Magdalen College School Paper 1

IndependentBoys

18 questions

Original PDFWorked solutions in progress

Questions

1
Work out:
1. 1.a
  $153 + 78$
2. 1.b
  $185 - 43$
3. 1.c
  $532 - 85$
4. 1.d
  $53 \times 9$
5. 1.e
  $37 \times 23$
6. 1.f
  $238 \div 7$
7. 1.g
  $442 \div 17$
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2
Find the perimeter and area of this shape:
The parallel horizontal sides are labelled 6 cm and 9 cm. The perpendicular left side is labelled 4 cm and has right-angle markers at both ends. The sloping right side is labelled 5 cm.
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3
Calculate, giving your answer as simply as possible:
1. 3.a
  $\dfrac{5}{12} + \dfrac{4}{12}$
2. 3.b
  $\dfrac{1}{6} + \dfrac{1}{3}$
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4
Find:
1. 4.a
  $30\%$ of $\rtqMathsSymbolPound 70$
2. 4.b
  a fifth of $\rtqMathsSymbolPound 70$
3. 4.c
  $80\%$ of a half of $\rtqMathsSymbolPound 70$
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5
Find the missing angles (diagrams not to scale):
1. 5.a
  A triangle stands on a baseline that rises slightly to the right and extends beyond the right vertex. The left interior angle is 30 degrees, the top angle is 100 degrees, the right interior angle is a, and the adjacent exterior angle above the extension is b.
2. 5.b
  A vertical line and a horizontal line meet at a marked right angle on the left. A descending diagonal crosses the horizontal line to the right. The angle between the vertical and diagonal at the upper-left point is 62 degrees. At the crossing, the upper-left angle is c and the vertically opposite lower-right angle is d.
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6
Find the next $2$ numbers in the following sequences:
1. 6.a
  $3, \rtqMathsListSeparator 7, \rtqMathsListSeparator 11, \rtqMathsListSeparator 15, \rtqMathsListSeparator 19, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
2. 6.b
  $3, \rtqMathsListSeparator 6, \rtqMathsListSeparator 12, \rtqMathsListSeparator 24, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
3. 6.c
  $3, \rtqMathsListSeparator 5, \rtqMathsListSeparator 9, \rtqMathsListSeparator 15, \rtqMathsListSeparator 23, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
4. 6.d
  $\dfrac{1}{5}, \rtqMathsListSeparator \dfrac{3}{10}, \rtqMathsListSeparator \dfrac{5}{17}, \rtqMathsListSeparator \dfrac{7}{26}, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
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7
Complete the table below, giving fractions in their lowest terms.

Fraction Decimal Percentage
$50\%$
$0.75$
$\dfrac{3}{5}$
$\dfrac{17}{20}$
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The table shows part of the railway timetable from Edinburgh to St Andrews. Some trains stop at every station and others are express trains. All stopping trains take the same time between each station as each other.

	Express	Stopping	Express	Stopping	Express	Stopping
Edinburgh	$13 \rtqMathsTimeSeparator 18$	$13 \rtqMathsTimeSeparator 43$	$14 \rtqMathsTimeSeparator 24$	$14 \rtqMathsTimeSeparator 41$	$15 \rtqMathsTimeSeparator 20$	$15 \rtqMathsTimeSeparator 34$
Haymarket		$14 \rtqMathsTimeSeparator 06$		$15 \rtqMathsTimeSeparator 04$
Kircaldy		$14 \rtqMathsTimeSeparator 18$		$15 \rtqMathsTimeSeparator 16$
Ladybank		$14 \rtqMathsTimeSeparator 23$		$15 \rtqMathsTimeSeparator 21$
St Andrews	$14 \rtqMathsTimeSeparator 02$	$14 \rtqMathsTimeSeparator 38$	$15 \rtqMathsTimeSeparator 08$	$15 \rtqMathsTimeSeparator 36$	$16 \rtqMathsTimeSeparator 04$

8.a
How many minutes does it take to travel between Edinburgh and Kircaldy?
8.b
Complete the times in the boxes in the table above for the stopping train that leaves Edinburgh at $15 \rtqMathsTimeSeparator 34$ .
8.c
How much longer does the stopping train take than the express train for the journey from Edinburgh to St Andrews?
8.d
James arrives at Edinburgh airport at $13 \rtqMathsTimeSeparator 05$ . It takes him $27 \rtqMathsUnit{minutes}$ to get from the plane and collect his baggage. It then takes him $45 \rtqMathsUnit{minutes}$ to get to Edinburgh railway station. How long does he have to wait for the next train to St Andrews?

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9
For each shape draw a rectangle that has the same area as the shape on the left. The first one is done for you.
A six-by-six square coordinate grid contains a shaded right triangle with vertices at grid positions (2, 2), (2, 4), and (4, 4). Its area is two square units. A six-by-six square coordinate grid contains the worked answer: a shaded rectangle two cells wide and one cell high, with area two square units.
1. 9.a
  A six-by-six square coordinate grid contains a shaded horizontal hexagon with vertices at (1, 3), (2, 4), (4, 4), (5, 3), (4, 2), and (2, 2).
2. 9.b
  A six-by-six square coordinate grid contains a shaded vertical rhombus with vertices at (2, 3), (3, 5), (4, 3), and (3, 1).
3. 9.c
  A six-by-six square coordinate grid contains a shaded four-point star. Its long top, right, bottom, and left points are joined by short inset vertices around the centre.
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10
James was given $\rtqMathsSymbolPound 15$ to buy supplies for the university year. He chose to spend it on pens and pencils.

Each pen costs $\rtqMathsSymbolPound 1.25$ .

Each pencil costs $80 \rtqMathsUnitCurrencyPence$ .
1. 10.a
  If James buys $5$ pens and $7$ pencils, how much money will he have left?
2. 10.b
  If instead James buys a set of $5$ pencils, what is the maximum number of pens he can buy?
3. 10.c
  If instead James ends up with $\rtqMathsSymbolPound 2.80$ left of his money how many pens and how many pencils did he buy?
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11
$12$ boy scouts will eat $30$ loaves in $4 \rtqMathsUnit{days}$ .
1. 11.a
  How many boy scouts will eat $60$ loaves in $4 \rtqMathsUnit{days}$ ?
2. 11.b
  How many days will it take $6$ boy scouts to eat $30$ loaves?
3. 11.c
  How many loaves will $3$ boy scouts eat in $8 \rtqMathsUnit{days}$ ?
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12
Put these numbers in order from smallest to largest:

$60\% \rtqMathsListSeparator \dfrac{17}{25} \rtqMathsListSeparator \dfrac{2}{3} \rtqMathsListSeparator 0.66$
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13
There are four unknown positive whole numbers.

The mean of the two smallest numbers is $3$ .

The mean of the three smallest numbers is $5$ .

The mean of all four numbers is $7$ .

All the numbers are different and odd.

What are the four numbers?
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14
Ten green bottles hanging on a wall

Ten green bottles hanging on a wall

If one green bottle should accidentally fall,

There'd be nine green bottles hanging on the wall

Nine green bottles...

If the first bottle fell at ten past five in the morning $(5.10 \rtqMathsTimeAm )$ and the others fell down at five minute intervals, at what time would the last bottle fall?
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15
The dotted line is a line of symmetry of a shape, which is partly drawn. On the grid complete the shape.
An eleven-column by eleven-row square grid has a dashed line of symmetry from its bottom-left corner to its top-right corner. Four solid segments form part of an outline on both sides of the line; the reflected completion is not shown.
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16
Here are five cards with numbers printed on them.

$\rtqMathsBoxedValue{7} \rtqMathsListSeparator \rtqMathsBoxedValue{6} \rtqMathsListSeparator \rtqMathsBoxedValue{2} \rtqMathsListSeparator \rtqMathsBoxedValue{4} \rtqMathsListSeparator \rtqMathsBoxedValue{8}$

The cards can be placed in order to form a $5$ -digit number.

For example the smallest number that could be made with all $5$ cards is:

$\rtqMathsBoxedValue{2} \rtqMathsBoxedValue{4} \rtqMathsBoxedValue{6} \rtqMathsBoxedValue{7} \rtqMathsBoxedValue{8}$
1. 16.a
  Using all $5$ cards what is the largest possible odd number?
2. 16.b
  Using all $5$ cards what is the number that is closest to $50{,}000$ ?
3. 16.c
  Using only two of the cards, what is the largest possible prime number?
4. 16.d
  Arrange any three of the number cards to give the largest possible answer to this multiplication.
  
  $\rtqMathsBoxedEmptyValueOneDigitWide \rtqMathsSpaceQuarterEm \rtqMathsBoxedEmptyValueOneDigitWide \times \rtqMathsBoxedEmptyValueOneDigitWide$
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17
For each of the following questions you need to find a whole number between $0$ and $100$ that has the following properties.
1. 17.a
  When the number is divided by $4$ the remainder is $0$ .
  
  When the number is divided by $7$ the remainder is $6$ .
  
  When the number is divided by $5$ the remainder is $0$ .
  
  What is the number?
2. 17.b
  When the number is divided by $5$ the remainder is $4$ .
  
  When the number is divided by $6$ the remainder is $0$ .
  
  When the number is divided by $7$ the remainder is $0$ .
  
  What is the number?
3. 17.c
  When the number is divided by $2$ the remainder is $1$ .
  
  When the number is divided by $3$ the remainder is $1$ .
  
  When the number is divided by $5$ the remainder is $0$ .
  
  When the number is divided by $7$ the remainder is $1$ .
  
  What is the number?
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18
Place each whole number from $1$ to $8$ inclusive in one of the blank boxes below to make the calculations correct. The calculations read left to right and top to bottom.

$\rtqMathsBoxedCellArrayFractionHighStyle \begin{array}{l} \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{\div} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{=} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{-} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHighSpacer \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHighSpacer \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHighSpacer \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{\times} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHighSpacer \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHighSpacer \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHighSpacer \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{=} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHighSpacer \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHighSpacer \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHighSpacer \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{=} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{+} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{=} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \end{array}$
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Fraction

Decimal

Percentage

50\%

0.75

\dfrac{3}{5}

\dfrac{17}{20}

Express

Stopping

Express

Stopping

Express

Stopping

Edinburgh

13 \rtqMathsTimeSeparator 18

13 \rtqMathsTimeSeparator 43

14 \rtqMathsTimeSeparator 24

14 \rtqMathsTimeSeparator 41

15 \rtqMathsTimeSeparator 20

15 \rtqMathsTimeSeparator 34

Haymarket

14 \rtqMathsTimeSeparator 06

15 \rtqMathsTimeSeparator 04

Kircaldy

14 \rtqMathsTimeSeparator 18

15 \rtqMathsTimeSeparator 16

Ladybank

14 \rtqMathsTimeSeparator 23

15 \rtqMathsTimeSeparator 21

St Andrews

14 \rtqMathsTimeSeparator 02

14 \rtqMathsTimeSeparator 38

15 \rtqMathsTimeSeparator 08

15 \rtqMathsTimeSeparator 36

16 \rtqMathsTimeSeparator 04

Fraction	Decimal	Percentage
		$50\%$
	$0.75$
$\dfrac{3}{5}$
$\dfrac{17}{20}$

Fraction	Decimal	Percentage
		$50\%$
	$0.75$
$\dfrac{3}{5}$
$\dfrac{17}{20}$