Yr7 2010 Sample Paper Maths

YEAR 7 (11+) ENTRANCE EXAMINATION
SAMPLE PAPER
MATHEMATICS
Your Name: ..
Your School: .
Time allowed: 1 hour

Equipment needed: Pen, pencil, eraser and ruler.
Calculators are not permitted.
Information for candidates:
1.
2.
3.
4.
Write your name and school on this sheet.

Write all of your answers on the question paper in the space provided and
show all your working.
Try to answer all the questions, but dont worry if you cannot complete all
of them. If you are stuck, just go on to the next question and, if you have
time, come back to the one you left.
There are 75 marks available for this paper in total. Marks for each
question are shown in square brackets [ ] after the question.
BLANK PAGE
1. Work out 56 69 + 311
Answer: . . . . . . . . . . . . . . . . [3]
2. Work out
813 72
Answer: . . . . . . . . . . . . . . . . [3]
3. Work out
4992 16
Answer: . . . . . . . . . . . . . . . . [3]
4. Subtract eight hundred and thirty one from one thousand and fifty:
Answer: . . . . . . . . . . . . . . . . [3]
5. Write the correct operations (+ or or or ) in these statements.
a .............. a = 0
a .............. a = 1
a .............. a = 2a
a .............. a = a2
[2]
6. Solve the following equations:

(a)
3x 5 = 31
Answer: x= . . . . . . . . . . . . . . . . [2]
(b)
5x 2 = 2x 8
Answer: x = . . . . . . . . . . . . . . . [2]
(c)
x
7 = 12
4
Answer: x = . . . . . . . . . . . . . . . . [3]
(d)
x7
= 12
4
Answer: x = . . . . . . . . . . . . . . . [3]
7.
(a)Write down the prime numbers between 10 and 20
Answer: . . . . . . . . . . . . . . . . [2]
(b) Write down the first three multiples of 15
Answer: . . . . . . . . . . . . . . . . [2]
(c) Write down the factors of 49
Answer: . . . . . . . . . . . . . . . . [2]
8. Write the following fractions as decimals:
(a)
3
5
(b)
3
1
8
Answer: . . . . . . . . . . . . . . . . [1]
Answer: . . . . . . . . . . . . . . . . [2]
9. A sunflower is one hundred and fifty centimetres tall.
How tall will it be if its height increases by ten per cent?
Answer: . . . . . . . . . . . . . cm [2]
10. In a box of pens, one half are black, one sixth are red and the rest are blue.
What fraction of the pens is blue?
Answer: . . . . . . . . . . . . . . . . [2]
11. Bella makes purple paint by mixing blue paint and red paint in the ratio of
4 : 3. How much blue paint is needed to make 21 litres of purple paint?
Answer: . . . . . . . . . . . .litres [3]
12. Look at this sequence of patterns made with hexagons.
pattern number 1
pattern number 2
pattern number 3
To nd the number of hexagons in pattern number n you can use these

rules:
Number of grey hexagons = n + 1
Number of white hexagons = 2n
Altogether, what is the total number of hexagons in pattern number 20?
Answer: . . . . . . . . . . . . . . . . [2]
13. Put these values in order of size with the smallest rst.
52
32
33
24
..............
smallest
..............
..............
..............
largest
[2]
14. Six cubes each have a surface area of 24 cm2

They are joined together to make a cuboid.
What could the surface area of this cuboid be?

There are two different answers. Write them both.
Answer: . . . . . . cm2 and . . . . . . . . cm2 [2]

15. The table below shows which sports pupils in Year 7 name as their favourite.
Football
48%
Rugby
12%
Hockey
24%
Table Tennis
Badminton
8%
(a) What percentage

(i)
Prefer football or rugby?

Answer: . . . . . . . . . . . . . . . . [1]
(ii)
Prefer table tennis?

Answer: . . . . . . . . . . . . . . . . [1]
(b) If there are 50 pupils in Year 7, how many prefer football?
Answer: . . . . . . . . . . . . . . . . [2]
16. Look at the triangle.

Not drawn
accurately
b
2a
Work out the value of a and b
Answer: a = . . . . . . . . . . . . . . .
b= ...............
[3]
17. (a)
I have a square piece of paper.

The diagram shows information about this square labelled A.
8 cm
8 cm
I fold square A in half to make rectangle B.
Then I fold rectangle B in half to make square C.

C
Complete the table below to show the area and perimeter of each shape.
Area
Perimeter
Square A
cm2
cm
Rectangle B
cm2
cm
Square C
cm2
cm
[6]
(b)
I start again with square A.
8 cm
8 cm
Then I fold it in half to make triangle D.
What is the area of triangle D?

Answer: . . . . . . . . . . . . cm2 [2]
(c)
One of the statements below is true for the perimeter of triangle D.

Tick the correct one.
The perimeter is less than 24 cm.
The perimeter is 24 cm.
The perimeter is greater than 24 cm.
Explain your answer.
Answer: . . . . . . . . . . . . . . . [2]
18.
Here are the rules for an algebra grid.

This value is the sum of the values
in the middle row.
5x + 2
5x
10x
This value is the product of the values

in the middle row.
Use these rules to complete the algebra grids below. Write your
expressions as simply as possible.
3x + 1
2x
x+1
4x
5x
6x 2
[6]
10
19. Sue and Owen are using square patterns of dots to find different expressions
for n.
Sue's work
(a) Sue wants to write an expression for 12.

Complete Sues expression for 12.
12 = 12 +. . . . . . . . . . . . . . . [2]
(b) Now sue wants to write an expression for n2
Complete Sues Expression for n2.
n = n +. . . . . . . . . . . . . . . [2]
Owens work:
(c) Write down Owens expression for n.
n = . . . . . . . . . . . . . . . . . . . [2]
END OF PAPER
11
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YEAR 7 (11+) ENTRANCE EXAMINATION

Time allowed: 1 hour

Write your name and school on this sheet.

1. Work out 56 69 + 311

6. Solve the following equations:

(a)Write down the prime numbers between 10 and 20

8. Write the following fractions as decimals:

Answer: . . . . . . . . . . . .litres [3]

12. Look at this sequence of patterns made with hexagons.

To nd the number of hexagons in pattern number n you can use these

14. Six cubes each have a surface area of 24 cm2

What could the surface area of this cuboid be?

Answer: . . . . . . cm2 and . . . . . . . . cm2 [2]

(a) What percentage

Prefer football or rugby?

Prefer table tennis?

(b) If there are 50 pupils in Year 7, how many prefer football?

16. Look at the triangle.

Work out the value of a and b

I have a square piece of paper.

I fold square A in half to make rectangle B.

Then I fold rectangle B in half to make square C.

I start again with square A.

Then I fold it in half to make triangle D.

What is the area of triangle D?

One of the statements below is true for the perimeter of triangle D.

Here are the rules for an algebra grid.

This value is the product of the values

(a) Sue wants to write an expression for 12.

(c) Write down Owens expression for n.

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