}\)% or 2.86%

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

volume of cylinder = \(\pi r^2\)h 0.216\(\pi\) m\(^3\) = \(\pi \times r^2 \times h\) Since r = h, 0.216 = r\(^3\) r\(^3\) = 0.216 r = \(\sqrt[3]{0.216}\) = 0.6

volume of cylinder = \(\pi r^2\)h 0.216\(\pi m^3 = \pi \times r^2 \times h\) But h = r, pi cancels pi Then, 0.216 = r\(^3\) r\(^3\) = 0.216 r = \(\sqrt[3]{0.216}\) = 0.60m

am + bn - an - bm am - an - bm + bn a(m - n) - b(m - n) (a - b)(m - n)

x2 - 3x = 7 x2 - 3x - 7 = 0 What can you add to both sides of the equation to give the same value of y = x2 - 3x - 3 The number is 4 x2 - 3x - 7 + 4 = 4 x2 - 3x - 3 = 4 but y = x2 - 3x - 3 y = 4; So are y = 4 draw a line parallel to x axis, to cut or intersect the graph. At these points look down to see the corresponding values on x axis This give -1.55 and 4.55