BBC Skillswise Problem Solving Quiz PDF 2011 - Level A, B

L1 Problem solving quiz Level A 1. You are going out for a meal with a friend. The time is 5pm and you have to meet her at 8pm. How long is it until you need to meet her? A) 2 hours B) 4 hours...

L1 Problem solving quiz Level A 1. You are going out for a meal with a friend. The time is 5pm and you have to meet her at 8pm. How long is it until you need to meet her? A) 2 hours B) 4 hours C) 3 hours 2. There are 27 people waiting for a coach. When the coach arrives it only has room for 15 people. How many people will have to wait for the next coach? A) 12 B) 11 C) 16 D) 13 3. At a shopping centre you buy a skirt which costs £17.00 and a top which costs £8. How much do you spend in total? A) £26 B) £25 C) £24 D) £28 4. A swimming pool is 10 metres in width. If you swim across and back twice how far will you swim? A) 20 metres B) 30 metres C) 60 metres D) 40 metres 5. A furniture shop has had a delivery of tables and a delivery of chairs. There are 3 tables and 18 chairs. How many chairs should be matched with each table? A) 15 B) 8 C) 4 D) 6 © BBC 2011  L1 Problem solving quiz 6. A car park has spaces for 75 cars but 110 turn up on a Saturday morning. How many cars cannot get into the car park? A) 30 B) 45 C) 185 D) 35 7. You go to a fast food outlet and order a burger at £2.80 and a tea at £1.20. How much do you pay? A) £3.00 B) £1.60 C) £5.00 D) £4.00 8. A gardener needs three lengths of fencing for a garden. He needs 2 lengths measuring 10 metres and one length measuring 5 metres. How much does he need altogether? A) 15 metres B) 25 metres C) 52 metres D) 20 metres 9. You need 100 tiles to tile your bathroom wall. The tiles are sold in boxes of 5. How many boxes will you need to buy? A) 15 B) 20 C) 10 D) 50 10. 6 flatmates go to the supermarket. They decide to divide the cost up between them. If they pay £36 in total how much will each flatmate have to pay? A) £5 B) £16 C) £6 D) £8 © BBC 2011  L1 Problem solving quiz Level B 1. A tree is 3 metres tall and is growing 25 cm each year, how high will it be in 3 years? A) 78 cm B) 4.35 m C) 3 m 75 cm D) 3 075 cm 2. The price of some fruit is 50% more expensive in winter, than in summer. If strawberries cost £1.60 for a punnet in summer, how much would they cost in winter? A) £2.00 B) £2.40 C) 80p D) £2.50 3. You are on a bus in slow moving traffic. The average speed of the bus is 10 mph. How long will it take to travel 5 miles? A) 30 minutes B) 45 minutes C) 1 hour D) 50 minutes 4. You need 100 tiles to cover a wall. The tiles are sold in boxes of 9. How many boxes will you need to buy? A) 10 B) 11 C) 12 D) 13 5. The temperature in London is 5°C, while in Oslo it is -3°C. What is the difference in temperature? A) 8° B) 2° C) 15° D) 6° © BBC 2011  L1 Problem solving quiz 6. A cyclist goes 14 miles to work each morning and the same back in the evening. How many miles will the cyclist do to work and back each day? A) 70 miles B) 42 miles C) 28 miles D) 27 miles 7. You have an 8 hour dvd and need to know how many 50 minute programmes you can record, and how much space will be left over. A) 9 programmes + 30 minutes space B) 8 programmes C) 9 programmes + 20 minutes space D) 8 programmes + 30 minutes space 8. Your friend is training for a 10 mile run. She aims to do training runs of 30 miles a week. If she trains for 5 days a week and runs the same distance each day, how many miles will she run each day? A) 5 miles B) 3 miles C) 6 miles D) 10 miles 9. A club trip has been organised. If 4 people are travelling together in a car, how many cars will be needed for 25 people? A) 4 cars B) 8 cars C) 6 cars D) 7 cars 10. An exercise machine costs £120 by mail order. If it can be paid for in 12 equal instalments, what will be the amount of each instalment? A) £10.00 B) £12.00 C) £22 D) £12.20 © BBC 2011  L1 Problem solving quiz Level C 1. A shop buys DVDs for £5 each. It sells them at £11 each, or 3 for £24. How much profit would they make on selling 2 DVDs? A) £16 B) £12.00 C) £10 D) £11.00 2. A car park has 1 000 spaces. When the car park is three-quarters full, how many spaces will still be free? A) 250 B) 750 C) 25 D) 75 3. You pay £1.80 for a 2 litre bottle of cola. What is the cost per litre? A) £1.00 B) 90p C) 80p D) 70p 4. In a survey of 600 people 25% said they could swim less than 100 m. The remainder said that they could swim 100 m or further. How many people said they could swim 100 m or further? A) 500 B) 550 C) 600 D) 450 5. In a quiz you score 5 for a correct answer and -2 for a wrong answer. What would be the score for 8 correct and 4 wrong? A) 9 B) 48 C) 36 D) 32 © BBC 2011  L1 Problem solving quiz 6. A man won £6 000 in a competition. When he went to collect his prize money hotel and travel expenses came to £250. He also spent a further £500 on celebrating. How much of his prize money was left? A) £5 200 B) £5 500 C) £5 250 D) £5 400 7. Have a look at the prices for car parking shown below. Up to 1 hour is 90p 1 to 2 hours is £1.50 2 to 3 hours is £2.30 Your friend parks at 14:15. She only has £2 in cash. When will she have to leave the car park? A) 16:15 B) 17:15 C) 15:15 D) 13:15 8. A friend wants to buy a music system. There are two ways of paying: 1) £399 cash 2) £95 deposit then payments totalling £350 What is the difference in price? A) £46 B) £36 C) £49 D) £146 9. The ingredients for 40 small buns include 400g butter and 160g of cherries. What amount of each would you need for 10 small buns? A) 100g butter and 80g cherries B) 200g butter and 80g cherries C) 100g butter and 40g cherries D) 100g butter and 60g cherries © BBC 2011  L1 Problem solving quiz 10. A child’s jacket is being made. It will need 3 buttonholes all evenly spaced. The distance from the bottom of the jacket to the top buttonhole will be 12 cm. What will be the distance between each buttonhole if there is a 2 cm space at the bottom? A) 2 cm B) 5 cm C) 4 cm D) 3 cm © BBC 2011  L1 Problem solving quiz Answers Level A 1. You are going out for a meal with a friend. The time is 5pm and you have to meet her at 8pm. How long is it until you need to meet her? The correct answer is: C. 3 hours. The calculation is 8 – 5 = 3. 2. There are 27 people waiting for a coach. When the coach arrives it only has room for 15 people. How many people will have to wait for the next coach? The correct answer is: A. 12. The calculation is 27 – 15 = 12. 3. At a shopping centre you buy a skirt which costs £17.00 and a top which costs £8. How much do you spend in total? The correct answer is: B. £25. The sum is 17 + 8 = 25. You spend a total of £25 on clothing. 4. A swimming pool is 10 metres in width. If you swim across and back twice how far will you swim? The correct answer is: D. 40 metres. The calculation is 10 + 10 + 10 + 10 = 40 or 4 × 10. You will swim 40 metres. 5. A furniture shop has had a delivery of tables and a delivery of chairs. There are 3 tables and 18 chairs. How many chairs should be matched with each table? The correct answer is: D. 6. The calculation is 18 ÷ 3 = 6. 6. A car park has spaces for 75 cars but 110 turn up on a Saturday morning. How many cars cannot get into the car park? The correct answer is: D. 35. The sum is 110 – 75 = 35. 35 cars cannot get into the car park. © BBC 2011  L1 Problem solving quiz 7. You go to a fast food outlet and order a burger at £2.80 and a tea at £1.20. How much do you pay? The correct answer is: D. £4.00. The sum is £2.80 + £1.20 = £4.00. You will pay £4.00. 8. A gardener needs three lengths of fencing for a garden. He needs 2 lengths measuring 10 metres and one length measuring 5 metres. How much does he need altogether? The correct answer is: B. 25 metres. The calculation is 10 + 10 + 5 = 25. 9. You need 100 tiles to tile your bathroom wall. The tiles are sold in boxes of 5. How many boxes will you need to buy? The correct answer is: B. 20. The writing is long but the sum is short: 100 ÷ 5 = 20. 10. 6 flatmates go to the supermarket. They decide to divide the cost up between them. If they pay £36 in total how much will each flatmate have to pay? The correct answer is: C. £6. £36 shared between 6 means that they will each need to pay £6. The sum is 36 ÷ 6 = 6. © BBC 2011  L1 Problem solving quiz Level B 1. A tree is 3 metres tall and is growing 25 cm each year, how high will it be in 3 years? The correct answer is: C. 3 m 75 cm. The height of the tree after 3 years will be 3 m 75 cm. 2. The price of some fruit is 50% more expensive in winter, than in summer. If strawberries cost £1.60 for a punnet in summer, how much would they cost in winter? The correct answer is: B. £2.40. 50% is a half: 50% of £1 will be 50p and half of 60p is 30p. This means a 80p increase which will mean that in winter strawberries will cost £2.40 for a punnet in winter. 3. You are on a bus in slow moving traffic. The average speed of the bus is 10 mph. How long will it take to travel 5 miles? The correct answer is: A. 30 minutes. If the bus travels an average of 10 miles in an hour then it will travel 5 miles in half the amount of time, that’s 30 minutes. 4. You need 100 tiles to cover a wall. The tiles are sold in boxes of 9. How many boxes will you need to buy? The correct answer is: A. You said: 12. If you divide 100 by 9, that makes 11 with a remainder of 1. You’ll need that one tile to finish covering the wall, so you need 12 boxes. 5. The temperature in London is 5°C, while in Oslo it is -3°C. What is the difference in temperature? The correct answer is: A. 8°. Did you count up from -3 to zero, then on to 5? © BBC 2011  L1 Problem solving quiz 6. A cyclist goes 14 miles to work each morning and the same back in the evening. How many miles will the cyclist do to work and back each day? The correct answer is: C. 28 miles. The sum is 14 + 14 = 28. The cyclist will cycle 28 miles each day. 7. You have an 8 hour dvd and need to know how many 50 minute programmes you can record, and how much space will be left over. The correct answer is: A. 9 programmes + 30 minutes space left. 8. Your friend is training for a 10 mile run. She aims to do training runs of 30 miles a week. If she trains for 5 days a week and runs the same distance each day, how many miles will she run each day? The correct answer is: C. 6 miles. To find how many miles a day she runs you divide 30 by 5, which makes 6 miles. 9. A club trip has been organised. If 4 people are travelling together in a car, how many cars will be needed for 25 people? The correct answer is: D. 7 cars. 25 divided by 4 is 6 with with 1 left over. So 7 cars will be needed. 10. An exercise machine costs £120 by mail order. If it can be paid for in 12 equal instalments, what will be the amount of each instalment? The correct answer is: A. £10. The sum is £120 ÷ 12 = £10. © BBC 2011  L1 Problem solving quiz Level C 1. A shop buys DVDs for £5 each. It sells them at £11 each, or 3 for £24. How much profit would they make on selling 2 DVDs? The correct answer is: B. £6. The profit on one bottle is 11 – 5 = £6. So the profit on two bottles is 2 × 6 = £12. 2. A car park has 1 000 spaces. When the car park is three-quarters full, how many spaces will still be free? The correct answer is: A. 250. A quarter of 1 000 is 250, so 250 spaces will still be free. 3. You pay £1.80 for a 2 litre bottle of cola. What is the cost per litre? The correct answer is: B. 90p. 2 litres cost £1.80, so the cost for 1 litre will be half of £1.80 which is 90p. 4. In a survey of 600 people 25% said they could swim less than 100 m. The remainder said that they could swim 100 m or further. How many people said they could swim 100 m or further? The correct answer is: D. 450. 600 people were surveyed and 25% of 600 is 150. So, if 150 people said they could swim less than 100 m, 450 people said they could swim 100 m or further. 5. In a quiz you score 5 for a correct answer and -2 for a wrong answer. What would be the score for 8 correct and 4 wrong? The correct answer is: D. 32. You could say that 8 × 5 = 40 scored for correct answers. And 4 lots of -2 for wrong answers = -8. So 40 – 8 = 32. © BBC 2011  L1 Problem solving quiz 6. A man won £6 000 in a competition. When he went to collect his prize money hotel and travel expenses came to £250. He also spent a further £500 on celebrating. How much of his prize money was left? The correct answer is: C. £5 250. You could solve the problem by using subtraction. 6 000 – 250 = 5 750 5 750 – 500 = 5 250 7. Have a look at the prices for car parking shown below. Up to 1 hour is 90p 1 to 2 hours is £1.50 2 to 3 hours is £2.30 Your friend parks at 14:15. She only has £2 in cash. When will she have to leave the car park? The correct answer is: A. 16:15. Your friend can stay for up to 2 hours, so she will have to leave at 16:15. 8. A friend wants to buy a music system. There are two ways of paying: 1) £399 cash 2) £95 deposit then payments totalling £350 What is the difference in price? The correct answer is: A. £46. For option 2 the total amount payable will be £99 + £350 = £445 The difference in price will be the difference between £399 and £445, which is £46. © BBC 2011  L1 Problem solving quiz 9. The ingredients for 40 small buns include 400g butter and 160g of cherries. What amount of each would you need for 10 small buns? The correct answer is: C. 100g butter and 40g cherries. The ingredients given are for 40 and you want ingredients for 10. Did you halve the amounts, then halve again – or divide by 4? 10. A child’s jacket is being made. It will need 3 buttonholes all evenly spaced. The distance from the bottom of the jacket to the top buttonhole will be 12 cm. What will be the distance between each buttonhole if there is a 2 cm space at the bottom? The correct answer is: B. 5 cm. Take the 2 cm space at the bottom from 12 cm, which gives 10 cm. For 3 buttonholes there are two gaps between them so you divide the 10 cm by 2, giving 5 cm. So the buttonholes will be 5 cm apart. © BBC 2011