For use only in Whitgift School. IGCSE Higher Sheets 1. IGCSE Higher

Transcription

1 IGCSE Higher Sheet H--0a- Fractions Sheet H- -0a- Fractions Sheet H- -04a-b- Surds Sheet H-4-04a-b- Surds Sheet H-5-04c- Indices Sheet H-6-04c- Indices Sheet H-7-04c- Indices Sheet H-8-04c-4 Indices Sheet H-9-04c-5 Indices Sheet H-0-04c-6 Indices Sheet H--04d-Primes Sheet H- -04d-Primes Sheet H- -05a- Sets Sheet H-4-05a- Sets Sheet H-5-05a- Sets Sheet H-6-05a-4 Sets Sheet H-7-06a-0 Percentages Sheet H-8-06a-0 Percentages Sheet H-9-06a-0 Percentages Sheet H-0-06a-04 Percentages-Non Calculator Sheet H--06a-05 Repeated Percentage changes Sheet H- -06a-06 Percentages

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3 Sheet H--0a- Fractions. Epress the following terminating decimals as fractions in their lowest form: (a) 0.5 (b) 0. (c) (e) (g) (d) (f ) (h) Calculate the following as terminating decimals: (a) (b) 8 5 (c) 7 (d) 40 6 (e) 7 (f ) 00 (g) 9 (h) Epress the following recurring decimals as fractions in their lowest form: (a) 0.6 (b) 0. (c) 0.7 (d) 0.08 (e) 0.5 (f ) 0.4 (g) 0.54 (h) Calculate the following as recurring decimals: (a) (b) 7 (c) (d) 7 (e) 5 (f ) 9 (g) 4 (h) 5

4 Sheet H- -0a- Fractions. Epress the following as fractions in their lowest form: (a) 0.6 (b) 0.70 (c) 0.8 (d) 0.06 (e) 0.45 (f ) Epress the following decimals as fractions in their lowest form: (a) 0.7 (b) 0.7 (c) 0. (d) 0.54 (e) (f ) 0.. Epress the following fractions as decimals: (a) 5 (b) 7 (c) 4 (d) 9 (e) (f ) (g) 5 (h) Epress the following numbers as fractions in their lowest form: (a) 0.6 (b) (c) 0.45

5 Sheet H- -04a-b- Surds. Simplify the following as far as possible: (a) 7 (b) 8 (c) 4 (d) 50 (e) 45 (f ) 44 (g) 8 (h) 80 (i) 00 (j) 0 (k) 6 (l) (m) 45 (n) 00 (o) 75 (p) 5 (q) 50 (r) 6. Find the following in the form n : (a) 7 (b) (c) 7 (d) 7 (e) (f ) 5 5. Simplify the following as far as possible, leaving your answer in the form a b: (a) + 5 (b) 7 (c) + (d) 7 + (e) (f ) (g) (h) (i) Simplify the following as far as possible: (a) 5 (b) 5 (c) 7 (d) 50 (e) 7 8 (f ) 5 75 (g) 4 8 (h) 48 (i) (j) 00 (k) 8 7 (l) 8 + +

6 Sheet H-4-04a-b- Surds. Simplify the following as far as possible: (a) (c) (e) ( 5 + ) (b) ( + ) ( 7 ) (d) ( 5 + )( 5 ) ( + 7 )( 7 ) (f ) ( 5 + ). Write the following, in the simplest possible form: ( a) (b) 75 (c) (d) (e) (f ) Write the following, in the simplest possible form (in the form a b): (a) 6 0 (b) (c) 5 (d) 5 (e) (f ) 7 5 (g) (h) 0 + (i) 00 5 (j) (k) + (l) (a) Epress 0 in the form a b, where a and b are positive integers. An isosceles right-angled triangle ABC has a right angle at B. The length of its equal sides is 0 cm. C 0 cm Diagram NOT accurately drawn A 0 cm B (b) (c) Find the area of the triangle. Give your answer as an integer. Find also the hypotenuse of the triangle. Give your answer as an integer.

7 Sheet H-5-04c- Indices. Epress the following as powers of (i.e. in the form n ): (a) 4 (b) 6 (c) 64 (d) (e) (f ) 0.5 (g) (h) (i) 8. Epress the following as powers of the stated numbers: (a) as a power of (b) 8 as a power of (c) 65 as a power of 5 (d) as a power of 4 6 (e) as a power of 7 (f ) as a power of (g) as a power of (h) as a power of Calculate the following: 6 (a) 4 (b) (c) 5 (d) (e) (f ) 0 (g) 9 (h) (i) (j) (k) (l) (m) (n) (o) Find in the following: (a) 7 = 49 (b) = (c) = 8 7 (d) 9 = 8 (e) 5 = (f ) = (g) = 6 (h) = (i) = Epress the following in the form 8 n where n is either an integer or a fraction: (a) (b) 8 (c) 8 (d) 64 (e) (f ) 64 5

8 Sheet H-6-04c- Indices. Calculate the following without using decimals: 5 (a) (b) 0 (c) 7 (d) 4 (e) 4 (f ) 0 (g) 4 (h) 9 (i) (j) 0 (k) 8 (l) 4. Epress the following as powers of : (a) (b) (c) 4 8 (d) 8 (e) (f ) 6. Find in the following: (a) = 64 (b) = 7 (c)7 = 49 (d) = (e) = (f ) 0 = (g) = 0.5 (h) = (i) 6 = 6 8 (j) = (k) = (l) 0 = Evaluate the following without using decimals: (a) (b) 5 (c) (d) 7 (e) (f ) 5 (g) 9 (h) 0 (i) Epress the following as powers of : (a) 8 6 (b) (c) Evaluate the following (without a calculator), leaving your answers as fractions where necessary: (a) (b) (c) (d) 5 (e) (f ) 4 (g) 4 (h) 8 (i) 5

9 Sheet H-7-04c- Indices. Find n in the following : n+ 5 n+ 5 (e.g. =. We write as. Hence we solve =. That is n+ = 5. n= ) n n+ (a) = 4 (b) = 8 n n (c) 7 = 49 (d) = 64 = = n+ n7 (e) (f ) 5 5 5n n (g) 64 (h) 7 = =. Evaluate the following, leaving your answers as fractions where necessary: (a) (b) 7 (c) (d) 5 (e) 9 (f ) 5 (g) (h) 0 (i) Write 7 as a power of (that is write it in the form n ). 4. Write as a power of. 5. Write as a power of (a) 4 7 Write 5 9 as a power of. (b) Write 4 as a power of. (c) Write 5 as a power of 5. (d) Write 5 as a power of 5. (e) Write 56 as a power of Given that = 7 6 find Given that = find. 4 7

10 Sheet H-8-04c-4 Indices. Calculate the following: (a) 4 (b) 8 (c) (d) 64 (e) 8 (f ) 7 5 (g) (h) 64 (i) 69. Epress the following as powers of 64: (a) 64 (b) 8 (c) 4 (d) (e) (f ) 64 (g) (h) (i) 8 4. Calculate the following: (a) 9 (b) 64 (c) (d) 0000 (e) (f ) (g) 44 (h) 49 (i) (j) (k) (l) Find in the following: (a) = (b) 8 = (c) 5 = 5 (d) 49 = 7 (e) = (f ) 7 = (g) 4 = (h) 56 = 6 (i) = ( j) 8 = (k) 5 = (l) 5 = 5 5. Evaluate the following without using decimals (show all working clearly): 4 (a) (b) 5 (c) 7 4 (d) 8 (e) 6 (f ) (g) (h) (i) Epress the following as powers of : (a) 4 8 (b) (c) 6 8 6

11 Sheet H-9-04c-5 Indices. Evaluate the following, leaving your answers as fractions where necessary: (a) 6 (b) 7 4 (c) 65 5 (d) (e) 9 (f ) (g) 8 (h) 0000 (i) Evaluate the following, leaving your answers as fractions where necessary: (a) 8 (b) 9 5 (c) (d) 000 (e) 7 (f ) 5 4 (g) 4 (h) 6 (i) 8. Find in the following: (a) 4 = (b) = 4 (c) = (d) 5 = 65 (e) = (f ) = (g) = (h) = (i) 5 = Find in the following: (a) 4 = (b) 5 = 5 (c) 64 = 4 (d) = 4 (e) 9 = 7 (f ) = Find in the following: (a) 4 = (b) 49 = (c) 000 = (d) 5 = (e) = (f ) = (g) = (h) = (i) = (j) = 04 (k) = (l) =

12 Sheet H-0-04c-6 Indices. Find in the following by first of all writing both numbers as the powers of the same number (e.g. in (b) write 5 = ( 5 ) = 5 5 = 5 = = ) 5 (a) 8 = 4 (b) 5 = (c) 4 = 5 (d) 64 = (e) 9 = 7 (f ) = (g) 5 = (h) 9 = (i) 00 = (j) 8 = 0.5 (k) 9 = 0. (l) = 6 7. Epress the following as powers of the stated numbers: (a) as a power of 4 (b) 7 as a power of 8 (c) 8 as a power of 4 (d) as a power of 4 8 (e) as a power of (f ) as a power of 4 6 (g) as a power of 9 (h) as a power of (i) as a power of 6 (j) 64 as a power of 8. Evaluate the following, leaving your answers as fractions where necessary: 4 5 (a) 7 (b) 8 (c) (d) 6 4 (e) 4 5 (f ) (g) (h) (i) ( ) ( ) ( ) ( ) ( ) (j) 0.5 (k) 0.04 (l).5 4. Find n in the following : (e.g. in (a) write ( ) n = so n = and so n = ) ( ) n n n (a) 9 = (b) 8 = (c) 5 = 5 = = + = n n n 7 (g) ( ) = 6 (h) = 6 (i) 7 = n 6 49 n n n n (d) 7 49 (e) (f ) 5

13 Sheet H--04d- Primes. Write the following as the product of prime numbers (e.g. (a) 0 (b) 4 (c) 8 (d) 8 (e) 05 (f ) 64 (g) 08 (h) 4 (i) 50 ( j) 00 (k) 78 (l) 44 (m) 85 (n) 6 (o) 40 (p) 45 (q) 60 (r) 75 7 = ). Use question to find the highest common factor of the following pairs of numbers: (a) 45 and 05 (b) 8 and 44 (c) 85 and 75 (d) 40 and 6 (e) 08 and 60. Use question to find the lowest common multiple of the following pairs of numbers: (a) 45 and 60 (b) 00 and 40 (c) 08 and 44 (d) 6 and 8 (e) 78 and Two cars complete laps of a circuit. One takes 5 seconds per lap, the other takes 55 seconds per lap. They start their circuits of the laps at the same time. (a) Epress 5 and 55 as the product of their primes. (b) Find the lowest common multiple of 5 and 55. (c) Use this to find how many laps the faster car will do before the cars first get to the starting point at the same time. 5. (a) Find the highest common factor and lowest common multiple of 0 and 550. (b) Multiply the two numbers that you found in (a) together. (c) Multiply 0 and 550 together. (d) What do you notice about the answers to (b) and (c)?

14 Sheet H- -04d- Primes. Write the following as the product of prime numbers (e.g. (a) 6 (b) 40 (c) 54 (d) 0 (e) 70 (f) 8 (g) 50 (h) 98 (i) 70 (j) 50 (k) 5 (l) 40 (m) 600 (n) 60 7 = ) 6. (a) Find the highest common factor of 5 and 50. Let this be h. (b) Find the lowest common multiple of 5 and 50. Let this be l. (c) Calculate h l and What do you notice? 7. (a) Find the highest common factor of 600 and 50. Let this be h. (b) Find the lowest common multiple of 600 and 50. Let this be l. (c) Calculate h l and What do you notice? 8. Use question to find the lowest common multiples of the following pairs of numbers: (a) 6 and 60 (b) 98 and 40 (c) 8 and 70 (d) 40 and Use question to find the highest common factor of the following pairs of numbers: (f) 600 and 5 (g) 70 and 50 (h) 98 and 60 (i) 54 and 6 (j) 8 and 70

15 Sheet H- -05a- Sets. In a class of 0 pupils, 9 like tomato sauce but not HP sauce, 6 like HP sauce but not tomato sauce and like neither. Copy and complete the following Venn diagram. Tomato HP. In a class of 0 pupils, 0 like football, like rugby and 4 like neither. Suppose n pupils like both football and rugby. (a) Write down an epression for the number of pupils who like football but not rugby. (b) Copy and complete the following Venn diagram using n. Rugby Football (b) By adding up all four values, find n.. In a year of 00 pupils, 70 enjoy Maths, 50 enjoy French and 0 enjoy neither. (a) Set up a Venn diagram showing this information. (b) Use this to find the number of pupils who enjoy both subjects. 4. In a shop there were 0 customers on a certain day. 60 paid using notes, 0 paid using coins and 50 paid using neither (cheques, cards etc.) (a) Set up a Venn diagram showing this information. (b) Use this to find the number of customers who used both notes and coins. 5. On an Athletics day 50 athletes are running. 60 are in the 00 metres, 50 are in the 00 metres and 80 are in neither. (a) Set up a Venn diagram showing this information. (b) Use this to find the number of athletes who ran in only one race. 6. A group of 00 adults were surveyed about holidays. 50 had been to Spain, 80 had been to France. Twice as many had been to both countries as had been to neither country. Suppose n adults had been to neither country. (a) Write down an epression for the number of adults who had been to both countries. (b) Set up a Venn diagram using n. (c) Hence find n and set up a new Venn diagram without using n.

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17 Sheet H-4-05a- Sets. A B In each of the following questions draw the Venn diagram shown above and shade the region. (a) A B (b) A B (c) A B (d) A B (e) A B (f ) A B (g) ( A B) (h) ( A B). In each of the following questions draw the Venn diagram shown below. A B C (a) (b) (c) (d) (e) (f ) A B C A B C ( A B) A B ( A C) A C

18 Sheet H-5-05a- Sets.. = A = B = C = C = { polygons} { quadrilaterals} { rectangles} { parallelograms} { triangles} Draw a Venn diagram showing A, B, C and D. = A= B = C = (a) { : is a number under 0} { : is an even number under 0} { : is a multiple of under 0} { : is a prime number under 0, including } Copy and complete the following: A B = 6,... { } (b) Find ( A B ). (c) Is it true that ( ) (d) Is it true that 7 A? (e) Calculate n( B ). A B C?. 4. = A = B = { : is a postive integer under 5} {,,, 5, 7,, } {, 4, 5, 9, 0,, 4} (a) List all the members of A. n A B. (b) Find ( ) = A= B = { : is a postive integer under } { : is an even number under } { : is a multiple of under } (a) List all the members of A. n B. (b) Find ( ) (c) Write down the members of A B. (d) Epress these numbers on a Venn diagram., 5, 7, in terms of A and B. (e) Epress the set { }

19 Sheet H-6-05a-4 Sets. A Copy and complete the Venn diagram shown above, drawing on the sets B and C where: A B = C B. A, B and C are sets with the following properties: n A = 5 ( ) ( B) ( B) n A = n A = B C = B ( ) nc = A C = (a) Draw a Venn diagram indicating the sets A, B and C. (b) Find the following: (i) n A B (ii) (iii) ( ) ( C) ( C) n A n B. {,, 5, 7} { : is an even number less than 0} A = B = Find the following: n A B (a) ( ) (b) A B (c) C such that C A and nc ( ) =.

20 Sheet H-6-05a-4 Sets (cont.) 4. Describe the following shaded areas: (a) A B (b) A B (c) A B (d) A B

21 Sheet H-7-06a-0 Percentages. The numbers of customers per day in a certain town increases by 5% at the weekend. (a) If there were 0 customers on a Friday in one shop then how many would there be on the Saturday? (b) If there were 95 customers on a Saturday in another shop then how many would there have been on the previous Friday?. A filing cabinet is selling at in a magazine with an advert net to it saying Only that s an amazing 45% off the retail price! What was the retail price?. A fan club had a membership of 5,90 in 999 which was, approimately, an % decrease from the year before. What was the membership (to the nearest ten) in 998? 4. A picture is reduced by 0% so that the copy measures 4cm by 0cm. (a) What were the dimensions of the original? (b) If the copy is now enlarged by 5% what will its new dimensions be? 5. 4,00 copies of a certain book were sold in March which was an decrease of ¼ on the number sold in February. In April there was an increase of 5 on the number sold in March. (a) How many were sold in February? (b) How many were sold in April? 6. In a summer sale a shop offered 0% off all goods. (a) What would be the sale price of a pair of shoes if they originally cost 40? (b) If the sale price of a jacket was 64 how much did it cost before the sale? 7. (a) How much would a computer cost including VAT (of 7.5%) if it cost 00 before the VAT had been added on? (b) Another computer cost 5 including VAT (of 7.5%) - how much would it cost without the VAT? PTO

22 Sheet H-7-06a-0 Percentages (cont.) 8. A woman sold a vase for 50. This was a profit of 5%. How much did she buy the vase for? 9. An employee s salary is increased by 5%. She now earns 7,090. What did she earn before her rise? 0. A garage sold a car at a loss of 4%. If it sold the car for 00 then what did the garage pay for the car?. The audience of a certain TV show increased by ¾ over 998. If million people watched it at the end of 998 how many watched it at the beginning of that year?. The monthly profits of a certain company fell by 5 over the summer period and their monthly profits were 0,000 in the Autumn then what were they in the previous spring?. If a boy sells a CD for.0 he makes a 0% profit. How much did he buy he CD for? 4. A man buys a computer. He sells it a year later for 00 but by doing so he makes a loss of 5%. What was the original price of the computer?

23 Sheet H-8-06a-0 Percentages. A document was photocopied so that the lengths of the copy were 70% of the original lengths. If the copy measured.6cm by 7.5cm what are the dimensions of the original document?. The attendance at a football match one week increased by from the previous week. If the new attendance was what the attendance the week before?. A boy s height increased by 5 over a year. If his height is now.68m what was his height a year ago? 4. The number at a school in 006 was 85% of the number at the school in 005. In 006 the number of pupils was 00. How many pupils were in the school in 005? 5. Find the original price of a car which was sold at 00 at a loss of 4%. 6. Find the original price of an antique which was sold at 545 at a profit of 9%. 7. The profit of a company in 004 was,500,000. In 005 the profit was 5% higher than it was in 004 but in 006 the profit fell by 40%. (a) Show that the profit made in 005 was,875,000. (b) What was the profit made in 006? 8. A travel agents offers a 5% reduction off all holidays. (a) What would be the new price of a holiday which originally cost 480? (b) The reduced price of another holiday is 765. What was its original price? 9. A supermarket has the following advert We are selling wine without VAT this is a reduction of 7.5% off the retail price. By considering the price of a bottle of wine which cost.75 after VAT (at 7.5%) comment on the accuracy of the advert. 0. If a boy buys a calculator for which included a 0% discount on the retail price. Find the retail price.. A house cost 80,000 in 999. The price rose by 7% over the net year. Find the price of the house in A man buys a computer from as shop which was making a 0% profit. If the man paid 0 then find the price which the shop paid.. A boy s height increased by ¼ over a year. If his height is now.5m what was his height a year ago? 4. The number of teachers at a school in 999 was 95% of the number of the teachers at the school in 998. In 998 the number of teachers was 80. How many teachers were in the school in 999? 5. Find the original price of a motorbike which was sold at 70 at a loss of 5%.

24 Sheet H-9-06a-0 Percentages. Find the original price of a painting which was sold at 680 at a profit of %.. Find the selling price of an antique which cost 500 and was sold at a profit of 75%.. The profits of a company in 998 were 7,000,000. In 999 the profits rose by 5%. What were the profits in 999? 4. An electrical shop offers a 5% reduction off all its products. (a) What would be the new price of a camera which originally cost 50? (b) The reduced price of a television is 90. What was its original price? 5. A petrol station increased all its prices by % from October to November. (a) In October a litre of unleaded cost 80p. What did it cost in November? (b) In November a litre of diesel cost 80.4p. What did it cost in October? 6. A man buys a desk for 0 in a sale in which all desks were reduced by 5%. What was the price before the sale? 7. A girl sees a bike for sale with the notice Price (inc. VAT 7.5%). What was the price before VAT? 8. A doctor s pay before ta was 0,000. If ta was at % what will he actually receive each year? 9. The number of cases of a certain disease fell by 5 in 999 to 40. How many cases were there in 998? 0. A photocopier is set to increase the sides of the original by. A picture measuring cm by 8cm is photocopied. (a) (b) What will the dimensions of the copy be? If that copy is then later reduced to get back to the size of the original then by what factor will its sides have been reduced?. An internet company claims to offer holidays at prices which are 5% cheaper than in the high street. (a) How much would it charge for a holiday which cost 450 in the high street (b) If the internet company charged 544 for a holiday then how much would you epect to pay for it in the high street?. The cost of a new car fell by 5% per month for the first three months of the year 000. The car cost 6,800 at the start of the year. (a) What did is cost after three months? (b) By what factor was its price reduced each month? (c) By what factor was its price reduced over these three months? (d) What is the connection between the answers to (b) and (c).. The profits of a certain factory rose by % over two years. (a) By what factor did the profits rise over this time? (b) On average, what was the average annual rise in the profits over this time?

25 Sheet H-0-06a-04 Percentages-Non Calculator. Find the original price of a car which was sold at 600 at a profit of 0%.. Find the selling price of a camera which cost 60 and was sold at a loss of 5%.. A man buys a set of garden furniture for 64 in a sale in which all garden furniture had been reduced by 0%. What was the price before the sale? 4. A policeman s pay after ta was 8,000. If ta was at 0% what was his annual salary before ta? 5. The number of cases of an infection fell by in the 990s to 600,000 per year. How many cases were there per year in the 980s? 6. A high street stationery shop offers 0% off the retail price of all its pens. (c) How much would it charge for a pen with a retail price of 0? (d) What was the retail price of a pen which was selling for 45 in the sale? 7. The average attendance at a football ground rose by ¼ over the season to 45,000. (a) Find the average attendance in the season. (b) The ground epected a further rise of over the season. What would its new attendance be? 8. The value of a company rose by 60% to million from 997 to 998. What was the value in 997? 9. A boy s height increased by 0% over a si month period. At the end of that period he was 99cm tall. What was he before those si months? 0. The number of visitors of a castle fell by 5% over a year. At the end of the year on average 50 people visited it per day. What was the average attendance at the start of that year?. The number of candidates from a certain school getting an A* in French fell by 0% from 999 to 000. If 0 got A*s in French in 999 then how many got A*s in 000?. A picture is reduced by 5%. The original size of the picture was 0mm by 60mm. What were the dimensions of the reduced copy?

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27 Sheet H--06a-05 Repeated Percentage changes. The shares in a certain company increased by 0% per year for three years. (a) By what factor do they increase each year? (b) If the shares were worth 750p three years ago then what are they worth now? (c) By what factor have they increased over the three years? (d) What is the connection between the two factors in (b) and (c)?. A bank offered 5% per annum (compound interest). If he invested 4000 then: (a) How much would the money be worth in one year? (b) By what single number (to sf) would the 4000 be multiplied by in order to calculate the amount of money in the account after 4 years? (c) Hence calculate how much money (to the nearest pound) would be in the account after 4 years.. Peter invests a sum of money for 0 years at 6% annum compound interest. Value Value O A Years O B Years Value Value O O C Years D Years Write down the letter of the graph which best shows how the value of Peter s investment changes over the 0 years. 4. A bank offered 8% per annum (compound interest). A man invested 70,000. By how much would his money have increased after two years? 5. The shares of a certain company fell by 0% per month for three consecutive months. If they were 780p before the fall then what were they after the fall? 6. A bank offers 5% interest on investments. A man invests,000 in the bank. (a) What is it worth after years? (b) What is the total percentage increase in his money? 7. An investment fund claims that it has increased by a total of % over the last two years. (a) If a man invested 000 in the fund two years ago then what would it be worth now? (b) If you asssume a constant rate of interest per year then find that rate of interest. 8. The number of burglaries in a certain country rose by 8% for two years in a row from 00 to 00. If there were 0,000 burglaries in 00 then: (a) How many burglaries were there in 00? (b) How many burglaries were there in 00? (c) What was the overall percentage increase in burglaries over the two years? (NB it is not 6%).

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29 Sheet H- -06a-06 Percentages. In April a lawnmower is selling for 65. In the September sale it was only 5.5. What was the percentage discount?. A garden table is selling for 48 with a sign saying Reduction of 0%. What was the price of the table before the sale?. A bleach bottle says 900ml for the price of 750ml % etra free where cannot be read. What is? 4. A boy s weight has increased by over two years. He now weighs 84kg. What was his weight two years ago? 5. A school claims that the pupils average mark in an eam has increased by 5% over 5 years. Two boys are told that the average mark is now 85.. George thinks that the average mark five years ago was 7.5 but James thinks it was 74. Who is right and how is the right answer obtained? 6. In sale all items are reduced by 5%. A carpet is selling for 5.0 per square metre. What was is before the sale? 7. A table measures 80cm by 0cm. A second table is said to be similar to this table but 0% bigger. (a) By what factor have the dimensions increased? (b) Find the dimensions of the new table. (c) By what factor has the area increased? 8. A TV station says that the audience for a particular programme has increased five fold over ten years (i.e the audience is five times what it was). What percentage increase is this? 9. A drill costs 66.7 after VAT of 7.5%. How much would it cost a builder who didn t have to pay VAT? 0. A man receives a cheque for after ta has been taken off. If he would have received 60. before ta then what rate (to the nearest %) was the ta?. A certain college states that the numbers in the college have increased by over two years. If there are now 45 people in the college then how many were there two years ago?. A boy is told that his height will increase by ¾ over the net eight years. If he is now 90cm tall then how tall will he be in eight years?. The shares in a certain company increased by 0% per year for three years. (e) If the shares were worth 600p three years ago then what are they worth now. (f) By what factor do they increase each year? (g) By what factor have they increased over the three years? (h) What is the connection between the two factors in (b) and (c)? PTO

30 Sheet H- -06a-06 Percentages (cont.) 4. An investment fund claims that it has increased by 450% over the last ten years. (c) If a man invested 000 in the fund ten years ago then what would it be worth now? (d) What is the average increase (to the nearest %) over a year of this fund? 5. What is the factor for the following: (a) An increase of % (b) A fall of 4% (c) A rise of 4.8% (d) A decrease by (e) An decrease by.5% (f) An increase by 50% (g) A fall by 5 (h) An increase of p%