The Haberdasher Aske’s Boys’ School11 Entrance Examination 2017 MATHEMATICS Online Quiz view all papers Welcome to your THE HABERDASHER'S ASKE'S BOYS' SCHOOL 11+ Entrance Examination 20171. Add: 88 + 37 125 115 135 112 120 None 2. Subtract: 96 - 47 49 31 41 51 59 None 3. Multiply: 58 x 7 406 356 456 416 410 None 4. Divide: 78 ÷ 6 13 10 12 16 14 None 5. Write down two numbers that add to 14 and multiply to 48. and -------- 8 & 6 5 & 7 4 & 2 12 & 8 8 & 10 None 6. You are given the number 2864. You are allowed to swap the position of any two digits. For example, 2 8 6 4 gives 2 6 8 4 or 2 8 6 4 gives 4 8 6 2 What is the largest possible number you can make using one swap? 8264 8624 2648 2468 8426 None What is the smallest possible number you can make using one swap? 2468 2486 2864 2648 2846 None 7. Work out the following: 21 − 5 × 2 + 6 17 18 16 14 32 None 8. What number is: Six less than −10 -16 16 4 -4 Both b & d None Twelve more than −8 4 -16 -4 16 None of the above None 9. Alison, Bethany and Catherine are three sisters. They are 6 years old, 7 years old and 12 years old. Bethany is older than Alison. Catherine’s age is a prime number. What is each girls’ age?Alison’s age ---------Bethany’s age ---------Catherine’s age --------- Alison's age=6, Bethany's ange= 12, catherine's age= 7 Alison's age=6, Bethany's ange= 7, catherine's age= 12 Alison's age=12, Bethany's ange= 7, catherine's age= 6 Alison's age=7, Bethany's ange= 6, catherine's age= 12 None of the above None 10. Draw the hour and minute hands on this clock to show the time 22:30 . What is the reflex angle between the two hands on this clock? 225 degree 150 Degree 120 Degree 180 Degree 60 Degree None 11. The sums below were correct before someone rubbed out the brackets. Write down the correct sums, including the brackets. (a) 8 - 5 + 2 = 1 (8-5)+2 = 1 8-5+2 = 1 8-5+2 = (1) 8-(5+2) = 1 None of the above None (b) 12 - 11 + 2 - 1 = 0 (12-11)+2-1 =0 12-(11+2-1) =0 (12-11)+(2-1) =0 (12-11+2)-1 =0 None of the above None 12. Geoff counted the number of lorries he saw on his journey to school each day. The results for Monday, Tuesday, Wednesday and Thursday are shown in the pictogram. How many lorries did Geoff see on his journey on Tuesday? 8 6 10 2 4 None How many lorries did Geoff see on his journey on Wednesday? 10 2 6 8 4 None On Friday Geoff saw six lorries on his journey into school.Complete the pictogram for Friday. None 13. Here is a map of Secret Island. What are the co-ordinates of the Sunken Treasure? (7, 8) (8, 7) (-7, 8) (-7,-8) None of the above None What are the co-ordinates of the Whirlpool? (8, -5) (-8, 5) (-8, -5) (8, 5) None of the above None There is a crocodile at (-7, 6).Mark the crocodile on the map. Label the crocodile with the word “CROCODILE”.Which of the features shown on the map is the crocodile closest to? Light House Sunken Treasure Whirlpool Pirate Ship None of the above None 14. What is the name of each of these three regular polygons? Pentagon Hexagon Nonagon Decagon None of the above None Hexagon Nonagon Pentagon Octagon None of the above None Nonagon Hexagon Pentagon Octagon None of the above None 15. From Year 10 all pupils must join the Combined Cadet Force (“CCF”) or opt for School Community Service (“SCS”). Pupils can not opt for both CCF and SCS. Rachel asked 150 Year 9 pupils whether they wanted to opt for CCF or SCS next year. 60% of the pupils said that they wanted to opt for CCF. \[\frac{1}{6}\] of the pupils said that they wanted to opt for SCS. The rest of the pupils said that they hadn’t yet decided. How many pupils hadn’t yet decided whether to do CCF or carry out SCS next year? 35 15 25 45 30 None 16. Sam thinks of a number. He multiplies that number by 5. Then he subtracts 12. Then he divides by 3. Finally he adds 17. His answer is 38. What number did Sam originally think of? 15 25 20 38 17 None 17. A bus can carry 52 passengers. How many buses will be needed to transport 993 people to a sports day? 20 15 25 18 10 None 18. In the American state of Kentucky sales tax is charged at 6%. Anila wants to buy a pair of jeans in Kentucky. They are priced at $72 before allowing for the sales tax. How much does Anila pay for the pair of jeans? $76.32 $72 $74.32 $73.32 Both a & b None Peter buys a bag of sweets in Kentucky.He pays $4.77 including sales tax.What was the price of sweets before sales tax was added? 4.5 4.75 3.75 3.7 4.77 None 19. I put the individual twelve letters of the word “HABERDASHERS” into an empty bag. I draw out a letter at random from the bag. What is the probability that I draw out: (a) The letter “B”? \[\frac{1}{12}\] \[\frac{1}{8}\] \[\frac{1}{20}\] \[\frac{1}{10}\] \[\frac{1}{15}\] None (b) The letter “T”? 0 3 1 2 None of the above None (c) A vowel? \[\frac{1}{3}\] \[\frac{1}{12}\] \[\frac{1}{4}\] \[\frac{3}{4}\] \[\frac{1}{2}\] None (d) A letter that is also in the word “ASKES”? \[\frac{1}{2}\] \[\frac{1}{3}\] \[\frac{1}{4}\] \[\frac{1}{5}\] 1 None 20. The sails of a windmill complete one full turn every 40 seconds. (a) How long does it take the sails to turn through a right angle? 10 Seconds 05 Seconds 18 Seconds 20 Seconds 15 Seconds None (b) How many turns do the sails make in fifty-six minutes? 84 64 82 74 80 None 21. A class has thirty pupils. Eight pupils are left-handed. Sixteen pupils are girls. Of the sixteen girls, thirteen are right handed. Enter this information into the table below. Then complete the rest of the table. Left handedRight handedTotalBoys Girls Total None How many boys in the class are right-handed? 9 10 6 5 3 None 22. Stuart’s patio is 5 metres long and 5 metres wide. Stuart wants to cover the patio with paving stones. Each paving stone is 50 centimetres long and 50 centimetres wide. How many paving stones does Stuart need to buy? 100 50 80 40 55 None Stuart has £200 left after buying the paving stones.Stuart wants to put a picket fence around three sides of his patio.Each panel of picket fencing is 1 metre long and costs £10.50. Stuart will also have to pay a delivery charge of £5 regardless of the number of panels of picket fencing he purchases.How much money does Stuart have left after buying the picket fencing? 37.5 47.5 27.5 17.5 25.7 None 23. Elizabeth writes down: One multiple of 13; and Two different factors of 77. Elizabeth adds up her three numbers. Her answer is greater than fifty but less than sixty. What three numbers could Elizabeth have written down? 39, 7, 11 19, 3, 7 9, 13, 17 49, 11, 18 29, 5, 13 None 24. A cube has side lengths of 5 cm. What is the volume of the cube? 125 50 75 25 120 None A second cube has a volume of 27 \[cm^{3}\] .What is the total surface area of the second cube? 54\[cm^{2}\] . 75\[cm^{2}\] . 80\[cm^{2}\] . 125\[cm^{2}\] . 65\[cm^{2}\] . None 25. Rinesh started painting his house two years ago. During that year, Rinesh painted one-third of his house. Last year, Rinesh painted another five-twelfths of his house. What fraction of his house does Rinesh need to paint this year, in order to finish completely painting his house? \[\frac{1}{4}\] \[\frac{1}{2}\] \[\frac{3}{4}\] \[\frac{1}{3}\] \[\frac{4}{3}\] None Bijal started weeding her garden two weeks ago.During that week, she weeded one-fifth of her garden.Last week, Bijal weeded two and a half times as much of her garden as she weeded two weeks ago.What fraction of her garden does Bijal need to weed this week, in order to finish completely weeding her garden? \[\frac{3}{10}\] \[\frac{3}{4}\] \[\frac{5}{8}\] \[\frac{10}{3}\] \[\frac{9}{10}\] None Nina is painting garden gnomes.She has four-fifths of a litre of paint.Each garden gnome needs one-twentieth of a litre of paint.How many garden gnomes can she paint? 16 10 12 14 20 None 26. Here is a portion of the Monday to Friday bus timetable for the 724 bus between St. Albans and Heathrow. HschHNschHschHNschHschHNschHschSt. Albans,Railway Station0555060306410715074508080909St. Albans,St Peter’s Street0600060806460721075108140915Garston Bus Garage0625063307160748083108450944Watford Junction Railway Station0637064507330803085309011002Watford,Town Hall0640064807370807085709051006Rickmansworth Railway Station0650065807540817090909151016Denham, Station Parade0709071308200832092509301031Uxbridge,Belmont Road0717072108330840093609381039Heathrow Airport0737073708570857095409541055 None HschHNschHschHNschHschHNschHschHeathrow Airport0610061507000710075508100915Uxbridge,Belmont Road0626063107170727081708270932Denham, Station Parade0634063907260736082808380941Rickmansworth Railway Station0650065507430753085008550957Watford,Clarendon Road0704070908040814091109111011Watford Junction Railway Station0707071208070817091409141014Garston Bus Garage0722072708230833092909291029St. Albans,St Peter’s Street0745075008500900095209521052St. Albans,Railway Station0756080109010911100310031103 Notes: Hsch – Hertfordshire schooldays only HNsch – Hertfordshire school holidays only None (a) Andy caught a bus at Denham at 6:39 am. What time does he arrive at Watford Junction Railway Station? 7:12 7:07 8:07 8:17 9:14 None (b) Ben wants to travel from Watford Town Hall to Uxbridge by bus. If he catches a bus at Watford Town Hall at 8:57 am how long will his journey take? 39 min 29 min 30 min 20 min 15 min None c. Charlie lives in Uxbridge and works 10 minutes walk away from Garston Bus Garage. He needs to arrive at work by 9:30 am. What time does he need to be at the bus stop in Uxbridge to get to work on time: i) if it is a Hertfordshire school day? 7:17 7:22 7:27 7:30 7:48 None ii) if it is a Hertfordshire school holiday? 7:27 7:22 7:17 7:30 7:48 None d. Tom has arranged to meet Nic at St. Peters Street in St. Albans at 8:30 am. Tom lives in Rickmansworth and is planning to travel by bus. Tom thinks that it is a Hertfordshire school holiday and arrives at the bus stop at Rickmansworthjust in time to catch the bus. Unfortunately, it is a Hertfordshire school day. How late does Tom arrive for his meeting with Nic? 20 min 10 min 25 min 15 min 30 min None 27. One angle of an isosceles triangle is 80°. What are the other angles? There are two possible solutions to this question. Answer One -------- and --------- and --------- Ans1: 50 & 50, Ans2 : 80 & 20 Ans1: 40 & 40, Ans2 : 70 & 30 Ans1: 60 & 50, Ans2 : 70 & 40 Ans1: 90 & 60, Ans2 : 50 & 30 Ans1: 80 & 40, Ans2 : 60 & 30 None 28. a) What is the area of this triangle? 10 4 5 9 8 None b) What is the area of this triangle? 24 18 16 26 28 None By thinking of two different ways to work out the area of the triangle, calculate the length of arrow. 4.8 5.8 3.8 2.8 1.8 None 29. Here is a map of the roads in Askeshire. None The route from Catsworth to Dogsville via Alysford is written “C->A->D”.There has been a robbery in Alysford. The thieves are planning to go to Habsville Airport to flee the country with their loot.The police want to go from Alysford to Habsville Airport by the shortest possible route. What route should the police take? 90 miles 70 miles 100 miles 60 miles 80 miles None The thieves also want to go from Alysford to Habsville Airport by the shortest possible route. However, the thieves also want to make sure that they don’t travel on any of the roads being used by the police. What route should the thieves take? 120 miles 110 miles 90 miles 70 miles 100 miles None 30. For each of the prime numbers in the table below: (a) Find the remainder when the prime number is divided by 4; and (b) Find whether the prime number can be expressed as the sum of two square numbers. If the prime number can be expressed as the sum of two square numbers, state the two square numbers. If the prime number cannot be expressed as the sum of two square numbers state “Not possible”. Complete the table below. The first two rows have been completed for you.Prime numberThe remainder when the prime number is divided by 4Can the prime number be expressed as the sum of two square numbers?33Not possible51\[1^{2}\] + \[2^{2}\]7 11 13 17 None What is the link between whether a prime number can be expressed as the sum of two square numbers and the remainder when that prime number is divided by 4? If you are not sure you can extend the table above and see what happens for other prime numbers.The first proof that this pattern is true for all prime numbers was claimed by Pierre de Fermat and is called Fermat’s Christmas Theorem (because Fermat’s claim was dated December 25, 1640).Circle “YES” for each of the following prime numbers that can be expressed as the sum of two square numbers.Circle “NO” for each of the following prime numbers that cannot be expressed as the sum of two square numbers.You do not need to find the two square numbers.Prime numberCan the prime number be expressed as the sum of two square numbers?58 031 YES NO58 043 YES NO58 049 YES NO58 057 YES NO Time's up
