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Log(0.0005957)\(^{\frac{1}{3}}\) = Log(\(\frac{5.957}{10000})^{\frac{1}{3}}\) = \(\frac{1}{3}\)Log(5.957) - \(\frac{1}{3}\)Log10\(^4\) = \(\frac{0.7750}{3}\) - \(\frac{4}{3}\) =\(\frac{\overline3.225}{3}\) = \(\overline{1}\).075

prob(p) = \(\frac{1}{5}\) prob(Q) = \(\frac{1}{4}\) Prob(neither p) = 1 - \(\frac{1}{5}\) \(\frac{5 - 1}{5} = \frac{4}{5}\) prob(neither Q) = 1 - \(\frac{1}{4}\) \(\frac{4 - 1}{4} = \frac{3}{4}\) prob(neither of them) = \(\frac{4}{5} \times \frac{3}{4} = \frac{12}{20}\) = \(\frac{3}{5}\)

number of sides = \(\frac{360^o}{\theta} = \frac{360^o}{306o}\) n = 12o Sum of interior angle = (n - 2) 180o (12 - 2) 180v = 10 x 180o = 1800o

T1, T2, T3 2, -9, -20 .... -141 l = a + (n - 1)d first term, a = 2 common difference d = T3 - T2 = T2 - T1 = -20 - (-9) = -9 -2 = -20 + 9 = -9 -2 = -20 + 9 = -11 -11 = -11 d = -1 last term l = -141 -141 = 2 + (\(\cap\) - 1) (-11) -141 = 2 + (-11 \(\cap\) + 11) = 2 - 11\(\cap\) + 11 -141 = 13 - 11\(\cap\) -141 - 13 = -11\(\cap\) -154 = -11\(\cap\) \(\cap\) = \(\frac{-154}{-11}\) \(\cap\) = 14

9 + 8 = 17 17 + mod 12 = 1 rem 5 it is mod 12

volume of cylinder = \(\pi r^2h\) volume of cylinder p = \(\pi r^2 \times 10\) = 10\(\pi r^2\) volume of cylinder Q = \(\pi (2r)^2 h\) = 4\(\pi r^2\)h 4\(\pi r^2h = 10 \pi r^2\) h = \(\frac{10}{4} = 2.5cm\)

score 0 = 4 students score 1 = 2 students score 2 = 5 students score 3 = 6 students score 4 = 3 students = 20 students

at most 2 marks = 5 + 2 + 4 students = 11 students probability(at most 2 marks) = \(\frac{11}{20}\)

y + z = 180o z = 180o - y x + k = 180o k = 180o - x the sum of angles in the \(\bigtriangleup\) are: n + z + k = 180 but n + 180o - y + 180o - x = 180o n + 180o - y - x = 0 but we want to find n n + 180o = x + y but x + y = 220o n + 180o = 220o n = 220o - 180o n = 40o

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

if m + n = 120o and n + r = 100o then m + n = 120o then r = 180o - 120o = 60o also n + r = 100o m = 180o = 80o m + r is = 80o + 60o = 140o

From the diagram SR//UW given that o and o o(corresponding angle) xo = 45

xo + zo = 180o (sum of o + zo = 180o zo = 180o - 45o z = 135o z + yo + 20o = 180o (sum of o + yo + 20o = 180o yo + 155o = 180o yo + 180o - 155o yo = 25o

Draw a straight line from point S to meet the y-axis, which cuts it at 2, and do the same for the x-axis which cuts it at 1. Therefore the coordinate of the point S is (1, 2) NOTE: for this graph, each box(square) = 2.5cm on both axes.

The minimum value of y is where the slope of the curve cuts the y - axis = - 1.25.