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

2.  Calculate 31.6 × 7

3. Calculate 60% of 765

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

5. Calculate 2.4 × (3.7 + 1.3) ÷  2

6. Fill in the missing numbers:

½ of 20  =  ¼  of 

¾  of  100  =  ½  of   

¹/3  of  60   =  ²/3  of  =   

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

       0.627 = 0.6 + 0.02 + 

8. Circle the number closest in value to 0.1

9. Here are some digit cards:


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

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

Answer:      ×      ×      =  231

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

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

Answer:           3    6    12    24    48   

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   

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?

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

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?

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?

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.

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:

       ×        

=       

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

Answer:   323 ×  7  =  1518 

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?

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 = 

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?

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?

(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?

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

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?

(b) How old is Alan ?

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?

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 ?

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?

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

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

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

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?

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

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

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

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

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

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

(b) Find the value of 

(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 =

(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 

(e) 

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?

(b) What does add up to ?

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:

(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.

(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

5. On the island of Mathia the people use patterns instead of numbers like ours.
Here are some facts about Mathian numbers:



Now answer these questions.
(Give your answer in Mathian numbers using just ONE symbol)
(a)

(b) 

(c)

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