Circumference of a circle

Area of a circle: Curved surface area of a cylinder: C = pd A = pr2 A = 2prh

Theorem of Pythagoras: c b a2 + b2 = c2

a

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Marks 1. It will take Hassan 3 hours 40 minutes to drive from Dundee to Stranraer. He must be in Stranraer by 2.15 pm. What is the latest time he should leave Dundee?

2. A recipe lists the ingredients needed to make 4 portions of chilli con carne. Ingredients for 4 portions of chilli con carne Minced beef Chilli powder Kidney beans Chopped tomatoes 700 grams 2 1 teaspoon 300 grams 300 grams

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Onions

How many grams of minced beef would be needed to make 9 portions of chilli con carne?

2

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Marks 3. This network diagram shows the journey times, in hours, between six cities. Exdale 6 2·5 Fenboro 1 Albany 2 Bloomsburg (a) How many arcs are there in the network diagram? 3 3 Clarkstown 4·5

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3·5 Denton

(b) Calculate the shortest journey time from Albany to Denton.

1

1

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Marks 4. The table below shows the monthly payments to be made on a loan of £1000. Period of Loan Monthly Payment on £1000 1 year £87·10 2 years £45·34 3 years £31·45 4 years £24·53

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(a) Gavin borrows £5000 over 3 years. Calculate his total payments.

2 (b) Calculate how much this loan cost Gavin.

1

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Marks 5. Carla likes to keep fit. She plans a workout by choosing activities from an exercise DVD. She can choose from the following activities. Activity Aerobics Yoga Jogging Toning Tums and Hips Activity time 30 minutes 25 minutes 20 minutes 15 minutes 12 minutes

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Carla wants to choose three different activities. She wants to exercise for a minimum of 60 minutes. One combination of three different activities that Carla can choose is shown in the table below.

Yoga Toning Tums and Hips Total Time Aerobics Jogging 30 minutes 25 minutes 20 minutes 15 minutes 12 minutes minutes 3 3 3 75

Complete the table to show all the possible combinations of three different activities that Carla can choose.

3

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Marks 6. The stem and leaf diagram below shows the heights of the girls in a Primary 7 class. HEIGHTS Girls 11 1 12 2 13 0 14 3 6 5 1 4 9 6 7 12 5 (a) What height is the tallest girl? represents 125 centimetres 8 8

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1 (b) Find the median height.

1

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Marks 6. (continued) The stem and leaf diagram below shows the heights of both the boys and the girls in this class. HEIGHTS Boys 9 8 7 8 4 6 5 3 2 1 11 1 3 12 2 1 13 0 7 14 3 6 5 1 4 9 6 7 represents 125 centimetres 8 8 Girls

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12 5

(c) Compare the heights of the boys with the girls in this class. Comment on the overall difference.

1

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Marks 7. Five people are selling tickets for a school show. The spreadsheet below is used to calculate the value of their ticket sales. • • Adult tickets cost £10 each Child tickets cost £7 each A 1 2 George 3 Karen 4 Ronan 5 Sally 6 Jamie 7 (a) The result of the formula =SUM(C2..C6) is to be entered in cell C7. What number would appear in cell C7? B Number of Adult tickets 15 12 23 29 18 C Number of Child tickets 11 13 9 18 5 D Total Value (£) 227 211

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1 (b) The total value of Jamie’s ticket sales is to be entered in cell D6. What formula should be used?

1

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Marks 8. The times (in seconds) taken by nine athletes to run 100 metres are shown below. 11·2 11·0 10·8 12·1 12·3 11·5 11·8 11·6 11·9 (a) Find the upper quartile.

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2 (b) Calculate the interquartile range.

2 9. Whistler downhill ski course is 3·1 kilometres long. Finlay completed the course in 2 minutes 5 seconds. Find his average speed in metres per second.

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10. The table below shows the number of visitors to Ballyvarick Castle from April to September.

Month Visitors (to nearest hundred) April 2000 May 3000 June 4400 July 7800 August 8600 September 5400

On the grid below, draw a line graph to show this information. 10 000

Visitors 0 April Month Marks 4

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Marks 11. Margaret insures her house which is worth £105 000. The annual premium is £3·20 for every £1000 worth of cover. She is given a discount of premium. 1 of her annual 8

HOUSE INSURANCE

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How much does Margaret pay to insure her house?

Special Offer 1 8

3

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Marks 12. A room in the Caledonian Hotel in New York costs 280 dollars per night plus 17% tax. The exchange rate is 1·51 dollars to the pound. Find the cost of the room per night. Give your answer in pounds and pence.

$280

per night plus 17% tax

4

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Marks 13. A cylinder has diameter 20 centimetres and height 15 centimetres.

15 cm

20 cm Calculate the curved surface area of the cylinder.

3

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Marks 14. The diagram shows the end view of a building.

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6·8

m

12 m 7·5 m

height

Calculate the total height of the building. Do not use a scale drawing.

4

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Marks 15. A market trader buys a box of twelve shirts for £80. He sells them for £9 each. (a) How much profit does he make altogether?

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1 (b) Express his profit as a percentage of what he paid for the shirts.

3

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Marks 16. A section of lawn edging consists of a rectangle with five equal semi-circles at the top.

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14 cm 60 cm Calculate the area of the section in square centimetres. Give your answer correct to the nearest square centimetre.

5

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