Latymer Upper School Paper 2

IndependentCo-ed

29 questions

Original PDFWorked solutions in progress

Questions

1
What is $483 + 58$ ?

$431$

$441$

$531$

$541$

$551$
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2
Subtract $108$ from $525$ .

$327$

$417$

$407$

$427$

$633$
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3
What is $55 \times 160$ ?

$8055$

$8000$

$8800$

$9800$

$8400$
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4
Jenny divides $344$ by $9$ . What remainder should she get?

$6$

$5$

$4$

$3$

$2$
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5
What is $912 \div 16$ ?

$58$

$57$

$56$

$54$

$52$
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6
Work out three eighths of $264$ .

$61$

$88$

$96$

$99$

$108$
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7
Which digit should replace the $\rtqMathsSymbolAsterisk$ below?

$\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & & \rtqMathsSymbolAsterisk & 5 & 7 \\ & - & 2 & 8 & 3 \\ \hline & & 4 & 7 & 4 \end{array}$

$1$

$2$

$4$

$6$

$7$
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8
$60\%$ of a number is $240$ . What is the number?

$60$

$144$

$240$

$300$

$400$
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9
Which of the following gives the largest answer?

$15 \times 16$

$12 \times 20$

$27 \times 9$

$22 \times 11$

$23 \times 10$
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10
Kofi leaves for the shops at $11 \rtqMathsTimeSeparator 23 \rtqMathsTimeAm$ and returns $2 \rtqMathsUnit{hours}$ $48 \rtqMathsUnit{minutes}$ later. At what time does he return?

$1 \rtqMathsTimeSeparator 01 \rtqMathsTimePm$

$1 \rtqMathsTimeSeparator 11 \rtqMathsTimePm$

$2 \rtqMathsTimeSeparator 10 \rtqMathsTimePm$

$2 \rtqMathsTimeSeparator 01 \rtqMathsTimePm$

$2 \rtqMathsTimeSeparator 11 \rtqMathsTimePm$
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11
Work out: $\dfrac{2}{5} - \dfrac{1}{3}$

$\dfrac{1}{2}$

$\dfrac{3}{8}$

$\dfrac{3}{15}$

$\dfrac{1}{8}$

$\dfrac{1}{15}$
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12
What is the perimeter of the shape below? [Diagram not to scale]
The L-shaped figure has a rectangular cutout at the upper right. The full bottom width is labelled 13 cm and the full height is labelled 5 cm. A horizontal double-headed arrow above the cutout labels its width 8 cm. Dotted horizontal and vertical lines complete the cutout's top and right sides; these are not solid edges of the L-shaped figure. The figure is not to scale.

$36 \rtqMathsUnit{cm}$

$29 \rtqMathsUnit{cm}$

$26 \rtqMathsUnit{cm}$

$18 \rtqMathsUnit{cm}$

More information needed
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13
I buy $4$ Mega Bars at $65 \rtqMathsUnit{pence}$ each and $3$ Star Bars at $83 \rtqMathsUnit{pence}$ each. How much change do I get from $\rtqMathsSymbolPound 10$ ?

$\rtqMathsSymbolPound 4.91$

$\rtqMathsSymbolPound 5.09$

$\rtqMathsSymbolPound 5.91$

$\rtqMathsSymbolPound 5.19$

$\rtqMathsSymbolPound 4.81$
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14
Two positive whole numbers add together to make $23$ . What is the smallest possible answer when the two numbers are multiplied together?

$132$

$1$

$42$

$22$

$23$
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15
Half of a number is $8$ bigger than three sevenths of the number. What's the number?

$140$

$126$

$119$

$112$

$98$
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16
Dave and Eddie are cycling around a track. Dave completes a lap every $30 \rtqMathsUnit{seconds}$ , and Eddie completes a lap every $25 \rtqMathsUnit{seconds}$ . How many laps will Eddie complete in the time it takes Dave to complete $15$ laps?

$15$

$16$

$18$

$20$

$25$
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17
The total of five different, positive odd numbers is $85$ . What's the most that the largest number could be?

$69$

$35$

$25$

$21$

$17$
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18
What is the area of the shaded diamond below? [Diagram not to scale]
The diamond joins the midpoints of a rectangle labelled 22 cm wide and 12 cm high. Dashed horizontal and vertical diagonals cross at the centre of the shaded diamond.

$34 \rtqMathsUnit{cm}^2$

$264 \rtqMathsUnit{cm}^2$

$198 \rtqMathsUnit{cm}^2$

$132 \rtqMathsUnit{cm}^2$

$66 \rtqMathsUnit{cm}^2$
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19
How many different ways are there of paying exactly $15 \rtqMathsUnitCurrencyPence$ using $1 \rtqMathsUnitCurrencyPence$ and/or $2 \rtqMathsUnitCurrencyPence$ pieces?

$2$

$3$

$7$

$8$

$15$
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20
I'm thinking of two numbers, one of which is three times as big as the other. When I double one of my numbers and then add it to the other I get $140$ . Which of the following cannot possibly be one of my numbers?

$20$

$28$

$50$

$60$

$84$
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21
Complete the missing numbers in each of the number sequences below:
1. 21.a
  $28, \rtqMathsListSeparator 25, \rtqMathsListSeparator 22, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 13, \rtqMathsListSeparator 10$
2. 21.b
  $3, \rtqMathsListSeparator 4, \rtqMathsListSeparator 6, \rtqMathsListSeparator 9, \rtqMathsListSeparator 13, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 31$
3. 21.c
  $5, \rtqMathsListSeparator -10, \rtqMathsListSeparator 20, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator -160, \rtqMathsListSeparator 320$
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22
1. 22.a
  What is the angle between the hour and minute hands of a clock at $6 \rtqMathsTimeSeparator 00 \rtqMathsTimePm$ ?
2. 22.b
  What is the angle between the hour and minute hands of a clock at $6 \rtqMathsTimeSeparator 30 \rtqMathsTimePm$ ? [Draw a picture to help]
3. 22.c
  At what time between $6 \rtqMathsTimePm$ and $6 \rtqMathsTimeSeparator 30 \rtqMathsTimePm$ will the hour and minute hands be exactly $125\degree$ apart?
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23
1. 23.a
  What is the remainder when $247$ is divided by $7$ ?
2. 23.b
  Work out $23 \times 438$ . Show all your working.
3. 23.c
  Put the following list of fractions in order, starting with the smallest:
  
  $\dfrac{5}{7} \rtqMathsListSeparator \dfrac{19}{28} \rtqMathsListSeparator \dfrac{27}{35} \rtqMathsListSeparator \dfrac{9}{14}$
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24
For each part of this question you should try to find all the possible answers.
1. 24.a
  Three different positive odd numbers add up to $15$ . What could the three numbers be?
2. 24.b
  Jenny has two younger brothers. The total of all three of their ages is $15$ , and Jenny's brothers are both an even number of years old. What could the ages of Jenny and her brothers be?
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The diagram below shows part of a train timetable:

Operator Notes		GW	GW	SW ★	GW	GW	SW ★	GW	SW H ★	SW ★	GW	SW H ★	SW ★	SW ★
Reading	d	$0434$	$0524$	$0539$	$0554$	$0606$	$0609$	$0634$		$0639$	$0704$		$0709$	$0721$
Earley	d	│	│	$0544$	│	│	$0614$	│		$0644$	│		$0714$	│
Winnersh Triangle	d	│	│	$0546$	│	│	$0616$	│		$0646$	│		$0716$	│
Winnersh	d	│	│	$0548$	│	│	$0618$	│		$0648$	│		$0718$	│
Wokingham	d	$0443\text{a}$	$0533\text{a}$	$0553$	$0603\text{a}$	$0615\text{a}$	$0623$	$0643\text{a}$		$0653$	$0712\text{a}$		$0723$	$0730$
Bracknell	d			$0559$			$0629$			$0659$			$0729$	$0736$
Martins Heron	d			$0602$			$0632$			$0702$			$0732$	$0739$
Ascot	d			$0607$			$0637$		$0656$	$0707$		$0726$	$0737$	$0744$
Sunningdale	d			$0610$			$0640$		$0659$	$0710$		$0729$	$0740$	$0747$
Longcross	d			│			│		│	│		│	│	│
Virginia Water	a			$0619$			$0649$		$0708$	$0719$		$0738$	│	$0755$
Egham	a			$0623$			$0653$		$0712$	$0723$		$0742$	$0750$	$0758$
Staines	a			$0628$			$0658$		$0717$	$0728$		$0747$	$0755$	$0804$
Ashford	a			$0636\text{b}$			$0711\text{b}$		$0721$	$0741\text{b}$		$0751$	$0811\text{b}$	│
Feltham	a			$0635$			$0705$		$0725$	$0735$		$0755$	$0802$	$0811$
Hounslow	a			$0646\text{c}$			│		$0737\text{c}$	│		│	$0812\text{c}$	│
Twickenham	a			$0640$			$0710$		$0733$	$0740$		$0803$	$0809$	$0817$
Richmond	a			$0645$			$0715$		$0737$	$0745$		$0807$	$0813$	$0823$
Putney	a			$0651$			$0721$		$0759\text{e}$	$0804\text{e}$		│	$0829\text{e}$	$0834\text{e}$
Clapham Junction	a			$0656$			$0726$		$0746$	$0753$		$0816$	$0822$	$0832$
Vauxhall	a			$0711\text{h}$			$0741\text{h}$		$0752$	$0811\text{h}$		$0822$	│	$0838$
London Waterloo	a			$0707$			$0737$		$0759$	$0806$		$0829$	$0836$	$0846$

25.a
How long does the $0548$ from Winnersh take to reach London Waterloo?
25.b
How long does the fastest train take to travel from Wokingham to Richmond?
25.c
Bob lives in Earley, and needs to be in Waterloo before $8.30 \rtqMathsTimeAm$ for work. If it takes him $8 \rtqMathsUnit{minutes}$ to walk from his house to Earley station, what's the latest time he can leave the house?

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26
1. 26.a
  Tommy thinks of a number. When he doubles the number and then subtracts $11$ , he gets the answer $17$ . What was his number?
2. 26.b
  Lilly thinks of a number. When she takes away $11$ from the number and then doubles the answer, she gets $82$ . What was her number?
3. 26.c
  I'm thinking of a number. When I subtract the number from $45$ , I get the same answer as when I double the number. What's my number?
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27
What is the area of the shape below?

(Diagram not to scale)
The shape is 9 centimetres wide and 13 centimetres high. Its rectangular opening is 4 centimetres wide and 8 centimetres deep. The left arm is 3 centimetres wide.
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28
Imran notices that when he takes the digits of the number $652$ and multiplies them together he gets $60$ .
1. 28.a
  How many three digit numbers are there whose digits multiply to give $60$ ? Write down all the ones you can find.
2. 28.b
  What's the biggest three digit number whose digits multiply together to give $40$ ?
3. 28.c
  Imran says he has found a three digit number whose digits multiply together to give $65$ . Explain carefully why he must be wrong.
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29
The diagram below is made using the following rule: the number in each square is the total of the numbers in the two squares below it:

$\rtqMathsBoxedCellArrayFractionHighStyle \begin{array}{c} \rtqMathsBoxedCellFourDigitsWideFractionHigh{17} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{9} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{8} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{2} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{7} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{1} \end{array}$
1. 29.a
  Complete the diagrams below using the same rule.
  29.a.i
  $\rtqMathsBoxedCellArrayFractionHighStyle \begin{array}{c} \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{19} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{8} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{3} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \end{array}$
  29.a.ii
  $\rtqMathsBoxedCellArrayFractionHighStyle \begin{array}{c} \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{28} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{8} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{12} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{9} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \end{array}$
2. 29.b
  The same rules are used in the diagram below. Also:
  
  $A$ and $B$ are positive, whole numbers
  
  $A$ is bigger than $B$
  
  $\rtqMathsBoxedCellArrayFractionHighStyle \begin{array}{c} \rtqMathsBoxedCellFourDigitsWideFractionHigh{21} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{2} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{A} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{B} \end{array}$
  
  What are the possible values of $A$ and $B$ ?
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Operator
Notes

SW
★

SW
H ★

SW
★

SW
H ★

SW
★

Reading

0434

0524

0539

0554

0606

0609

0634

0639

0704

0709

0721

Earley

│

0544

│

0614

│

0644

│

0714

│

Winnersh Triangle

│

0546

│

0616

│

0646

│

0716

│

Winnersh

│

0548

│

0618

│

0648

│

0718

│

Wokingham

0443\text{a}

0533\text{a}

0553

0603\text{a}

0615\text{a}

0623

0643\text{a}

0653

0712\text{a}

0723

0730

Bracknell

0559

0629

0659

0729

0736

Martins Heron

0602

0632

0702

0732

0739

Ascot

0607

0637

0656

0707

0726

0737

0744

Sunningdale

0610

0640

0659

0710

0729

0740

0747

Longcross

│

Virginia Water

0619

0649

0708

0719

0738

│

0755

Egham

0623

0653

0712

0723

0742

0750

0758

Staines

0628

0658

0717

0728

0747

0755

0804

Ashford

0636\text{b}

0711\text{b}

0721

0741\text{b}

0751

0811\text{b}

│

Feltham

0635

0705

0725

0735

0755

0802

0811

Hounslow

0646\text{c}

│

0737\text{c}

│

0812\text{c}

│

Twickenham

0640

0710

0733

0740

0803

0809

0817

Richmond

0645

0715

0737

0745

0807

0813

0823

Putney

0651

0721

0759\text{e}

0804\text{e}

│

0829\text{e}

0834\text{e}

Clapham Junction

0656

0726

0746

0753

0816

0822

0832

Vauxhall

0711\text{h}

0741\text{h}

0752

0811\text{h}

0822

│

0838

London Waterloo

0707

0737

0759

0806

0829

0836

0846