Number Topic Questions (4MB1 Edexcel) page3

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51	(Edexcel/Math B/2014/jan/paper01/q1) $y$ varies inversely as the cube of $x$. Given that $y = 12.5$ when $x = 2.5$, find the value of $x$ when $y = 100$.	4
52	(Edexcel/Math B/2014/jan/paper01/q1) $y$ varies inversely as the cube of $x$.  $y = 256$ when $x=\frac{1}{2}$.  Find the value of $x$ when $y = \frac{4}{27}$.	4
53	(Edexcel/Math B/2014/jan/paper01/q1) $y$ varies inversely as the cube of $x$. Given that $y = 24$ when $x = 2$, find the value of $x$ when $y = -3$.	4
54	(Edexcel/Math B/2014/jan/paper01/q1) Here are the first 4 terms of a sequence \[ 1 \quad -3 \quad 9 \quad -27 \] (i) Write down the next 2 terms of the sequence. (ii) Explain how you found your answer.	2 1
55	(Edexcel/Math B/2014/jan/paper01/q1) The \(n\)th term of a sequence is given by \(3n - 4\).  Write down the first three terms of the sequence.	2
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56	(Edexcel/Math B/2014/jan/paper01/q1) The height of cone \(A\) is ${6}{cm}$ and the height of a similar cone \(B\) is ${10}{cm}$.  The surface area of cone \(B\) is ${550}{cm^2}$.  (a)Calculate the surface area, in \(\text{cm}^2\), of cone \(A\). The volume of cone \(B\) is \(189 cm^2\)   (b)Calculate the volume, in \(\text{cm}^3\), of cone \(B\).	3 3
57	(Edexcel/Math B/2014/jan/paper01/q1) The scale of a map is such that ${3}{cm}$ on the map represents an actual distance of ${15.6}{km}$. (a)Express the scale of the map as a ratio in the form \(1 : n\) where \(n\) is an integer. The actual area of a park is ${676}{km^2}$. (b) Calculate the area, in \(\text{cm}^2\), of the park on the map.	2 3
58	(Edexcel/Math B/2014/jan/paper01/q1) The first four numbers in the sequence of triangle numbers are \(1, 3, 6, 10\). (a)Write down the 5th number in this sequence. (b) Write down the difference between the 100th number and the 99th number in this sequence.	1 1
59	(Edexcel/Math B/2014/jan/paper01/q1) The \(n\)th term of a sequence is \(2n - 1\).  Find the difference between the \((n+1)\)th term and the \(n\)th term of this sequence.	2
60	(Edexcel/Math B/2014/jan/paper01/q1) Given that \((12 - 2n)\) is the \(n\)th term of a sequence, write down: (a) the 5th term, the difference between the first term and the third term. (b) the difference between the first term and the third term.	1 1
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61	(Edexcel/Math B/2014/jan/paper01/q1) The \(n\)th term of a sequence is given by \(u_n = 2^n\) where \(n = 1, 2, 3, 4, \dots\). (a) Write down the first four terms of this sequence. (b) Find the value of \(\frac{u_{200}}{u_{199}}\) giving your answer as a power of 8.	2 3
62	(Edexcel/Math B/2014/jan/paper01/q1) The \(n\)th term of a sequence is \(2 - 7n\).  Find the difference between the 4th term and the 8th term of this sequence.	2
63	(Edexcel/Math B/2014/jan/paper01/q1) (a)Express \(\frac{5\sqrt{60}}{6}\) in the form \(m\sqrt{15}\). (b) Hence show that \(\frac{\sqrt{3} + \sqrt{5}}{2\sqrt{3}}\) can be written in the form \(a + b\sqrt{3}\), where \(a\) and \(b\) are integers. Show all your working and give the values of \(a\) and \(b\).	1 3
64	(Edexcel/Math B/2014/jan/paper01/q1) (a) Express  (i) \(\sqrt{32}\) in the form \(a\sqrt{2}\). (ii) \(\sqrt{72}\) in the form \(b\sqrt{2}\). (b) Hence show that \((3 + \sqrt{32})(\sqrt{72} - 3)\) can be written in the form \(c + d\sqrt{2}\) where \(c\) and \(d\) are integers to be found.	2 3
65	(Edexcel/Math B/2014/jan/paper01/q1) Express \(\sqrt{245} - \sqrt{45}\) in the form \(4\sqrt{m}\) where \(m\) is a prime number. Show all your working.	3
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66	(Edexcel/Math B/2014/jan/paper01/q1) Showing all your working, express \(\sqrt{2} + \sqrt{18}\) in the form \(a\sqrt{2}\) where \(a\) is an integer. Write down the value of \(a\).	2
67	(Edexcel/Math B/2014/jan/paper01/q1) Showing all your working, express \((5 + 2\sqrt{75})(3 - \sqrt{48})\) in the form \(a + b\sqrt{c}\) where \(a\), \(b\) and \(c\) are integers.	4
68	(Edexcel/Math B/2014/jan/paper01/q1) Given that \(p\) and \(q\) are positive integers, express \[ \frac{18\sqrt{36}}{3\sqrt{24}} = \frac{6\sqrt{12}}{3\sqrt{24}} \] in the form \(\sqrt{p} - \sqrt{q}\). Show all your working.	3
69	(Edexcel/Math B/2014/jan/paper01/q1) Without using a calculator, and showing all your working, evaluate \[ \frac{\sqrt{27} + \sqrt{48}}{\sqrt{75}} \]	3
70	(Edexcel/Math B/2014/jan/paper01/q1) (a) Express  (i) \(\sqrt{1944}\) in the form \(m\sqrt{24}\) where \(m\) is an integer, (ii) \(\sqrt{384}\) in the form \(n\sqrt{24}\) where \(n\) is an integer. (b) Hence, find the value of \(\frac{\sqrt{1944} - \sqrt{384}}{\sqrt{24}}\).	2 1
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