MERCHANT TAYLORS’ SCHOOL 11 PLUS MATHS SPECIMAN PAPER - 2

Welcome to your MERCHANT TAYLORS’ SCHOOL 11 PLUS MATHS SPECIMAN PAPER - 2

Time Allowed: 60 minutes
Instructions:
Answer as many questions as possible. Some of them
are easy at the start and become more difficult. You
should show all your working on this question paper.

1 (a) Write in digits the number seventy three thousand and forty six.

73046 73406 73604 73640 73456

(b) Write the answer to the sum of two hundred and six plus two thousand three
hundred and twenty in words.

Two thousand Five Hundered andTwenty Six two hundred twenty six Two thousand one Hundered andTwenty Six two thousand two hundred and fifty six None of the Above

2.

From the numbers in the box above write down:

(a) A multiple of 7:

28 24 15 36 14

(b) A square number:

36 24 15 28 18

(c) The product of two of the other numbers in the box:

45 53 2 5 45

3. (a) Calculate the angles marked x and y in the diagram below:

Answer: x = %BLANK% , y = %BLANK%

x = 47, y = 123 x = 47, y = 143 x = 57, y = 153 x = 60 , y = 237 x = 45, y = 120

(b) Calculate the angles marked p, q, r, s and t in the diagram below:

p = \[132^{o}\], q = \[66^{o}\], r = \[66^{o}\], s = \[114^{o}\], t = \[66^{o}\], u = \[114^{o}\] p = \[142^{o}\], q = \[60^{o}\], r = \[60^{o}\], s = \[114^{o}\], t = \[60^{o}\], u = \[100^{o}\] p = \[120^{o}\], q = \[76^{o}\], r = \[56^{o}\], s = \[90^{o}\], t = \[96^{o}\], u = \[114^{o}\] p = \[129^{o}\], q = \[60^{o}\], r = \[60^{o}\], s = \[124^{o}\], t = \[60^{o}\], u = \[124^{o}\] None of the Above

4. (a) Sean scored 27 out of 45 in a test. Write this as a percentage.

60% 50% 40% 30% 20%

(b) In a class of 30 pupils, 21 are girls. What percentage of the class is boys?

30% 50% 60% 40% 20%

(c) Write 0.8 as a fraction in its simplest form.

\[\frac{4}{5}\] \[\frac{3}{8}\] \[\frac{8}{5}\] \[\frac{2}{5}\] \[\frac{9}{5}\]

(d) Write 85% as a fraction in its lowest terms.

\[\frac{17}{20}\] \[\frac{20}{17}\] \[\frac{3}{5}\] \[\frac{3}{14}\] \[\frac{4}{15}\]

(e) Rearrange the following in order of size, smallest to largest.

\[\frac{9}{25}\] .0.371 , 38% , \[\frac{2}{5}\] \[\frac{2}{5}\] . 38% , 0.371 \[\frac{2}{5}\] 0.371 , \[\frac{9}{25}\] . 38% , \[\frac{2}{15}\] 38% ,\[\frac{9}{25}\] .0.371 , \[\frac{2}{5}\] None of the above

5 Sarah sat by the river Thames and recorded the number of cyclists that passed by
every minute. She plotted a bar chart of her results.

(a) What was the largest number of cyclists to pass in one minute?

5 4 3 6 1

(b) What was the most frequent number of cyclists per minute?

1 3 2 6 5

(c) For how many minutes, in total, was Sarah recording cyclists?

20 15 12 10 25

6. A gardener measures the night time temperatures over two evenings and records the
results in the table shown below:

(a) At what time and on which day was the lowest temperature recorded?

Tuesday 3:00 a.m Tuesday 4:00 a.m Tuesday 5:00 a.m Tuesday 3:00 a.m Tuesday 6:00 a.m

(b) What was the difference between the lowest and highest temperature on
Tuesday?

7 4 3 6 5

(c) He realises his thermometer is recording incorrectly and that each temperature
should be 5℃ lower than was recorded. What is the correct temperature at
1am on Monday?

-4 -3 2 4 3

d) On Wednesday the forecast is for all temperatures to drop by 3º C from what
they were on Tuesday. Bearing in mind his thermometer is broken, what will
the actual temperature be on Wednesday at 2am?

-9 8 9 -7 -6

7. Solve the following equations:

(a) 3x = 36

Answer: x =

12 8 18 10 14

(b) c + 7 = −15

Answer: c =

-22 22 23 -24 28

(c) 4p − 2 = 14

Answer: p =

4 12 7 8 6

8. On the grid below draw the reflection of the shape shown in the mirror line AB:

9. Write the next two terms in each of the following sequences:

(a) 5, 11, 17, 23

29,35 28, 34 27, 33 30, 36 23,25

(b) 10, 7, 4, 1

-2 , -5 -1, -3 -1, -4 0, -3 0, -5

(c) 2, 8, 32, 128

512, 2048 256, 512 384, 1152 640, 3200 680, 4200

10. The perimeter of a rectangle is 22cm. One of the sides has length 8cm. Calculate the
lengths of the other three sides.

3, 8, 3 8, 18, 8 7, 12, 7 6, 11, 6 5 , 9 , 5

11. Estimate the following by first rounding each number to the nearest whole number:

(a) 9.47 × 34.5

315 327 318 415 427

(b) 3.752 − 11.63 × 2.87

-20 7 20 6 24

12 (a) Explain why 91 is not a prime number.

not a prime number It is a prime number Odd Number Neither prime nor Odd number Even number

(b) What is the 7th prime number?

17 21 13 29 23

13. The contents of part of a wardrobe are shown in the pie chart below:

What fraction, in its simplest form, of Footwear are boots?

\[\frac{1}{8}\] \[\frac{2}{8}\] \[\frac{3}{8}\] \[\frac{5}{18}\] \[\frac{5}{8}\]

14. (a) Find the highest common factor (HCF) of 66 and 30.

6 5 3 2 1

(b) Find the lowest common multiple (LCM) of 12 and 8.

24 12 8 6 34

15. Fazal has £2.60 and Gareth has £5.30. Gareth gives Fazal some 5p coins. Each boy
now has the same amount of money. How many 5p coins did Gareth give Fazal?

27 50 30 29 79

16. Circle the most appropriate unit of measure for the following:

(i) The length of an airplane

meters kilometres centimetres millimeters milliliters

(ii) The weight of a cat

Pounds tons Ounces stones kilometers

(iii) The capacity of a bath

gallons pints fluid ounces millilitres millimeters

17. A box of celebrations contains one Twix, one Snickers, one Milky Way, and ten
Bounty chocolates. Jane chooses a chocolate at random. Put a ring around the correct
answer in the list to show the probability that the chocolate will be:

(a) A Bounty

likely unlikely even chance impossible certain

(b) A Twix

unlikely impossible even chance likely certain

(c) A Galaxy

impossible unlikely even chance likely certain

18.(a) Which is the greater?

3 × 2³ or 2 × 3²

3 x \[2^{3}\] 2 x \[3^{2}\] 3 x \[2^{2}\] both are same 2 x \[2^{3}\]

(b) By how much?

6 5 8 3 2

(c) Write down two cube numbers which are also square numbers.

64, 729 8, 4 9, 27 16, 25 161, 2564

19.

Calculate the value of x.

8 16 18 24 36

20. There are x horses, y cows and one three legged dog in a field.

(a) Write down an expression in algebra for the total number of legs in the field.

4x + 4y = 3 4x + 4y - 3z 4x + 4y +3 4x - 4y - 3 4x - 4y = - 3

Half of the cows and one quarter of the horses leave the field.

(b) Write down an expression in algebra for the number of heads that remain in the
field.

\[\frac{3x}{4}\] + \[\frac{y}{2}\] + 1 \[\frac{x}{4}\] + \[\frac{3y}{2}\] + 1 \[\frac{3x}{2}\] + \[\frac{y}{4}\] + 1 \[\frac{x}{4}\] + \[\frac{3y}{2}\] - 1 \[\frac{3x}{8}\] + \[\frac{y}{5}\] + 1

21. An alloy contains iron and tungsten in the ratio 5 parts to 1 part.

(a) If the mass of the alloy is 72kg, how much iron and tungsten does it contain?

Iron =60kg, & Tungsten = 12kg Iron =50kg, & Tungsten = 10kg Iron =55 kg, & Tungsten = 14kg Iron =64kg, & Tungsten = 8kg Iron =48kg, & Tungsten = 18kg

(b) If there is 15kg of iron in a quantity of the alloy, how much tungsten is there?

3 5 2 1 4

22. A large cube is made by gluing together smaller white and grey cubes of volume 1cm³
as shown. If five grey cubes are removed from each face of the larger cube, what is
the total volume remaining?
Diagram not drawn to scale

95\[cm^{3}\] 89\[cm^{3}\] 100\[cm^{3}\] 79\[cm^{3}\] 69\[cm^{3}\]

23. If a basketball weighs 300g plus half its own weight, how much does it weigh?

600 g 300 g 400 g 150 g 500 g

24. 25 students have taken an exam and the mean number of marks is recorded as 83.
The examiner subsequently awards 5 additional marks to 9 of the students and takes
away 2 marks from 10 other students.
What will the new mean mark be?

84 80 75 94 70

25. The centre of a square is at the point (1 , 2) and one of the vertices (corners) of the
square is at the point (4 , 7).
(a) Plot the centre of the square and one of the vertices on the grid below.

(6, -1), (-2, -3), (-4, 5) (6, 1), (2, -3), (4, -5) (4, 7), (6, 1), (4, 5) (4, -1), (-2, 4), (-6, 5) (4, 2), (-2, 4), (-6, 8)

(b) Plot the other three vertices of the square on the grid above, and write down
the co-ordinates of the three points you have just plotted.

(6, -1), (-2, -3), (-4, 5) (6, 1), (2, -3), (4, -5) (4, 7), (6, 1), (4, 5) (4, -1), (-2, 4), (-6, 5) (4, -2), (-2, 5), (-6, 8)

26. The number of leaf cutter ants doubles every day for the first week.

(a) If there were 10 at the end of the first day how many are there at the end of the
second day?

20 18 16 24 30

(b) How many were there at the end of the week?

640 720 940 856 664

27. Find in terms of x the perimeter of the following triangle:

4x + 3 4x + 6 4x + 8 4x - 3 4x - 5

28. (a) An egg box holds 6 eggs. How many boxes are needed for 100 eggs?

17 28 18 10 25

(b) A toy train travels 6 metres in two seconds. How far will it travel in one
minute?

180 240 360 456 756

29.One of the angles of an isosceles triangle is 96° . Find the sizes of the other two
angles.

\[42^{o}\] , \[42^{o}\] \[42^{o}\] , \[56^{o}\] \[46^{o}\] , \[60^{o}\] \[30^{o}\] , \[48^{o}\] \[50^{o}\] ,\[42^{o}\]

30. Mrs Jones is 24 years older than her daughter. The sum of their ages is 70 years. How
old is Mrs Jones?

47 52 43 56 65

31. A metal rod is metres long. How many short rods ³/10 metres long can be cut from the longer rod?
Show full working.

36 48 56 46 32

32. Two different clocks show the time 3 o’clock. The first gains 5 minutes per hour and
the second gains 20 minutes per hour. How long will it be in hours before both clocks
look as though they show the same time?

48 36 40 28 44

33. A “double–decker” sandwich has three slices of bread and two layers of filling. (e.g.
bread/filling/bread/filling/bread). Each slice of bread has to be buttered on each side
that is in contact with the filling. I make as many of these sandwiches as possible from
a sliced loaf which has 22 usable slices, excluding crusts which are not used. How
many sides of bread do I have to butter?

28 18 16 24 14

MERCHANT TAYLORS’ SCHOOL 11 PLUS MATHS SPECIMAN PAPER – 2

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