St Anselm's College Paper 3

GrammarBoys

22 questions

Original PDFWorked solutions in progress

Questions

1
The planet Jupiter has $69$ moons. The closest moon is called Io and is $421{,}800 \rtqMathsUnit{km}$ from Jupiter. Write this distance in words.
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2
Callisto is another moon of Jupiter and its maximum distance from Jupiter as it orbits is $1{,}882{,}700 \rtqMathsUnit{km}$ . Write this distance in words.
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3
A double-framed sign reads Museum, entrance fee, £1.20 per person.
$240$ people paid to go to the museum on Monday. How much money is that altogether?
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4
The museum took a total of $\rtqMathsSymbolPound 600$ in entrance fees one Friday. How many people paid to visit the museum that Friday?
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Look at the New York Subway train timetable below and then answer the questions on the next page.

Brooklyn Bridge	$12 \rtqMathsTimeSeparator 08$	$12 \rtqMathsTimeSeparator 18$	$12 \rtqMathsTimeSeparator 28$	$12 \rtqMathsTimeSeparator 38$	$12 \rtqMathsTimeSeparator 48$	$13 \rtqMathsTimeSeparator 00$	$13 \rtqMathsTimeSeparator 15$
Bleecker Street	$12 \rtqMathsTimeSeparator 12$	$12 \rtqMathsTimeSeparator 22$	$12 \rtqMathsTimeSeparator 32$	$12 \rtqMathsTimeSeparator 42$	$12 \rtqMathsTimeSeparator 52$	$13 \rtqMathsTimeSeparator 04$	$13 \rtqMathsTimeSeparator 19$
Astor Place	$12 \rtqMathsTimeSeparator 14$	$12 \rtqMathsTimeSeparator 24$	$12 \rtqMathsTimeSeparator 34$	$12 \rtqMathsTimeSeparator 44$	$12 \rtqMathsTimeSeparator 54$	$13 \rtqMathsTimeSeparator 06$	$13 \rtqMathsTimeSeparator 21$
Grand Central Terminal	$12 \rtqMathsTimeSeparator 21$	$12 \rtqMathsTimeSeparator 31$	$12 \rtqMathsTimeSeparator 41$	$12 \rtqMathsTimeSeparator 51$	$13 \rtqMathsTimeSeparator 01$	$13 \rtqMathsTimeSeparator 13$	$13 \rtqMathsTimeSeparator 28$
$68^\text{th}$ Street	$12 \rtqMathsTimeSeparator 25$	$12 \rtqMathsTimeSeparator 35$	$12 \rtqMathsTimeSeparator 45$	$12 \rtqMathsTimeSeparator 55$	$13 \rtqMathsTimeSeparator 05$	$13 \rtqMathsTimeSeparator 17$	$13 \rtqMathsTimeSeparator 32$
$125^\text{th}$ Street	$12 \rtqMathsTimeSeparator 35$	$12 \rtqMathsTimeSeparator 45$	$12 \rtqMathsTimeSeparator 55$	$13 \rtqMathsTimeSeparator 05$	$13 \rtqMathsTimeSeparator 15$	$13 \rtqMathsTimeSeparator 27$	$13 \rtqMathsTimeSeparator 42$
$3^\text{rd}$ Ave & $138^\text{th}$ Street	$12 \rtqMathsTimeSeparator 38$	$12 \rtqMathsTimeSeparator 48$	$12 \rtqMathsTimeSeparator 58$	$13 \rtqMathsTimeSeparator 08$	$13 \rtqMathsTimeSeparator 18$	$13 \rtqMathsTimeSeparator 30$	$13 \rtqMathsTimeSeparator 45$
Hunts Point Avenue	$12 \rtqMathsTimeSeparator 47$	$12 \rtqMathsTimeSeparator 57$	$13 \rtqMathsTimeSeparator 07$	$13 \rtqMathsTimeSeparator 17$	$13 \rtqMathsTimeSeparator 27$	$13 \rtqMathsTimeSeparator 39$	$13 \rtqMathsTimeSeparator 54$
Parkchester	$12 \rtqMathsTimeSeparator 53$	$13 \rtqMathsTimeSeparator 03$	$13 \rtqMathsTimeSeparator 13$	$13 \rtqMathsTimeSeparator 23$	$13 \rtqMathsTimeSeparator 33$	$13 \rtqMathsTimeSeparator 45$	$14 \rtqMathsTimeSeparator 00$
Pelham Bay Park	$13 \rtqMathsTimeSeparator 02$	$13 \rtqMathsTimeSeparator 12$	$13 \rtqMathsTimeSeparator 22$	$13 \rtqMathsTimeSeparator 32$	$13 \rtqMathsTimeSeparator 42$	$13 \rtqMathsTimeSeparator 54$	$14 \rtqMathsTimeSeparator 09$

5.a
I need to catch a train from Bleecker Street to ensure I arrive at Pelham Bay Park before $13 \rtqMathsTimeSeparator 30$ . What time does the latest train I could catch leave Bleecker Street?
5.b
How many minutes does the train's journey from Brooklyn Bridge to $125^\text{th}$ Street take?
5.c
Write $14 \rtqMathsTimeSeparator 00$ using am or pm time.

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6
I live $0.6 \rtqMathsUnit{miles}$ from Goodison Park football stadium. There are $1760 \rtqMathsUnit{yards}$ in a mile.
1. 6.a
  How many yards away from Goodison Park do I live?
2. 6.b
  I live $4{,}400 \rtqMathsUnit{yards}$ from Anfield football stadium. How many miles from Anfield football stadium do I live?
3. 6.c
  A kilometre is five eighths of a mile. How many kilometres away from Anfield do I live?
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7
My clock shows the following time. Both hours and minutes are multiples of $3$ , as shown.
A double rounded rectangular frame surrounds a seven-segment display reading 09:15. Dotted circles group 09 and 15 separately, and a curved arrow labelled multiple of 3 points to each group.
1. 7.a
  Write a different time when the hours and minutes are both multiples of $3$ .
2. 7.b
  Later, my clock shows:
  A double rounded rectangular bezel surrounds a seven-segment display reading 11:58, with two dots separating the hour and minute groups.
  How many minutes will it be before the next time the hours and minutes are both multiples of $6$ ?
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8
Solve the following:
1. 8.a
  I think of a number, multiply it by $17$ and then subtract $19$ . The result is $66$ . What was the number I first thought of?
2. 8.b
  What number must $k$ be to make this mathematical statement true?
  
  $10 \times k + 23 = 4 \times k + 35$
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9
Look at these angles:

angle P Two rays meet at a vertex to form an acute angle. angle Q Two rays meet at a vertex to form an obtuse angle. angle R Two rays meet at a vertex and the marked sector is reflex. angle S Two rays meet at a vertex to form a small acute angle. angle T Two rays meet at a vertex and the marked sector is reflex.

One of the angles measures $120 \degree$ .

Write down which angle it must be.
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10
Write the next two numbers for each of the following sequences.
1. 10.a
  $1 \rtqMathsListSeparator 7 \rtqMathsListSeparator 13 \rtqMathsListSeparator 20 \rtqMathsListSeparator 27 \rtqMathsListSeparator \rtqMathsSequenceEllipsis \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
2. 10.b
  $7 \rtqMathsListSeparator 14 \rtqMathsListSeparator 28 \rtqMathsListSeparator 56 \rtqMathsListSeparator 112 \rtqMathsListSeparator \rtqMathsSequenceEllipsis \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
3. 10.c
  $1 \rtqMathsListSeparator 1.75 \rtqMathsListSeparator 2.5 \rtqMathsListSeparator 3.25 \rtqMathsListSeparator 4 \rtqMathsListSeparator \rtqMathsSequenceEllipsis \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
4. 10.d
  $500 \rtqMathsListSeparator 100 \rtqMathsListSeparator 20 \rtqMathsListSeparator 4 \rtqMathsListSeparator 0.8 \rtqMathsListSeparator \rtqMathsSequenceEllipsis \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
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Here is the $65$ times table:

$1$	$\times$	$65$	$=$	$65$
$2$	$\times$	$65$	$=$	$130$
$3$	$\times$	$65$	$=$	$195$
$4$	$\times$	$65$	$=$	$260$
$5$	$\times$	$65$	$=$	$325$
$6$	$\times$	$65$	$=$	$390$
$7$	$\times$	$65$	$=$	$455$
$8$	$\times$	$65$	$=$	$520$
$9$	$\times$	$65$	$=$	$585$
$10$	$\times$	$65$	$=$	$650$

Use the table to answer the following questions:

11.a
What is $12 \times 65$ ?
11.b
What is $20 \times 65$ ?
11.c
Use values in the table to work out $4.55 \div 6.5$ .

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12
Look at the shape on the grid below:
A shaded kite on a square coordinate grid has vertices (1, 7), (3, 9), B at (5, 7) and A at (3, 3). The axes run from 0 to 10 with one-unit grid spacing, compact even-number labels and arrowheads at their positive ends.
1. 12.a
  Circle two words from the list that are both names of the shape.
  
  Quadrilateral
  
  Trapezium
  
  Pentagon
  
  Kite
  
  Parallelogram
2. 12.b
  Write down the co-ordinates of point $B$ .
3. 12.c
  Now look at the diagram which shows the shape reflected. Put a cross on the grid to show where $B$ is reflected to.
  On a square coordinate grid from 0 to 10, a shaded original kite has vertices (1, 7), (3, 9), B at (5, 7) and A at (3, 3). A second shaded kite shares A and has its other vertices at (7, 5), (9, 3) and (7, 1). The grid uses one-unit spacing and compact even-number labels. No transformed point B is marked.
4. 12.d
  Now look at the diagram which shows the shape rotated. Put a cross on the grid to show where $B$ is rotated to.
  On a square coordinate grid from 0 to 10, a shaded original kite has vertices (1, 7), (3, 9), B at (5, 7) and A at (3, 3). A second shaded kite shares A and has its other vertices at (7, 5), (9, 3) and (7, 1). The grid uses one-unit spacing and compact even-number labels. No rotated point B is marked.
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13
In a survey, some football fans were asked “Who was England's best player at the World Cup?” The results are shown in the chart below (with the club the player plays for in brackets).
Henderson has 23 votes, Pickford 17, Sterling 0, Kane 7, Trippier 5, Maguire 8 and Stones 2. The vertical Frequency scale runs from 0 to 26 in steps of 2.
1. 13.a
  How many fans said Maguire?
2. 13.b
  In total, how many fans were questioned in the survey?
3. 13.c
  Which player is the mode?
4. 13.d
  The fans who completed the survey were all pupils at St Anselm's College.
  
  Do you think this is a fair way to do the survey?
  
  Explain your answer.
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14
1. 14.a
  What fraction of the shape below is shaded? Give your answer as simply as possible.
  A long, narrow shaft extends three grid cells above a broad downward-pointing arrowhead. Four triangular half-cells around the lower sides are shaded medium gray. The full grid uses thin strong-gray strokes, while the arrow outline uses a regular ink stroke.
2. 14.b
  What percentage of the shape below is shaded?
  On a seven-by-six square grid, the outlined figure has a four-cell top bar and a two-cell-wide, three-cell-high stem. The four cells across the top bar are shaded medium gray and the six cells in the stem are unshaded. Thin strong-gray strokes define the full grid; the figure perimeter is regular-weight ink.
3. 14.c
  Which of the two shapes below has a greater percentage shaded? Explain how you know.
  A circle centred on a grid intersection has its upper-right quarter shaded medium gray. The caption Shape A sits below the circle. Thin strong-gray strokes define the full grid; the circle outline is regular-weight ink. The outlined shape has a broad top, inset shoulders and projecting side and lower arms. The top trapezoid and central square are shaded medium gray. The caption Shape B sits beneath it. One empty grid row precedes the figure; thin strong-gray strokes define the grid and the shape outline is regular-weight ink.
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15
Round each of the following measurements to the accuracy given in brackets.
1. 15.a
  $76.49 \rtqMathsUnit{cm}$ (nearest $\text{cm}$ )
2. 15.b
  $127569 \rtqMathsUnit{km}$ (nearest one thousand $\text{km}$ )
3. 15.c
  $1.073 \rtqMathsUnit{cm}$ (nearest $\text{mm}$ )
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16
Write the following numbers in order of size, starting with the smallest.

$0.2 \rtqMathsListSeparator \dfrac {3} {10} \rtqMathsListSeparator 0.21 \rtqMathsListSeparator \dfrac {37} {100} \rtqMathsListSeparator 0.36$
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17
I am thinking of three different, positive, whole numbers.

The mean of my three numbers is $8$ .

The median of my three numbers is $9$ .

Write down one possible set of three numbers that my numbers could be.
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18
I have a bag containing red, blue and white counters. A counter is chosen at random from the bag. There are $24$ red counters in the bag and the probability of choosing a red counter is $\dfrac {1} {6}$ . The bag contains $15$ blue counters.

How many white counters are there in the bag?
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19
Which of the following distances is the most likely height of the Eiffel Tower in Paris? Circle your answer.

$1250 \rtqMathsUnit{m}$

$305 \rtqMathsUnit{feet}$

$300 \rtqMathsUnit{metres}$

$36,000 \rtqMathsUnit{inches}$
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20
On a farm $80$ sheep gave birth. $30\%$ of the sheep gave birth to two lambs. The rest of the sheep gave birth to one lamb.

In total, how many lambs were born?
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21
Look at the list of numbers below.

$6 \rtqMathsListSeparator 10 \rtqMathsListSeparator 17 \rtqMathsListSeparator 30 \rtqMathsListSeparator 52 \rtqMathsListSeparator 81 \rtqMathsListSeparator 96$
1. 21.a
  Which of the numbers has an odd number of factors? (Hint: there is only one)
2. 21.b
  Give another example of a number with an odd number of factors.
3. 21.c
  These numbers have a special name. What is it?
4. 21.d
  Which of the numbers is a prime number?
5. 21.e
  Using each of the first four numbers in the list once $(6, 10, 17, 30)$ and any of the four operations $(+, -, \div, \times)$ show how you can make $33$ .
  
  (You must use all the four numbers and use each number only once. You can use any of the $(+, -, \div, \times)$ as many times as you like and you do not need to use all of them).
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22
In September $2015$ Mary was seven years older than Anna and Rebecca was three years older than Mary.

In September $2018$ Rebecca's age is three times Anna's age.

How old were the three girls in September $2015$ ?
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Brooklyn Bridge

12 \rtqMathsTimeSeparator 08

12 \rtqMathsTimeSeparator 18

12 \rtqMathsTimeSeparator 28

12 \rtqMathsTimeSeparator 38

12 \rtqMathsTimeSeparator 48

13 \rtqMathsTimeSeparator 00

13 \rtqMathsTimeSeparator 15

Bleecker Street

12 \rtqMathsTimeSeparator 12

12 \rtqMathsTimeSeparator 22

12 \rtqMathsTimeSeparator 32

12 \rtqMathsTimeSeparator 42

12 \rtqMathsTimeSeparator 52

13 \rtqMathsTimeSeparator 04

13 \rtqMathsTimeSeparator 19

Astor Place

12 \rtqMathsTimeSeparator 14

12 \rtqMathsTimeSeparator 24

12 \rtqMathsTimeSeparator 34

12 \rtqMathsTimeSeparator 44

12 \rtqMathsTimeSeparator 54

13 \rtqMathsTimeSeparator 06

13 \rtqMathsTimeSeparator 21

Grand Central Terminal

12 \rtqMathsTimeSeparator 21

12 \rtqMathsTimeSeparator 31

12 \rtqMathsTimeSeparator 41

12 \rtqMathsTimeSeparator 51

13 \rtqMathsTimeSeparator 01

13 \rtqMathsTimeSeparator 13

13 \rtqMathsTimeSeparator 28

68^\text{th}

Street

12 \rtqMathsTimeSeparator 25

12 \rtqMathsTimeSeparator 35

12 \rtqMathsTimeSeparator 45

12 \rtqMathsTimeSeparator 55

13 \rtqMathsTimeSeparator 05

13 \rtqMathsTimeSeparator 17

13 \rtqMathsTimeSeparator 32

125^\text{th}

Street

12 \rtqMathsTimeSeparator 35

12 \rtqMathsTimeSeparator 45

12 \rtqMathsTimeSeparator 55

13 \rtqMathsTimeSeparator 05

13 \rtqMathsTimeSeparator 15

13 \rtqMathsTimeSeparator 27

13 \rtqMathsTimeSeparator 42

3^\text{rd}

Ave &

138^\text{th}

Street

12 \rtqMathsTimeSeparator 38

12 \rtqMathsTimeSeparator 48

12 \rtqMathsTimeSeparator 58

13 \rtqMathsTimeSeparator 08

13 \rtqMathsTimeSeparator 18

13 \rtqMathsTimeSeparator 30

13 \rtqMathsTimeSeparator 45

Hunts Point Avenue

12 \rtqMathsTimeSeparator 47

12 \rtqMathsTimeSeparator 57

13 \rtqMathsTimeSeparator 07

13 \rtqMathsTimeSeparator 17

13 \rtqMathsTimeSeparator 27

13 \rtqMathsTimeSeparator 39

13 \rtqMathsTimeSeparator 54

Parkchester

12 \rtqMathsTimeSeparator 53

13 \rtqMathsTimeSeparator 03

13 \rtqMathsTimeSeparator 13

13 \rtqMathsTimeSeparator 23

13 \rtqMathsTimeSeparator 33

13 \rtqMathsTimeSeparator 45

14 \rtqMathsTimeSeparator 00

Pelham Bay Park

13 \rtqMathsTimeSeparator 02

13 \rtqMathsTimeSeparator 12

13 \rtqMathsTimeSeparator 22

13 \rtqMathsTimeSeparator 32

13 \rtqMathsTimeSeparator 42

13 \rtqMathsTimeSeparator 54

14 \rtqMathsTimeSeparator 09