Elstree, Herts
11+ Entrance Examination 2011
MATHEMATICS
Time : One Hour
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Full Name
Candidate Number
Please follow these instructions
• Do not open this paper until you are told to do so.
• There are 30 questions on this paper. Do not forget to turn over.
• Work quickly but accurately. You are recommended to use pencil, but you can use pen or biro if you wish.
WRITE YOUR ANSWERS TO THE QUESTIONS IN THE SPACES PROVIDED. YOU MAY USE THE SPACE AT THE BOTTOM OF EACH PAGE FOR WORKING.
Answer
1. Add: _______ 4827
2. Subtract: _______ 9125
3. Multiply: 627 _______
4. Divide: _______ 924
5. I have £8.17 credit on my mobile phone. At the end of a phone call this falls to £7.65. How much did the call cost? _______
6. The drink “Raspberry Heaven” is 1 part raspberry juice, 2 parts orange juice and 3 parts apple juice. How much raspberry juice does a 300 ml glass of Raspberry Heaven contain? _______
7. Work out the product of 528 and 99. _______________
8. Barbie earns £23,450 a year and her partner Ken earns £700
less than Barbie. How much do the couple earn altogether? __________
9. Convert 7.4 kilograms into grams. _________
10. Arrange the following numbers in order of size starting with
the smallest: 32.043, 0.099, 1.072, 0.491, 0.5
_______________________________________________________________
11. The opening hours of my local supermarket are 7am to 9pm Mondays to Saturdays and 10:30am to 4:30pm on Sundays. For how many hours
does this supermarket open each week? __________
12. Arrange the numbers, 5, 3, 7 and 2 to make the largest possible four-digit number which is a multiple of 5. _________
13. Work out 0.08 multiplied by 5. _________
SPACE FOR WORKING
Answer
14. The new TV channel, Lazy Living, broadcasts for 98 hours a week. If two-sevenths of its output is devoted to make-over programmes and the rest to celebrity gossip, for how many hours each week
does the channel broadcast programmes on celebrity gossip? _________
15. For breakfast I eat a slice of buttered toast and a cup of coffee. The time taken to complete these activities is as follows: Brown toast in toaster 3 minutes Butter the toast 1 minute Make coffee in machine 2 minutes
Jonathan thinks that the shortest time taken for me to prepare my breakfast is 6 minutes. Explain briefly why Jonathan is wrong.
________________________________________________________________
What is the correct shortest time? ________
16. The chart below shows the mileage between five places in North London. For example it gives the distance between Kenton and Hampstead as 4 miles.
KENTONDENED191145HARPEN182013SOUTHGAT89HAMTPSEA10HABS
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Daisy lives in Hampstead and drives her son to school at Haberdashers’ in the morning before continuing on to the office in Southgate. She then visits her sister in Harpenden before driving home via Habs. How far does she travel altogether? _________
Answer
17. The rate of VAT (value-added tax) in this country is 20%. In the shop CoCost, the price of a TV excluding VAT is £550.
Work out the cost of the TV after the VAT is added on. ________
The price of a diamond ring, including VAT is £1200.
Work out the cost of the ring before the VAT was added on. ________
18. Train A leaves Birmingham New Street station at 1747 travelling
due North on the slow line at 90 km/hour.
How many kilometres has this train travelled when the time
is 1817? ____________
Train B leaves Birmingham New Street station at 1817 also travelling due North but on the fast line. The speed of train B is 135 km/hour.
At what time does train B overtake train A? _____________
19. The diagram below shows a piece of abstract art hanging up on Andrew’s
bedroom wall. To make this look even more interesting he decides to
rotate this painting through 90 degrees clockwise. In the space provided show what the painting will look like in its new position.
SPACE FOR WORKING
Answer
20. Every evening Diana has a bath. She turns on the taps and waits patiently for the bath to fill before she turns them off and steps in. At the end of her bath she steps out of the water before pulling out the plug to empty the bath.
A graph of the volume of water (measured in litres) plotted against time (measured in minutes) is shown below.
Volume of watern tres1000750500250051015202530Time n mnutes
How long does she spend in the bath? __________
Work out the number of litres of water that flow into the bath per minute as the bath fills up. __________ Does the bath empty at a faster, slower or the same rate as it fills?
Faster, slower or same? _______________
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Answer
21. Amar (form captain), Brian (vice captain), Charles and Daniel are
best friends in the same class at school. They always like to stand next to each other in the lunch queue.
On Mondays it is a school rule that the form captain is at the front of the queue followed by the vice captain. There are two ways in which these boys can queue up on a Monday: ABCD and ABDC.
On Tuesdays, the form captain must again queue up first but the remaining three boys can follow in any order. There are six ways in which these boys can queue up on a Tuesday. Four of these ways are listed below. Write down the remaining two: ABCD, ABDC, ACBD, ACDB, _______, _________
On Wednesdays there are no restrictions and all four boys can queue up together in any order. In how many ways can this be done? ____________
22. Isolde enjoys making cubes. She first draws out shapes on pieces of
cardboard and then folds them along the lines to form a cube.
The diagrams below show six attempts. Unfortunately only five of these actually work. Cross out the shape which is impossible.
SPACE FOR WORKING
23. As part of a mathematics project a class is asked to look up the lengths of objects on the internet. These objects are listed in the rectangles below and the measurements are given in the triangles. Unfortunately these objects and measurements have been muddled up. Draw lines on the diagram to match each object with its correct length.
Width of Wembley Stadium pitchHeight of an average manDistance from London to New YorkLength of a piece of standard A4 paperHeight of the London EyeHeight of Mount Everest
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300 mm5600 km135 m1750 mm8800 m6900 cm
Answer
24. In this question you may assume the following exchange rates: 1 British pound (£) = 1.5 American dollars (US$) 1 British pound (£) = 2 New Zealand dollars (NZ$)
The price of a hoodie in the London branch of Abergavenny and Filtch is £80. In New York the price is US$90. How much do I save by buying the hoodie in New York? Give your answer both in US dollars and pounds. Saving = US$ ___________ and £ ___________
My friend Sheila lives in Auckland, New Zealand. She saves US$60 if she buys this hoodie in New York. How much does it cost in New Zealand? Give your answer in New Zealand dollars. NZ$ ___________
Work out the exchange rate for converting New Zealand dollars into American dollars: 1 New Zealand dollar (NZ$) = ______ American dollars (US$)
25. Seven children, A, B, C, D, E, F, G take part in a competition.
Use the information below to fill in the table:
Position Child 1st 2nd 3rd 4th 5th 6th 7th
▪ There are no tied positions ▪ D beat A
▪ C was the winner
▪ If you multiply the positions of A and D you get the position of F ▪ A and E are in next to each other in the table. ▪ B beat G
SPACE FOR WORKING
Answer
26. The average of a set of numbers is worked out by adding the numbers together and then dividing by the number of numbers.
Work out the average of: 1, 1, 1 _______ 1, 1, 4 _______ 1, 4, 7 _______ 4, 7, 13 _______
Describe, in words, a simple pattern that you notice about these answers:
_______________________________________
Class 6A go on a Geography trip to Eastbourne and investigate the size of pebbles on the beach. Jonnie picks up seven small pebbles and measures their lengths in millimetres. The lengths of the first six pebbles are:
1, 1, 1, 4, 7, 13
Assuming that the pattern that you observed above continues to hold, work out the length of Jonnie’s seventh pebble. ________
27. Tristan is given six bags of fruit.
Bag A contains 2 apples, 4 oranges and 3 pears. Bag B contains 3 apples, 1 orange and 2 pears. Bag C contains 4 apples, 5 oranges and 3 pears. Bag D contains 4 apples, 6 oranges and 4 pears. Bag E contains 6 apples, 4 oranges and 3 pears Bag F contains 7 apples, 7 oranges and 7 pears. He is allowed to choose one of these bags and then pick just one piece of fruit from that bag at random. Which bag should he choose if he is to maximise his chance of picking an apple? _________ Which bag should he choose if he is to minimise his chance of picking a pear? _________
SPACE FOR WORKING
Answer 28. The diagram below shows a sequence of squares drawn on a grid. The coordinates of the centre of square number 1 are (1,1). The coordinates of the centre of square number 2 are (2,3). The first number in the pair is the x-coordinate and the second number is the y-coordinate. Write down the coordinates of the centre of square number 3 ___________________ square number 4 ___________________ square number 10 ___________________ square number 234 ___________________ The y-coordinate of the centre of one of the squares in this sequence is 2177. Work out the x-coordinate of this square. ________________
y653432211123456xSPACE FOR WORKING
29. In the triangles shown below each number is the sum of the two numbers
directly underneath it. For example, 26 = 12 + 14 and 5 = 1 + 4.
26
12 14 5 7 7
1 4 3 4
Complete the triangle of numbers:
____
____ ____
____ 8 7 1
____
____
Complete the triangle of numbers:
101 54
____
____
____
12
____ 8
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5
____
____
Answer
30. The diagram below shows a rectangle, 9 units long, 6 units wide and with
parts of non-overlapping circles drawn all over it. The circles all have the same radius and the area of each is 7 square units. Work out the shaded area.
9 units6 units
Shaded area = _________ square units
The diagram below shows a square which is 3 units long with four identical semi-circles drawn on each edge. These semi-circles overlap to create four petals which are shaded on the diagram. The area of each semi-circle is 3.5 square units. Work out the shaded area.
3 units
SPACE FOR WORKING
Shaded area = ________ square units
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