St Pauls School FIRST YEAR ENTRANCE EXAMINATION 2016 EXAMPLE MATHEMATICS Online Quiz

Welcome to your ST PAUL'S GIRLS SCHOOL SAMPLE MATHS PAPER - 3

PLEASE READ THESE INSTRUCTIONS VERY CAREFULLY
Use pencil. No calculators or protractors or rulers are allowed.
There are 20 questions. Answer all of them if you can.
Show all your working in the spaces provided and write your answers on the
lines provided
Please do not rub out your working.
If you cannot do a question, leave it and go on to the next one.
Try again later.
Do not ask a teacher to explain a question to you.
If you finish before the end of 25 minutes go back and check your answers
and try to fill in any answers you have left out.
If you do not finish, or if you cannot understand all the questions, do not
worry. People work at different speeds.

SECTION A

You have 25 minutes to complete this section. There are 20 questions.

1. Calculate 15.05 – 14.84

0.21 1.81 0.11 0.31 0.81

2. Calculate 31.6 × 7

221.2 214.2 222.2 224.2 217.2

3. Calculate 60% of 765

459 359 559 449 259

4. 85 people go to the school concert. They pay £1.30 each. How much money is collected?

£110.5 £115.5 £120.5 £100.5 £130.5

5. Calculate 2.4 × (3.7 + 1.3) ÷ 2

6 6.2 5.6 6.8 None of the Above

6. Fill in the missing numbers:

½ of 20 = ¼ of ____

40 30 50 60 20

¾ of 100 = ½ of ___

150 120 110 130 140

¹/3 of 60 = ²/3 of = ____

30 20 40 60 10

7. Write in the missing number to make this correct:

0.627 = 0.6 + 0.02 + ____

0.007 0.002 0.009 0.07 0.7

8. Circle the number closest in value to 0.1

0.01 0.08 0.13 0.2 0.9

9. Here are some digit cards:

Write all the three-digit numbers, greater than 500, that can be made using these cards.

624 642 646 626 All of the Above

10. Write the three prime numbers which multiply to make 231:

Answer: _____ × _____ × _____ = 231

3, 7, 11 4, 8, 12 2, 7, 12 4, 7, 13 3, 8, 12

11. Halid makes a sequence of 5 numbers. The first number is 2. The last number is 18. His rule is to add the same amount each time.

Write in the missing numbers:

Answer: 2 ____ _____ _____ 18

6, 10, 14 4, 8, 12 8, 10, 16 6, 12, 16 None of the Above

12. In this sequence each number is double the previous number.
Write in the missing numbers.

Answer: _____ _____ 3 6 12 24 48 _____

\[\frac{3}{4}\] , \[\frac{3}{2}\] , 96 \[\frac{1}{4}\] , \[\frac{1}{2}\] , 76 \[\frac{3}{2}\] , \[\frac{3}{4}\] , 64 \[\frac{1}{3}\], \[\frac{2}{3}\] , 72 \[\frac{1}{4}\] , \[\frac{1}{3}\], 81

13. Alysha and Julia have some biscuits. Altogether they have 14 biscuits. Alysha has 2 more biscuits than Julia.
How many biscuits do Alysha and Julia each have?

Answer: Alysha has ____ Julia has ____

Alysha has 8, Julia has 6 Alysha has 6, Julia has 4 Alysha has 4, Julia has 2 Alysha has 6, Julia has 8 Alysha has 7, Julia has 5

14. Jemma thinks of a number. She says, “Add 3 to my number and then multiply the result by 5. The answer is 35.” What is Jemma's number?

4 5 3 2 6

15. A box contains 220 matches and weighs 45 grams. The empty box weighs 12 grams. Calculate the weight of one match.

\[\frac{3}{20}\] grams \[\frac{1}{20}\] grams \[\frac{7}{20}\] grams \[\frac{9}{20}\] grams \[\frac{12}{20}\] grams

16. Sapna makes a fruit salad using bananas, oranges and apples. For every one banana, she uses 2 oranges and 3 apples. Sapna uses 24 fruits. How many oranges does she use?

8 6 4 2 10

17. In a country dance there are 3 boys and 2 girls in every line. 42 boys take part in the dance. How many girls take part?

28 girls 20 girls 38 girls 18 girls None of the Above

18. The diagram shows a shaded triangle inside a larger triangle:

The area of the shaded triangle is 52 cm². The area of the shaded triangle is 4/9 of the area of the larger triangle. Calculate the area of the larger triangle.

117cm² 107cm² 127cm² 120cm² 115cm²

19. 17 multiplied by itself gives a 3-digit answer:

Find the smallest 2-digit number that can be multiplied by itself to give a 4-digit
answer, and put all the numbers in the boxes below:

_____ _____ × _____ _____ = ____ ____ ____ _____

32 x 32 = 1024 30 x 30 = 900 31 x 31 = 964 34 x 34 = 1156 None of the Above

20. Write in the missing digits (one digit in each space):

Answer: 323 × _____ 7 = 1518 _____

4 & 1 2 & 5 1 & 4 3 & 6 4 & 3

END OF SECTION A. NOW GO BACK AND CHECK YOUR ANSWERS

SECTION B
You have 25 minutes to complete this section. There are 10 questions.

1. In the diagram below, we want to complete the pattern of 3 shaded and 4 unshaded hexagons. Which hexagon do I shade for my final pattern to have exactly 2 lines of symmetry?

C A B D E

2. In the grid below, each letter represents a number. The numbers on the right hand side represent the total of each row, and the numbers at the bottom show the totals of each column. Which numbers should replace each of the letters?

A = ______ B = ______

C = ______ D = ______

X = _____ Y = _____

A=8, B=6, C=9, D=7, x=30, y=29 A=6, B=4, C=7, D=5, x=25, y=28 A=4, B=5, C=5, D=8, x=22, y=30 A=7, B=7, C=8, D=6, x=28, y=25 None of the Above

3. I am thinking of a number that when I multiply it by two and divide the result by four, then multiply the result of that by itself, gives me a number that when I subtract four and divide by ten, gives me six. What is the number that I originally thought of?

16 24 12 14 18

4. My watch is set to show the correct time at 12 noon on Wednesday. It gains 4 minutes every 3 hours.

(a) What time does the watch show when the correct time is 12 noon on Friday, assuming the watch has not been reset again?

13:04 13:00 11:04 11:00 12:54

(b) The watch is reset again to show the correct time at 12 noon on Friday. What is the correct time when the watch is showing 19:40 on Friday night?

19:30 18:50 19:40 18:30 None of the Above

5. Three apples and a banana cost 32p. Six apples and a banana cost 53p. How much does one banana cost?

11p 7p 10p 15p 9p

6. The combined age of Alan and Ben is forty three. The combined age of Alan and Carl is fifty five and the combined age of Ben and
Carl is sixty-six.

(a) What is the combined age of Alan, Ben and Carl?

82 72 92 62 86

(b) How old is Alan ?

16 6 20 18 15

7. A palindromic number is a number that can be read the same forwards and backwards, e.g. 33 and 797. How many of such numbers are there between 10 and 1000?

99 91 89 98 100

8. After a card game, four gamblers had £234 between them. Harry had £20 more than Dana, Charlotte had £53 more than Dana and Sid had £71 more than Dana. How much did each of them have ?

£22.50, £42.50, £75.50, £93.50 £25.50, £45.50, £70.50, £90.50 £21.50, £40.50, £72.50, £92.50 £20.50, £41.50, £74.50, £91.50 None of the Above

9. There are 6 fangos in a rango and 15 rangos in a bango.
(a) Alex has 9 rangos and 4 fangos. Barbara has 7 rangos and 3 fangos.
How many fangos do they both have in total?

103fangos 100fangos 108fangos 104fangos 102fangos

(b) What fraction of a bango do 12 fangos represent?

\[\frac{2}{5}\] \[\frac{1}{5}\] \[\frac{3}{5}\] \[\frac{4}{5}\] \[\frac{5}{7}\]

(c) How many whole bangos are there in 274 fangos? How many fangos are left over?

3 bangos, 4 fangos 5 bangos, 6 fangos 2 bangos, 5 fangos 4 bangos, 3 fangos 3 bangos, 3 fangos

10. Four of the five jigsaw pieces shown below fit together to make a square. Which one of these diagrams does not fit?

A B C D E

END OF SECTION B. NOW GO BACK AND CHECK YOUR ANSWERS

SECTION C
You have 25 minutes to complete this section. There are 5 questions.

1. The numbers 1 to 500 are arranged in order in a table:

Only rows 1, 2, 3 and 4 are shown, but there are many more rows.

(a) What do you notice about the numbers in column 7?

Multiples of 7 Multiples of 5 Multiples of 8 Multiples of 6 Multiples of 9

(b) What is the last number in row 8?

56 42 64 49 72

(c) What is the last number in row 100?

No Row Row 1 Row 2 Row 3 Row 4

(d) 77 is the last number in which row?

Row 11 Row 8 Row 12 Row 10 Row 13

(e) What is the number in row 12 and column 3?

80 74 77 70 None of the Above

(f) What row and column will contain the number 400?

row 58 & column 1 row 48 & column 2 row 68 & column 1 row 38 & column 3 None of the Above

2. You are told that
N5 means ‘add up the first 5 counting numbers’, so N5 = 1 + 2 + 3 + 4 + 5 = 15
O3 means ‘add up the first 3 odd numbers’, so O3 = 1 + 3 + 5 = 9
E4 means ‘add up the first 4 even numbers’, so E4 = 2 + 4 + 6 + 8 = 20
and so on.

(a) Work out the following

56 46 49 66 72

36 46 25 38 40

45 48 47 49 56

(b) Find the value of

401 400 410 402 None of the Above

(c) There is a different way of finding, for example, Ο7:

Ο1 = 1 = 1²
Ο2 = 1 + 3 = 4 = 2²
Ο3 = 1 + 3 + 5 = 9 = 3³
Ο7 = 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 = 7²

Find the value of

Ο13 =

169 144 121 100 181

(d) Notice that N6 can be split into 2 parts to make the calculation easier:

Complete the following line by filling in the boxes.

Ν10 = Ο ____ + E _____

5, 5 4, 4 6, 6 4, 5 5, 6

(e)

10100 10000 11000 101010 101001

40200 42000 40401 41200 42100

3. The letters on the 7 cards below have a number 1, 2, 3, 4, 5, 6 or 7 on the back,
but not in that order.

add up to 8,

add up to 9,

add up to 11.

(a) What does add up to?

11 10 12 14 16

(b) What does add up to ?

17 15 11 13 16

4. You are told that the opposite sides of a cube add up to 13.
Find the sum of the faces that border with the marked corner:

For example, the sum of the faces = 3 + 5 + 9 = 17.

(a) Find the sum of the faces that border with the marked corner for the following:

19 15 14 11 17

15 19 14 11 17

(b) The same cube is rolled so a 10 is on top.
Fill in the missing sides so that the sum of the faces that border with the marked
corner is 27.

8 & 9 4 & 6 7 & 8 5 & 6 None of the Above

(c) The same cube is rolled so an 8 is on top.
Write down all possibilities for the sum of the missing faces that border with the
marked corner.
You MUST show your working

20 22 27 15 All of the Above

END OF SECTION C. NOW GO BACK AND CHECK YOUR ANSWERS

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