St Paul's Girls' School Paper 2

IndependentGirls

35 questions
3 sections

Original PDFWorked solutions in progress

Questions

Section A
Questions 1–20
1. 1
  Write, in the box, the missing numbers:
  1.a
  $\rtqMathsBoxedEmptyValueThreeDigitsWide + 121 = 212$
  1.b
  $6 \times \rtqMathsBoxedEmptyValueThreeDigitsWide = 96$
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2. 2
  The signs are missing from these number sentences.
  
  Write in the missing signs $+, -, \times$ or $\div$ , in the circle.
  
  The first has been done for you:
  
  $7 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxed{+} \rtqMathsSpaceQuarterEm 9 = 8 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxed{\times} \rtqMathsSpaceQuarterEm 2$
  2.a
  $13 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 5 = 60 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 5$
  2.b
  $36 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 4 = 23 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 14$
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3. 3
  The sum of two numbers is $250$ .
  
  Write in the missing digits in the boxes:
  
  $\rtqMathsSizeEight{\rtqMathsBoxedValue{7}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm + \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{6}} \rtqMathsSpaceQuarterEm = \rtqMathsSizeEight{\rtqMathsBoxedValue{2}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{5}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{0}}$
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4. 4
  Calculate $37 \times 4 \times 5$ .
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5. 5
  Calculate $483 \div 21$ .
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6. 6
  Calculate $1.1 \times (1.2 + 1.3) \times 2$ .
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7. 7
  Write these numbers in the boxes below, in order of size, starting with the smallest:
  
  $6.01 \rtqMathsListSeparator 16.0 \rtqMathsListSeparator 0.61 \rtqMathsListSeparator 1.60 \rtqMathsListSeparator 6.1$
  
  $\rtqMathsBoxedEmptyValueThreeDigitsWide \rtqMathsListSeparator \rtqMathsBoxedEmptyValueThreeDigitsWide \rtqMathsListSeparator \rtqMathsBoxedEmptyValueThreeDigitsWide \rtqMathsListSeparator \rtqMathsBoxedEmptyValueThreeDigitsWide \rtqMathsListSeparator \rtqMathsBoxedEmptyValueThreeDigitsWide$
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8. 8
  Write these fractions in the boxes below, in order of size, starting with the smallest:
  
  $\dfrac{3}{4} \rtqMathsListSeparator \dfrac{3}{5} \rtqMathsListSeparator \dfrac{9}{10} \rtqMathsListSeparator \dfrac{17}{20}$
  
  $\rtqMathsBoxedEmptyValueFraction \rtqMathsListSeparator \rtqMathsBoxedEmptyValueFraction \rtqMathsListSeparator \rtqMathsBoxedEmptyValueFraction \rtqMathsListSeparator \rtqMathsBoxedEmptyValueFraction$
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9. 9
  Put a circle around all the numbers that are between $2.2$ and $2.6$ .
  
  $2 \dfrac{1}{2} \rtqMathsListSeparator 2 \dfrac{1}{7} \rtqMathsListSeparator 2 \dfrac{6}{11} \rtqMathsListSeparator 2 \dfrac{2}{5} \rtqMathsListSeparator 2 \dfrac{1}{10}$
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10. 10
  Mary, Jess and Jo run a race.
  
  Jess's time is $18 \rtqMathsUnit{seconds}$ .
  
  Jo finishes $6 \rtqMathsUnit{seconds}$ before Jess.
  
  Mary finishes $4 \rtqMathsUnit{seconds}$ after Jo.
  
  What is Mary's time in seconds?
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11. 11
  Write one number which fits all three of these statements:
  
  It is a multiple of $3$
  
  It is a multiple of $8$
  
  It ends in “ $2$ ”
  
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12. 12
  Put a circle around all the amounts that can be made with three coins:
  
  $13 \rtqMathsUnitCurrencyPence \rtqMathsListSeparator 23 \rtqMathsUnitCurrencyPence \rtqMathsListSeparator 33 \rtqMathsUnitCurrencyPence \rtqMathsListSeparator 43 \rtqMathsUnitCurrencyPence \rtqMathsListSeparator 53 \rtqMathsUnitCurrencyPence$
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13. 13
  Here is part of a number sequence.
  
  The numbers increase by the same amount each time.
  
  $150, \rtqMathsListSeparator 165, \rtqMathsListSeparator 180, \rtqMathsListSeparator 195, \rtqMathsListSeparator 210$
  
  The sequence continues.
  
  Circle all of the numbers below that would appear in the sequence:
  
  $315, \rtqMathsListSeparator 561, \rtqMathsListSeparator 240, \rtqMathsListSeparator 620, \rtqMathsListSeparator 964$
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14. 14
  Abigail gets up at $07 \rtqMathsTimeSeparator 40$ in the morning.
  
  $25 \rtqMathsUnit{minutes}$ later she starts her breakfast, which takes $10 \rtqMathsUnit{minutes}$ to finish.
  
  She then leaves for school. Her journey takes $35 \rtqMathsUnit{minutes}$ in total.
  
  She arrives $5 \rtqMathsUnit{minutes}$ late for registration.
  
  At what time is registration?
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15. 15
  Emily scores $30$ out of $60$ in a test.
  
  Hebe scores $60\%$ in the same test.
  
  How many more marks did Hebe get than Emily?
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16. 16
  A shop sells apples and oranges.
  
  Kate buys $1$ apple and $2$ oranges. She paid $48 \rtqMathsUnitCurrencyPence$ .
  
  Jade buys $1$ apple and $1$ orange. She paid $31 \rtqMathsUnitCurrencyPence$ .
  
  How much does $1$ orange cost?
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17. 17
  Alysha and Julia each have some money.
  
  Altogether they have $\rtqMathsSymbolPound 3.20$ .
  
  Alysha gives Julia $20 \rtqMathsUnitCurrencyPence$ so that they both have the same amount.
  
  How much money did each have at the start?
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18. 18
  $70$ children need $3$ pens each.
  
  Pens are sold in packs of $8$ .
  
  How many packs of pens need to be bought?
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19. 19
  The cost for using a minibus is $\rtqMathsSymbolPound 2.42$ for each kilometre.
  
  $11$ friends go on a $32 \rtqMathsUnit{kilometre}$ journey using $1$ minibus.
  
  They share the cost equally.
  
  How much does each person pay?
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20. 20
  Two whole numbers are each between $40$ and $60$ .
  
  They multiply to make $2385$ .
  
  Write in the missing numbers in the boxes below.
  
  $\rtqMathsBoxedEmptyValueFourDigitsWide \times \rtqMathsBoxedEmptyValueFourDigitsWide = 2385$
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Section B
Questions 1–10
1. 1
  If I treble a number and add $6$ , I get the same answer as when I add $16$ to that number.
  
  What is my original number?
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2. 2
  My money box contains an equal number of $5 \rtqMathsUnitCurrencyPence, 10 \rtqMathsUnitCurrencyPence$ and $20 \rtqMathsUnitCurrencyPence$ coins and no other coins.
  
  How many coins are there altogether if there is $\rtqMathsSymbolPound 4.90$ in the money box?
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3. 3
  3.a
  Winston thinks of two different whole numbers that add together to make $20$ and multiply to give $84$ .
  
  What are his two numbers?
  3.b
  He then thinks of a new number, multiplies it by $9$ and subtracts $15$ . The result is $66$ .
  
  What was his original number?
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4. 4
  $A$ and $B$ are two points on a straight line. The point $A$ is $(1, 6)$ .
  
  4.a
  What is point $B$ ?
  4.b
  Two other points, $C$ and $D$ , also lie on the same line, but are not shown in the diagram.
  
  Work out the missing values.
  
  $C \rtqMathsSpaceOneSixthEm (6, \rtqMathsEmptyValueTwoDigitsWide)$
  
  $D \rtqMathsSpaceOneSixthEm (\rtqMathsEmptyValueOneDigitWide, 38)$
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5. 5
  A company makes bricks to export to builders. To ship them, they put the bricks into packing cases. The lengths of the sides of the bricks and the cases are shown below. All measurements are in $\text{cm}$ .
  
  What is the maximum number of bricks which can be fitted into the packing case?
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6. 6
  There are $3 \rtqMathsUnit{moos}$ in a quack and $13 \rtqMathsUnit{quacks}$ in an oink.
  6.a
  How many moos are there in $3 \rtqMathsUnit{quacks}$ and $1 \rtqMathsUnit{oink}$ ?
  6.b
  What fraction of an oink does $9 \rtqMathsUnit{moos}$ represent?
  6.c
  $800 \rtqMathsUnit{moos}$ are sorted into piles $2 \rtqMathsUnit{oinks}$ high.
  
  How many complete piles will there be and how many moos and quacks will be left over?
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7. 7
  A clock is $18 \rtqMathsUnit{minutes}$ slow, but is gaining $7 \dfrac{1}{2} \rtqMathsUnit{seconds}$ every hour.
  7.a
  How long will it take for the clock to show the correct time?
  7.b
  Another clock is $30 \rtqMathsUnit{minutes}$ fast, but is losing $11 \dfrac{1}{4} \rtqMathsUnit{seconds per hour}$ .
  
  How many minutes fast will the second clock be when the first clock shows the right time?
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8. 8
  You have $5$ pieces of card shaped like this:
  
  8.a
  Name $2$ different pieces that can fit together to form a square.
  8.b
  Name $2$ different pieces that can fit together to form a trapezium.
  8.c
  Name $3$ different shapes which can fit together to form a parallelogram.
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9. 9
  $3$ cats can catch $3$ mice in $3 \rtqMathsUnit{hours}$ .
  9.a
  How long would it take $3$ cats to catch $1$ mouse?
  9.b
  How long would it take for $1$ cat to catch $1$ mouse?
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10. 10
  Put the numbers $1$ to $9$ in the square so that each row, column and diagonal add up to $15$ .
  
  $9$
  $6$
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Section C

Questions 1–5

1
Claire makes squares with matches.

To make $1$ square she needs $4$ matches.

To make $2$ squares she needs $7$ matches.
1. 1.a
  Fill in the table below:
  
  Number of squares $1$ $2$ $3$ $4$ $5$ $\rtqMathsSequenceEllipsis$
  Number of matches $\rtqMathsSequenceEllipsis$ $28$
2. 1.b
  How many matches will she need to make $40$ squares?
3. 1.c
  If she used $94$ matches how many squares did she make?
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2
The instruction “ $a \rtqMathsBinaryOperatorWhiteSmilingFace b$ ” means multiply $a$ by $b$ , then add on $a$ . For example:

$5 \rtqMathsBinaryOperatorWhiteSmilingFace 2 = 5 \times 2 + 5 = 10 + 5 = 15$
1. 2.a
  Work out the value of
  2.a.i
  $4 \rtqMathsBinaryOperatorWhiteSmilingFace 3 =$
  2.a.ii
  $4 \rtqMathsBinaryOperatorWhiteSmilingFace 0 =$
2. 2.b
  What is the value of $b$ if $3 \rtqMathsBinaryOperatorWhiteSmilingFace b = 15$ ?
3. 2.c
  What is the value of $a$ if $a \rtqMathsBinaryOperatorWhiteSmilingFace a = 20$ ?
4. 2.d
  $(a \rtqMathsBinaryOperatorWhiteSmilingFace b) \rtqMathsBinaryOperatorWhiteSmilingFace c$ means work out $(a \rtqMathsBinaryOperatorWhiteSmilingFace b)$ first and then work out “your answer” $\rtqMathsBinaryOperatorWhiteSmilingFace c$ .
  
  For example:
  
  $(5 \rtqMathsBinaryOperatorWhiteSmilingFace 2) \rtqMathsBinaryOperatorWhiteSmilingFace 3$ means do $5 \rtqMathsBinaryOperatorWhiteSmilingFace 2 = 5 \times 2 + 5 = 15$ first, then work out $15 \rtqMathsBinaryOperatorWhiteSmilingFace 3 = 15 \times 3 + 15 = 45 + 15 = 60$
  
  Work out $(2 \rtqMathsBinaryOperatorWhiteSmilingFace 3) \rtqMathsBinaryOperatorWhiteSmilingFace 4 =$
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Number of squares	$1$	$2$	$3$	$4$	$5$	$\rtqMathsSequenceEllipsis$
Number of matches						$\rtqMathsSequenceEllipsis$	$28$

The numbers $6, 12$ and $15$ can be divided by $3$ without leaving a remainder. We say they are “divisible by $3$ ”.

The sum $6 + 12 + 15 = 33$ is also divisible by $3$ .

The number $5$ is not divisible by $3$ , so $5 + 12 + 15 = 32$ is not divisible by $3$ , even though $12$ and $15$ are divisible by $3$ .

Finally, $5 + 12 + 4$ is divisible by $3$ , since $12$ is divisible by $3$ and $4 + 5 = 9$ is divisible by $3$ again.

3.a

Tick whether the following statements are true or false.

The first has been done for you.

		True
$6 + 12 + 15$	is divisible by $3$	$\rtqMathsSymbolCheckmarkPendingReview$
$12 + 15 + 36$	is divisible by $3$
$16 + 39 + 81$	is divisible by $3$
$34 + 23 + 99$	is divisible by $3$

3.b
$5 + 12 + 15 = 32$ divided by $5$ leaves a remainder of $2$ since $5$ and $15$ are divisible by $5$ and $12$ divided by $5$ leaves a remainder of $2$ .

Work out the remainders for the following questions:

Remainder
$25 + 17 + 200$ divided by $5$
$45 + 135 + 205$ divided by $5$
$315 + 43 + 57$ divided by $5$
3.c
You are told that $1! = 1, 2! = 1 \times 2 = 2$ and $3! = 1 \times 2 \times 3 = 6$ .

What is the remainder when $1! + 2! + 3! + 4! + 5! + 6! + 7! + 8! + 9! + 10!$ is divided by $5$ ?

		Remainder
$25 + 17 + 200$	divided by $5$
$45 + 135 + 205$	divided by $5$
$315 + 43 + 57$	divided by $5$

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4
Amitha started adding odd numbers and put her results in a table:

$\begin{aligned} 1 &= 1 = 1^2 \\\\ 1 + 3 &= 4 = 2^2 \\\\ 1 + 3 + 5 &= 9 = 3^2 \end{aligned}$
1. 4.a
  Write down the next three lines of this table:
2. 4.b
  Use the idea in the table to find the missing numbers $W$ and $X$ .
  4.b.i
  $1 + 3 + 5 + \rtqMathsSequenceEllipsis + 49 = W$
  4.b.ii
  $1 + 3 + 5 + \rtqMathsSequenceEllipsis + 99 + 101 = X$
3. 4.c
  Work out the missing numbers $Y$ and $Z$ :
  4.c.i
  $1 + 3 + 5 + \rtqMathsSequenceEllipsis + Y = 144$
  4.c.ii
  $1 + 3 + 5 + \rtqMathsSequenceEllipsis + Z = 400$
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Dividing $35$ by $8$ gives $4$ and leaves a remainder of $3$ . We write: $35 \div 8 = 4 \rtqMathsSpaceQuarterEm r \rtqMathsSpaceQuarterEm 3$ . So we can write:

	Column A	Column B	Column C
Line $1$ :	$35 \div 8 =$	$4$	$r \rtqMathsSpaceQuarterEm 3$
Line $2$ :	$26 \div 8 =$	$3$	$r \rtqMathsSpaceQuarterEm 2$
Line $3$ :	$61 \div 8 =$	$\rtqMathsBoxedEmptyValueTwoDigitsWide$	$r \rtqMathsSpaceQuarterEm \rtqMathsBoxedEmptyValueTwoDigitsWide$

5.a
Fill in the blank boxes in the table above.

5.b

Fill in the blank boxes in the table below.

	Column A	Column B	Column C
Line $4$ :	$21 \div 5 =$	$\rtqMathsBoxedEmptyValueTwoDigitsWide$	$r \rtqMathsSpaceQuarterEm \rtqMathsBoxedEmptyValueTwoDigitsWide$
Line $5$ :	$33 \div 5 =$	$\rtqMathsBoxedEmptyValueTwoDigitsWide$	$r \rtqMathsSpaceQuarterEm \rtqMathsBoxedEmptyValueTwoDigitsWide$
Line $6$ :	$54 \div 5 =$	$\rtqMathsBoxedEmptyValueTwoDigitsWide$	$r \rtqMathsSpaceQuarterEm \rtqMathsBoxedEmptyValueTwoDigitsWide$

5.c

Now look at columns $B$ and $C$ in the tables above. Given the information in the table below, work out the remainder of $577767777 \div 7$ without performing the division.

Write your answer in the blank box.

	Column A	Column B	Column C
Line $7$ :	$343424345 \div 7 =$	$49060620$	$r \rtqMathsSpaceQuarterEm 5$
Line $8$ :	$234343432 \div 7 =$	$33477633$	$r \rtqMathsSpaceQuarterEm 1$
Line $9$ :	$577767777 \div 7 =$	$82538253$	$r \rtqMathsSpaceQuarterEm \rtqMathsBoxedEmptyValueTwoDigitsWide$

5.d
Given that $343424345 - 234343432 = 109080913$ , predict the remainder of $109080913 \div 7$ without performing the division.

5.e

Given the information in the tables below work out the remainder of $470807973 \div 8$ and write your answer in the blank box.

	Column A	Column B	Column C
Line $10$ :	$21 \div 8 =$	$2$	$r \rtqMathsSpaceQuarterEm 5$
Line $11$ :	$14 \div 8 =$	$1$	$r \rtqMathsSpaceQuarterEm 6$
Line $12$ :	$35 \div 8 =$	$4$	$r \rtqMathsSpaceQuarterEm 3$

	Column A	Column B	Column C
Line $13$ :	$349858934 \div 8 =$	$43732366$	$r \rtqMathsSpaceQuarterEm 6$
Line $14$ :	$120949039 \div 8 =$	$15118629$	$r \rtqMathsSpaceQuarterEm 7$
Line $15$ :	$470807973 \div 8 =$	$58850996$	$r \rtqMathsSpaceQuarterEm \rtqMathsBoxedEmptyValueTwoDigitsWide$