2011 tonbridge 13+ paper

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13+ Entry Paper: Higher Level

6th November 2010

Name:……………………………………………

School:……………………………………………

Answer all 14 questions in the spaces provided.

Do all rough working in the spaces provided. If you run out of spacefor questions 12, 13 and 14 do ask for extra paper.

Total marks 100.

Time: 60 minutes.

You are NOT allowed to use a calculator in this exam.



2

b) A circle has radius . Estimate the area of the circle.

Answer: ………………………….. [3]

3. If

find the value of

i)

Answer: ………………………… [1]

ii)

Answer: ………………………… [2]

iii)

Answer: ………………………… [ 3]



3

4. A bumper pack of mixed biscuits contains biscuits. The biscuits are either plain,

chocolate or cream. of the biscuits in the pack are plain.

i) Write down the ratio of plain biscuits to non-plain biscuits in its simplest form.

Answer: plain : non-plain is ……… : ……………. [ 2]

Of those which are not plain, are chocolate and the rest are cream.

ii) How many biscuits are cream?

Answer: ………………………………. [2]

Peter gives away all the plain biscuits and eats half the chocolate ones.

iii) What fraction of the remaining biscuits are chocolate?

Answer: ………………………………. [3 ]



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5. Solve the following equations:

a)

Answer: ………………………… [ 1]

b)

Answer: ………………………… [2]

c)

Answer: ………………………… [3]

d)

Answer: ………………………… [3]



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6. a) Simplify the following expressions:

i)

Answer: ………………………… [2]

ii)

Answer: ………………………… [2]

b) Multiply out the brackets and simplify

Answer: ………………………… [ 3]

c) Factorise completely

Answer: ………………………… [2]



6

7. A slope which rises 1 metre for every 5 metres travelled horizontally is said to have agradient of 1 in 5.

This can also be written as a gradient of because

i) Write down the percentage equivalents of the following slopes:

a) 1 in 4

Answer: ………………………… % [1]

b) 3 in 8

Answer: ………………………… % [1]

c)

Answer: ………………………… % [3]

ii) For water to run safely off a roof, the gradient must be greater than 1 in 12.Giving a reason, state whether an 8% gradient is safe.

Answer: ……………………………………………………………………………...

…………………………………………………………………………………… [2]

Not to scale



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8. Here is a rectangle. The length is twice the width.

a) If the width is , write down an expression, in terms of x , for the perimeterof the rectangle.

Answer: ………………………… [2]

b) If the perimeter is , what is the area of the rectangle?

Answer: ………………………… [2]

ii) In another rectangle, the length is more than the width. The perimeter of this

rectangle is .

Set up an equation first and hence find the area of the rectangle.

Answer: ………………………… [3]

Not to scale



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9. It is Greg’s birthday. This is his birthday cake.

Greg eats of the cake and his friend Tim eats of the cake.

i) What fraction of the cake is left after Greg and Tim have eaten their portions.

Answer: ………………………………. [3]

Greg shares the remaining cake equally between his six sisters.

ii) What fraction of the original cake does each sister receive?

Answer: ………………………………. [2]



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10. The cross-section of a symmetrical garden shed is shown in the diagram below.

i) Calculate the area of the cross-section.

Answer: ………………………… [4]

ii) The shed is 2.5 metres long. Calculate the volume of the shed.

Answer: ………………………… [2]

Not to scale



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11. i) Complete the table of values for the function

[2]

ii) On the grid below, draw the graph of

[2]

iii) On the same grid, plot the graph of [2]

iv) Write down the co-ordinates of the points where the graphs intersect.

Answer: ( ……………, ……………) ( ……………, ……………) [3]

-3 -2 -1 0 1 2 3

-4

-2

2

4

6

8

x

y



11

12. Look at the number puzzle set out below. We wish to find the value of X and the value of Y .

row total

X Y Y Y

X X Y Y

X X X Y

column total

The boxes contain the sum of X ’s and Y ’s in that row or column.

i) Write an equation for the second row of the puzzle and show that is simplifies to

[2]

ii) Write a similar equation for the third row of the puzzle.

Answer: ………………………………. [1]

26

23



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iii) Solve the two equations in i) and ii) to find the values of X and Y .

Answer: X

= ……………..………

Answer: Y = …….......…………… [3]

iv) Fill in the remaining boxes to complete the puzzle. [3]

v) Most positive integers can be written as a sum of whole numbers of X s and Y s.e.g. 3 X + 2Y , 6 X or 4Y .

Which integers between 20 and 30 cannot be written in this way?

Answer: ………………………………………… [3]



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13. In the diagram below, APR and BRQ are isosceles triangles and ARB is a straight line.

a) If and , find .

b) In general, show that is always the average (mean) of and .

[5]

xa b

BA

P

Q

R

Not to scale



14

14. A pair of tetrahedral (four sided) dice with the first one labelled with sides 1, 2, 2 and 3and the second with sides 1, 3, 3 and 5 are thrown onto a desk. The numbers on the sidesface down on the table of the two dice are added together to get a total score.

(a)

Complete the following table showing the probability of each total score.

Total Score 2 3 4 5 6 7 8

Probability

(b) What is the probability that both dice land showing the same number?[5]

2011 tonbridge 13+ paper

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