THE G C SCHOOL OF CAREERS

ENTRANCE EXAMINATION

SCHOOL YEAR 2017-2018

MATHEMATICS

(This examination paper consists of 18 pages, including this page).

Number _____________

Surname _____________________________

Name _____________________________

Father’s name ____________________________

2

THE G C SCHOOL OF CAREERS

ENTRANCE EXAMINATION

SCHOOL YEAR 2017-2018

GOOD LUCK

Time: 1 hour and 30 minutes

MATHEMATICS

This paper consists of 25 questions.

Answer ALL the questions in the space provided.

Show all your workings.

The use of a calculator is not allowed.

Write your answers clearly.

3

1. Calculate the following:

a)

321

54321 (1 mark)

Answer: ______________________

b)

2

2

321

54321

(2 marks)

Answer: ______________________

c) 2

12

2

1222222222

(2 marks)

Answer: ______________________

d)

3

116.0

3

16

(3 marks)

Answer: ______________________

4

2. a) What number is halfway between – 2 and 6?

(1 mark)

Answer: ______________________

b) Marina said: «I can multiply the number 6 with another number and get a result which is less than 6».

Costas said: «No, you cannot! If you multiply a number with 6 then the result will be either a 6 or a number greater than 6».

Who is right? Justify your answer.

(2 marks)

Answer: ______________________

3. If a number is divided by 5, find the possible remainders of this division.

(3 marks)

Answer: ______________________

5

4.

Use 3 of the above cards to make the following operation true.

(3 marks)

+ + =

5. Find the largest number which is smaller than 1000, ends in 2, its sum of

digits is 9 and can be divided (exactly) by 4.

(3 marks)

Answer: ______________________

5

1

4

1

10

1

20

1

40

1

2

1

6

6. Find the missing number χ.

(2 marks)

Answer: ______________________

7. The grid below is made up of small squares. What percent of the grid is

shaded?

(3 marks)

Answer: ______________________

χ

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8. In the figure below the triangle DE is equilateral.

a) Find the angles

,X and

.

(4 marks)

Answer:

X = ______

= ________

=________

b) Write the type of triangle ΕΒΖ.

(1 mark)

Answer: ______________________

8

9. The table below gives information on boat rentals.

Four friends rented a boat for five hours and split the cost.

a) Find how much each paid.

(2 marks)

Answer: ______________________

Maria’s family rented a boat and paid €15.

b) Find how many hours they rented the boat for.

(2 marks)

Answer: ______________________

Boat Rentals

€4.50 for the boat

and

€3.50 per hour

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10. In the figure below you can see 3 identical rectangles.

a) If the area of the whole shape is 90 ,2cm find the value of x.

(Diagram not accurately drawn)

(2 marks)

Answer: ______________________

b) Find the perimeter of the whole shape.

(2 marks)

Answer: ______________________

12 cm

x cm

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11. In a library 25% of the books are Scientific, 40% of the rest are History books and the rest are Mathematics books. If I choose a book at random, find the probability that:

(5 marks)

a) I will get a History book.

Answer: ______________________

b) I will not get a Mathematics book.

Answer: ______________________

b) If you know that the number of Mathematics books is 135, find how many books there are altogether in the library.

Answer: ______________________

12. The lowest common multiple of two numbers is 105 and the highest common factor is 5. Find the sum of the two numbers if you know that the sum is less than 100.

(3 marks)

Answer: ______________________

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13. A cake can be sold as a whole or can be divided into 16 equal pieces.

Someone bought half of the cake and paid €6 more than someone else who

bought three pieces. Find how much will I pay for two such cakes.

(4 marks)

Answer: ______________________

14. A Maths test was made up of 50 multiple choice questions. For each correct answer Nick earned 2 marks and for every wrong answer he lost 1 mark. If he didn’t answer a question he would neither earn nor lose a mark. Nick answered all the questions and got a total of 76 marks. Find how many questions he answered correctly.

(4 marks)

Answer: ______________________

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15. Christina’s watch stops for 15 minutes every time it shows an integer hour.

During the time it takes this watch to move from 12 noon until 12 midnight,

find the number of real hours that elapse.

(4 marks)

Answer: ______________________

16. Helen: “If you give me one pencil, we will have the same number of pencils.”

Maria: “If you give me one pencil, I will have twice as many pencils as you

have.”

Find: (4 marks)

a) how many pencils Helen and Maria have together.

Answer: ______________________

b) how many pencils each girl has.

Answer: Helen: ___________________, Maria : ___________________

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17. A particular spiral notebook with 3 subjects is sold at a price which is twice

the price of a similar spiral notebook with 1 subject. I buy 3, three subject

spiral notebooks and 2 one subject spiral notebooks for €6. Find the price of a

three subject notebook.

(4 marks)

Answer: ______________________

18. A bookseller is organising his books on shelves. He places 125 books on 3 shelves. In the bookstore there are 8 bookshelves each with 6 shelves and 15 bookshelves each with 11 shelves. The bookseller filled the bookshelves with books. How many books are there in the store?

(4 marks)

Answer: ______________________

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19. The following diagram shows a square. If C is the centre of the square, find

the coordinates of points A and B. (Diagram not accurately drawn)

(3 marks)

Answer: Α = __________, Β = __________

20. The mean of 30 numbers is 40. We add two more numbers to this series such that one of the two is three times as big as the other. The mean of all the numbers now is 41. Find the two numbers that were added to the original series.

(4 marks)

Answer: ______________________

Β

x

y

0

(-12,20)

. C(13,-5)

A

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21. In a group of traditional dancers there are 39 boys and 23 girls. 6 new boys

and 8 new girls join the group every week. A few weeks later the number of

boys will be the same as the girls’ in the group. Find:

(4 marks)

a) in how many weeks the boys will be equal to the girls.

Answer: ______________________

b) when they are equal, how many boys will be in the group.

Answer: Boys ______________________

22. If Irene’s birthday this year was on November 17th on a Saturday, find the day of her husband’s birthday which was 86 days earlier.

(3 marks)

Answer: ______________________

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23. In a bag there are red and blue balls in the ratio of 4:7. I add 10 more red balls to the bag. Now there are red and blue balls in the ratio 6:7. Find how many blue balls are in the bag.

(4 marks)

Answer: ______________________

24. Peter, John and Nick are baking cakes. When Peter and John work together

they can bake 45 cakes in an hour, whilst Peter and Nick can bake 50 cakes

per hour and John with Nick can bake 55 cakes per hour. If Peter works by

himself, how many cakes will he bake in an hour?

(3 marks)

Answer: ______________________

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25. The following table shows (displays) Mr. Gregory’s bank account transactions for the past five days.

Day Monday Tuesday Wednesday Thursday Friday

Transactions (per day) 150€ 400€ 200€ –300€ 550€

a) Construct a bar chart to represent the information given above.

(3 marks)

Find: b) the maximum and the minimum value of Mr. Gregory’s transactions.

(2 marks)

Answer: maximum: __________, minimum: __________

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c) the average value of his transactions for this week.

(2 marks)

Answer: ______________________

d) on which day, the transactions were equal to 20% of his total deposits.

(2 marks)

Answer: ______________________

END