Number [topic by topic] Math B

1	( Edexcel/MathB/2016/june/paper01/q11) $$a=2^{-1},b=2^0,c={\left(\frac{1}{2}\right)}^{-1},d={\left(\frac{1}{8}\right)}^{\frac{1}{3}},e={\left(\frac{1}{4}\right)}^{-2},f=2^{2 }$$ From the list of numbers, (a) write down the letters of the two equal numbers, (b) write down the letter of the largest number.	2 1
2	( Edexcel/MathB/2014/june/paper01/q6) Evaluate $\frac{7.2\;\times\;10^{-3}-8.4\;\times\;10^{-4}}{3.6\;\times\;10^{-1}}$, giving your answer to  (a) 3 significant figures (b) 3 decimal places	1 1
3	( Edexcel/MathB/2015/jan/paper01/q1) Work out $3\frac18\;\div\;4\frac{1}{10}$ Show all your workings and give your answer as a fracrion in its simplest form.	2
4	( Edexcel/MathB/2015/jan/paper01/q8) (a)Calculate the exact value of$$\frac{4.4\times {10}^5}{2.6\times {10}^{-3}-4.0\times {10}^{-4 }}$$ (b) Write your answer to part (a) in standard form	1 2
5	( Edexcel/MathB/2015/janR/paper01/q9) (a)calculate the exact value of $$\frac{(27.25{)}^2-(12.75{)}^2}{0.75-0.25 }$$ (b)Write your answer in part (a) in standard form. (c)Write your answer in part (a) to 2 significant figures.	1 1 1
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6	( Edexcel/MathB/2015/june/paper01/q15) Given that $P\;=\;(243)^{-\frac{4}{5}}$ (a)Write down the value of integer m so that $P=\frac1m$ (b)Write P in standard form , giving your answer to 3 significant figures.	1 2
7	( Edexcel/MathB/2016/jan/paper01/q13) Show that $3\frac13 \div 1\frac12\;=\;2\frac29$ Show your working clearly.	3
8	( Edexcel/MathB/2016/jan/paper01/q19) Showing all your working. (a)express $(64x^6)^{\frac13}$ in the form $(mx)^m$. (b)express $(64x^6)^{-\frac16}$ in the form $\frac{1}{nx}$.	2 2
9	( Edexcel/MathB/2016/janR/paper01/q2) Work out $\frac{3^2+2^2}{3^5-2^5}$ (a)Give your answer as a decimal to 3 significant figures. (b)Give your answer as a decimal to 3 decimal places.	1 1
10	( Edexcel/MathB/2016/janR/paper01/q11) (a) Write 75 000 in standard form. A computer can carry out a simple calculation in 1 picosecond where   1 picosecond = $10^{–12}$ seconds (b) Write down in standard form the time, in seconds, for this computer to carry out 75 000 pico seconds.	1 2
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11	( Edexcel/MathB/2016/june/paper01/q11) The mass $M_e$ of the Earth is $5.9722\times10^{24}$ kg The mass $M_i$ of the planet Jupiter is $1.8981\times10^{27}$kg (a) Find the value of $\frac{M_{j}}{M_{e}}$ to the nearest integer. (b) Express your answer to part (a) in standard form.	1 2
12	( Edexcel/MathB/2016/juneR/paper01/q24) $a= 1.2\times 10^{101}\quad $and$\quad b= 2\times 10^{34}$ Showing all your working, calculate, giving your answer in standard form, the value of (a) $ab$ (b) $b^3-a$ (c) $\frac{a}{b^3}$	2 2 2
13	( Edexcel/Math~B/2014/jan/paper01/q5) $p=\frac{1}{16}$ (a) Write down the value of $p$ to 3 decimal places. (b) Write down your answer to part (a) in standard form.	1 1
14	(Edexcel/MathB/2016/juneR/paper01/q1) Write down $\frac{1}{24}$ as a decimal (a) correct to 3 decimal places, (b) correct to 3 significant figures.	1 1
15	( Edexcel/MathB/2014/june/paper01/q3) Express 625 grams as a fraction of l kilogram. Give your answer in its simplest form.	2
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16	(Edexcel/MathB/2015/janR/paper01/q3) $\left\{\sqrt{36},\frac{\pi}{5},\frac{5}{7},\sqrt[3]{9},\sqrt{\frac{121}{144}}\right\}$ Write down the two elements in the above set which are irrational	2
17	( Edexcel/MathB/2015/june/paper01/q21) Here is a list of numbers $(-2)^0\quad\frac{63}{105}\quad4\quad0.5$  (a) Write down  (i) the smallest number in the list, (ii) the largest number in the list. (b) Calculate the mean of the four numbers in the list.	2 2
18	(Edexcel/Math~B/2014/jan/paper01/q12) A recipe requires the weight of sugar and the weight of flour to be in the ratio 2: 5 When 420 g of flour are to be used, work out the weight, in g, of sugar that is needed.	2
19	(Edexcel/Math B/2014/june/paper01/q19) A mixture of sand and cement is to be used to plaster a wall. In the original mixture, the ratio of sand to cement by weight is 3 : l Given that the weight of sand used is 9 kg,  (a) write down the weight, in kg, of cement used in the original mixture.  It is decided to use the same weight of cement but to change the ratio of sand to cement by weight to 5:1 for a new mixture. (b) Calculate the weight of sand, in kg, that has to be added to the original mixture to make the new mixture.	1 3
20	( Edexcel/Math B/2014/juneR/paper01/q10) 1050 Chinese yuan (¥) is to be divided between three people in the ratios 3:5:7 Find the difference, in ¥, between the largest share and the smallest share.	3
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21	(Edexcel/Math B/2015/jan/paper01/q7) The weights of two bags are in the ratio 5 : 8 The weight of the heavier bag is 408 grams. Calculate the weight, in grams, of the other bag	2
22	(Edexcel/Math B/2015/june/paper01/q29) The diagram shows a rod of length L cm, divided into two unequal lengths of A cm and B cm. Given that A:L = λ:1 and that A:B = μ:1 where λ and μ are constants, find μ in terms of λ.	4
23	(Edexcel/Math B/2015/juneR/paper01/q3) Express 3.6 kg : 75g in the form m : 1, where m is an integer.	2
24	(Edexcel/Math B/2016/jan/paper01/q4) Two numbers a and b are in the ratio a : b = 2 : 5 Given that a = 8, calculate the value of b.	2
25	(Edexcel/Math B/2016/janR/paper01/q16) $\$$112 was divided between three prize winners in a competition in the ratios 9 : 4 : 1 The winner of the largest prize gave $6 to each of the other two prize winners. Calculate the ratios of the amounts of money that the three prize winners now have. Give your answer in its simplest form.	4
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26	(Edexcel/Math B/2016/janR/paper01/q21) Two solid spheres have surface areas in the ratio 9 : 16 The volume of the smaller sphere is 13.5 cm3 Calculate the volume, in cm3, of the larger sphere.	4
27	(Edexcel/Math B/2016/june/paper01/q13) Given that x:y = 5:8 and that y:z = 6:7, find x:z Give your answer in its simplest form.	3
28	(Edexcel/Math B/2014/june/paper01/q10) Find the Highest Common Factor (HCF) of 30, 36 and 138 Show your working clearly	2
29	(Edexcel/Math B/2015/jan/paper01/q3) Find the Lowest Common Multiple (LCM) of 28, 30 and 45	2
30	(Edexcel/Math B/2015/june/paper01/q8) Find the Highest Common Factor (HCF) of 42, 84 and 154	2
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