2016

ENTRANCE AND SCHOLARSHIP

13+ SAMPLE PAPERS

ENGLISH AND MATHS SAMPLE

Forest School 13+ Mathematics

Non-Calculator

TIME ALLOWED = 1 hour

INSTRUCTIONS

Calculators are NOT allowed. You are advised to show all working. You have 1 hour to complete all the questions. Write all your answers and working in the space provided on this

question paper. Check your working carefully.

SAMPLE

1. Calculate the following:

(a) 9876 + 6789 (b) 987 × 14

Answer: ................................. Answer: ................................. (c) 30485 ÷ 13 (d) 1.7 × 2.1

Answer: ................................. Answer: ................................. (e) 7.45 – 2.61 (f) 0.4 ÷ 0.002 Answer: ................................. Answer: .................................

2. Calculate the following:

(a) 22 – (-67) = …………………………

(b) (-3)4 = ………………………….

(c) -8 – 17 = …………………………

(d) 27 ÷ -3 = ………………………….

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3. If x = -5, y = -10 and z = -15 calculate the following:

(a) x – y + z (b) 2x2

Answer: ................................. Answer: ................................. 4. (a) Round the following to 2 decimal places:

(i) 1.2468 Answer………………………

(ii) 1.8989 Answer………………………

(b) Sana says that x = 7.3 to 1 decimal place.

(i) What is the least possible value of x? Answer………………….

(ii) What is the largest possible value of ? Answer………………….

(iii) Charlie says that the largest x can be is 7.34.

Is he right? Explain clearly your reasoning.

.................................................................................................................................................................... .................................................................................................................................................................... .................................................................................................................................................................... .................................................................................................................................................................... .................................................................................................................................................................... ................................................................................................................................................................... .................................................................................................................................................................... ....................................................................................................................................................................

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5. Molly draws 5 straight lines. What is the most number of different intersection points she can make?

Answer………………….

6. The area of a circle is πr2 and the circumference (perimeter) is 2πr where π ≈ 3.1415 Estimate the area and the perimeter of this semicircle, where AB = 10cm.

10cm

Area: .............................. Perimeter: .............................. 7. What fraction is halfway between one third and one quarter? You should show your working clearly. Answer:……………………………………….

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8. Fill in the gaps. Put your fractions in their lowest terms. 9. A rectangle has width x cm and its length is 4 cm longer than its width. Its perimeter is 50 + x cm. Find an equation which x must satisfy and hence find the length of the rectangle.

Length = …………………………………………… 10. In a farmyard the ratio of peacocks to ducks is 2:3 and the ratio of ducks to hens is 4:5. What is the ratio of peacocks to hens?

Answer:…………………………………

Percentage Fraction

55%

18

2%

320

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11. (a) Faizan buys a car for £2000. Its value depreciates (goes down) by 2% each year.

How much is it worth after 1 year? Answer:............................................................ (b) How much is it worth after 2 years?

Answer: ..............................

12. Liverchester United are playing 2 matches against their arch rivals, Manpool City. They have won 6 out of their last 10 matches against Manpool City.

(a) Based on these results, what is the probability that Liverchester beat Manpool in the first match?

Answer:................................. (b) What is the probability they win both matches?

Answer:....................................... (c) Having won the last 6 out of 10 matches, how many games would Liverchester then have to win

in a row so that their probability of winning is ?

Answer:..........................................

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13. The scattergram shows how some pupils at Forest did in a maths test against their height.

Hibban says “Being tall makes a pupil better at maths”

Do you agree?........................................ Explain your reasoning clearly: :……………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Height (in metres)

Mat

hs T

est M

ark

(%)

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14. Andreas wants to estimate how many fish there are in a lake. One day he catches 20 fish, marks them, and returns them to the lake. The next day he catches 10 fish, of which 4 are marked. Use this information to estimate the number of fish in the lake. Answer:……………………………. 15. Remove the brackets and simplify these expressions fully:

(a) 4(f - g) + 5(2f + g) = ……................................................................................ =.........................................................................................

(b) 7(2e + 8) – 3(3e – 5) = ……………..................................................................

=........................................................................................

(c) w(2w + 5v) – 3v(5w – 2v) = ………………………………………………........

= ………..................................................................

16. Factorise the following expressions fully:

(a) 15a + 27b (b) 27c2d2 – 36c5d

Answer: ................................. Answer: .................................

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17. Find the three missing angles in the diagram below, you must give the full reasoning for each answer. ABC is an isosceles triangle, the lines with arrows are parallel.

43o

y

............ Reasons:................................................................................................................................................

.................................................................................................................................................................

y = ............. Reason:................................................................................................................................................

z = ..............

Reason…:................................................................................................................................................

................................................................................................................................................................. 18. Class A has 10 pupils and achieved a mean of 40% in a maths test. Class B has 15 pupils and achieved a mean of 80% in the same test. What is the overall mean for both classes? Answer…………………………….

A B

C

x z

SAMPLE

19. Draw all the lines of symmetry on these shapes:

(a) An equilateral triangle

(b) A rectangle 20. (i) Label the lines with their equations.

Line A:……………………………………………….. Line B:…………………………………………………

(ii) A triangle has its vertices (corners) at (-2, -2), (-2, 1) and (-3, 1). Plot these points, and draw the triangle on the diagram. Reflect the triangle in Line A.

Line A Line B SAMPLE

21. The Fibonacci sequence is formed by adding the previous two numbers to get the next:

1, 1, 2, 3, 5, 8, 13,…

What are the next three numbers in this sequence?

The Lucas Sequence has the same rule but starts with 1 and 3.

(i) Write out the first 7 terms of the Lucas sequence.

(ii) Write down the first 7 terms, in terms of x and y, for the sequence with the same rule whose first terms are x and y.

(iii) Mia says: “If x is a multiple of 5 then the 6th term of the sequence is also a multiple of 5 whatever y is”.

Do you agree? Explain your reasoning carefully.

(iv) Steph says: “Every 5th term of the Fibonacci sequence is a multiple of 5”.

Do you agree? Explain your reasoning carefully.

SAMPLE

22. (i) Show that the interior angle of a regular pentagon is 108 degrees.

NOT TO SCALE

(ii) A regular pentagon and a regular hexagon overlap as shown. Find the angle x. Show your reasoning clearly.

NOT TO SCALE x

END OF EXAMINATION

CHECK THROUGH ALL YOUR ANSWERS CAREFULLY

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13+ ENGLISH ENTRANCE and SCHOLARSHIP

PASSAGE

SAMPLE

Section A: Reading Read the following text. Answer the questions in the booklet provided. Just Walking the Dog. I don't enjoy chasing squirrels or rolling on my back in something unspeakable in the grass or standing up to my middle in a muddy pond; but I know those who do and am often to be found in their company. For over half a century, since long before people started to say 'like' every second 5

word, I have been walking dogs. Mostly I've taken a succession of dogs around Richmond Park, with excursions sometimes to Sheen or Wimbledon Common. These latter two are appropriate places for the more recalcitrant canines who have gained a reputation for somewhat boisterous behaviour. In the last eight years I've extended my range to include some of the muddier, less salubrious parts of Epping 10

Forest. I am, though I say it myself, 'known' in these spots; but it's sometimes the dogs that get the greetings. 'Good morning, Micky,' people will say, ignoring the panting human close on the four hairy heels of a Norfolk Terrier. Or 'How's Polly today?' 15

After five decades I still find this hard to comprehend. On the whole, however, dog-walkers are, in my experience, agreeable, benevolent souls who are happy to chat for a few minutes about this and that. It's safest, of course, that neither this nor that should be politics or religion. The contemporary art 20

and music scenes are probably to be avoided, too. One's best bet for an opening line is something with a canine focus. 'What a happy-looking dog!' is usually a winner. Or 'There's a lovely dog! Now what sort is she?' 25

Questions about the dog's attractive colour, attractive collar, or age are usually welcomed. Perhaps then the owner will volunteer some detail about the creature's habits or behaviour, dietary preferences or family background which will take things a step further. 30

Names can be a tricky issue. 'Stanley? Yes, he looks just like a Stanley' is likely to please; but it's quite hard to say, 'Dagenham? That's an excellent name!' and sound altogether convincing. Better to try, 'Ah, because he was born there?' 35

However, if the reply is, 'No, he's from Dorking,' you're wise to regroup and retreat in good order.

SAMPLE

A famous poet said that the true test of one's ability to manage language was finding an apt name for a puppy. With the passing of the years this challenge does not 40

appear to have got easier. Names of 'breeds', though, are much more fun than they once were. Only this morning my canine companion and I met a Jug in Epping Forest. Now, you probably know that this is a cross between a Pug and a Jack Russell, just as a Cockerpoo is a 45

Cocker Spaniel-Poodle cross. Labradoodle is easy. But what about a Speagle or an Almation? They're out there, I promise. Recent years have also produced the novelty of the professional dog-walker, a very different figure from the enthusiastic amateur such as myself. Like the personal 50

trainer, the professional dog-walker has become a familiar figure in parks and woodland. Sometimes she or he even has a special flak-jacket or gilet with the job-title in shamelessly large white letters. As someone who exercises the dogs of his friends and asks no reward beyond a 55

decent walk, I catch myself being somewhat suspicious of these pros, especially if they have a large pack with them. Different breeds, ages, and even sizes, of dog require different sorts of exercise. And the lowest common denominator level necessary to a large mixed group satisfies no one. 60

Nor does the situation bring out the best in those being exercised. Thus, for example, a normally reticent and law-abiding Poodle may find the peer pressure from her new, wilder-spirited and more gregarious companions impossible to resist and show herself capable of things that would appal her owners. 65

Crowds are not always good for us. Furthermore, large groups of dogs under no very definite control can intimidate young children and instil in them a fear which may last a lifetime, thus robbing them of a potentially enriching source of companionship. 70

If you're sceptical of this last idea, you need only recall how enriched the human species has been through its pact with the dog. And a sort of pact it truly was. Some anthropologists studying human development claim that humans domesticated dogs, or vice-versa, over thirty thousand years ago and point out the clear 75

advantages for any group of hunter-gatherers who had dogs on their team. Dogs will warn of danger, help to fight off enemies and predators, can be taught to hunt and sniff out food, and provide warmth on cold nights on the savanna. Their behaviour, being more predictable than that of humans, can be a source of 80

confidence and consolation to those who hunt with them. When we feed them they approve of us, and approval, within reasonable limits, is something we tend to thrive on. All in all, this human-canine arrangement has been of great use to us as a species. 85

SAMPLE

Consequently, our proverbs and figures of speech are full of dogs, whose bite is less to be feared than their bark, who should, if lying asleep, be left that way, whose vigorous squabbles with cats are echoed by heavy rain, and every one of whom has his day, but can't, in his more advanced years, hope to master new tricks, and so on. 90

Even today the uncritical companionship of dogs is recommended as helping to draw out introverted children or simply cheer up the depressed. While we clearly don't always delight in the same things as dogs - rolling in the grass, muddy ponds, scaring squirrels and so on - we can enjoy their enjoyment. And any addition to our stock of innocent enjoyment is not to be lightly dismissed. 95

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13+ ENGLISH ENTRANCE and SCHOLARSHIP 1 hour

Question Paper & Answer Booklet

Candidate Number

Instructions to Candidates

Write your candidate number clearly on the front of this booklet.

This examination is divided into four questions, which relate to the reading passage.

The questions will assess both your reading and the quality of your writing. You are reminded of the need to answer the question carefully and use a good quality of written English.

You should answer all the questions in the spaces provided. If you need additional space, there is an extra page at the back of this booklet.

Total: /30

SAMPLE

Questions Read the passage in which the writer reflects on his experience of dog walking. 1. How does the writer capture the reader’s attention in the opening

paragraph? (2 marks)

2. Explain in your own words what is meant by the following: (10 marks)

a. These latter two are appropriate places for the more recalcitrant canines who have gained a reputation for boisterous behaviour (lines 7-8).

b. And the lowest common denominator level necessary to a large

mixed group satisfies no one (lines 58-60).

Marks 1. ___ 2.a ___ 2.b ___

SAMPLE

c. Their behaviour, being more predictable than that of humans, can be a source of confidence and consolation to those who hunt with them (lines 79-81).

3. Why does the writer feel that “names can be a tricky issue” (line 32)?

(3 marks)

2.c ___ 3.___

SAMPLE

4. How does the writer feel about: a. amateur dog walkers? b. professional dog walkers?

You should refer closely to the passage in your answer and use quotations to support your ideas. (5 marks) a.

b.

4. a___ 4. b___

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5. What, does the writer suggest, are the benefits of dogs to mankind?

You should use quotations from the text to support your answer. (5 marks)

5.. ___

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6. Pick out four points that you are think are particularly effective or well chosen. What do they contribute to the argument? You might like to think about the writer’s tone/choice of language/attitude to the reader. (10 marks)

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6. ___

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Additional space:

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