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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
7
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
9
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
10
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: ______________________
11
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: ______________________
12
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 : ___________________
13
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: ______________________
14
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
15
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: ______________________
16
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: ______________________
17
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: __________
18
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