St Paul's Girls' School Paper 1

IndependentGirls

35 questions
3 sections

Original PDFWorked solutions in progress

Questions

Section A
Questions 1–20
1. 1
  Calculate $15.05 - 14.84$ .
  Worked solution
  Being written
2. 2
  Calculate $31.6 \times 7$ .
  Worked solution
  Being written
3. 3
  Calculate $60\%$ of $765$ .
  Worked solution
  Being written
4. 4
  $85$ people go to the school concert. They pay $\rtqMathsSymbolPound 1.30$ each.
  
  How much money is collected?
  Worked solution
  Being written
5. 5
  Calculate $2.4 \times (3.7 + 1.3) \div 2$ .
  Worked solution
  Being written
6. 6
  Fill in the missing numbers:
  6.a
  $\dfrac{1}{2}$ of $20 = \dfrac{1}{4}$ of $\rtqMathsUnderlineEmptyValueMedium$
  6.b
  $\dfrac{3}{4}$ of $100 = \dfrac{1}{2}$ of $\rtqMathsUnderlineEmptyValueMedium$
  6.c
  $\dfrac{1}{3}$ of $60 = \dfrac{2}{3}$ of $\rtqMathsUnderlineEmptyValueMedium$
  Worked solution
  Being written
7. 7
  Write in the missing number to make this correct:
  
  $0.627 = 0.6 + 0.02 + \ldots$
  Worked solution
  Being written
8. 8
  Circle the number closest in value to $0.1$ .
  
  $0.01 \rtqMathsSpaceOneEm 0.08 \rtqMathsSpaceOneEm 0.13 \rtqMathsSpaceOneEm 0.2 \rtqMathsSpaceOneEm 0.9$
  Worked solution
  Being written
9. 9
  Here are some digit cards:
  
  $\rtqMathsSizeSeven{\rtqMathsBoxedValue{2}} \rtqMathsSpaceOneEm \rtqMathsSizeSeven{\rtqMathsBoxedValue{4}} \rtqMathsSpaceOneEm \rtqMathsSizeSeven{\rtqMathsBoxedValue{6}} \rtqMathsSpaceOneEm \rtqMathsSizeSeven{\rtqMathsBoxedValue{6}}$
  
  Write all the three-digit numbers, greater than $500$ , that can be made using these cards.
  Worked solution
  Being written
10. 10
  Write the three prime numbers which multiply to make $231$ :
  
  $\ldots \times \ldots \times \ldots = 231$
  Worked solution
  Being written
11. 11
  Halid makes a sequence of $5$ numbers. The first number is $2$ . The last number is $18$ .
  
  His rule is to add the same amount each time.
  
  Write in the missing numbers:
  
  $2 \rtqMathsListSeparator \ldots \rtqMathsListSeparator \ldots \rtqMathsListSeparator \ldots \rtqMathsListSeparator 18$
  Worked solution
  Being written
12. 12
  In this sequence each number is double the previous number.
  
  Write in the missing numbers:
  
  $\rtqMathsSequenceEllipsis \rtqMathsSpaceOneEm \rtqMathsSequenceEllipsis \rtqMathsSpaceOneEm 3 \rtqMathsSpaceOneEm 6 \rtqMathsSpaceOneEm 12 \rtqMathsSpaceOneEm 24 \rtqMathsSpaceOneEm 48 \rtqMathsSpaceOneEm \rtqMathsSequenceEllipsis$
  Worked solution
  Being written
13. 13
  Alysha and Julia have some biscuits. Altogether they have $14$ biscuits.
  
  Alysha has $2$ more biscuits than Julia.
  
  How many biscuits do Alysha and Julia each have?
  Worked solution
  Being written
14. 14
  Jemma thinks of a number. She says,
  
  “Add $3$ to my number and then multiply the result by $5$ . The answer is $35$ .”
  
  What is Jemma's number?
  Worked solution
  Being written
15. 15
  A box contains $220$ matches and weighs $45 \rtqMathsUnit{grams}$ .
  
  The empty box weighs $12 \rtqMathsUnit{grams}$ .
  
  Calculate the weight of one match.
  Worked solution
  Being written
16. 16
  Sapna makes a fruit salad using bananas, oranges and apples.
  
  For every one banana, she uses $2$ oranges and $3$ apples.
  
  Sapna uses $24$ fruits.
  
  How many oranges does she use?
  Worked solution
  Being written
17. 17
  In a country dance there are $3$ boys and $2$ girls in every line.
  
  $42$ boys take part in the dance. How many girls take part?
  Worked solution
  Being written
18. 18
  The diagram shows a shaded triangle inside a larger triangle:
  
  The area of the shaded triangle is $52 \rtqMathsUnit{cm}^2$ .
  
  The area of the shaded triangle is $\dfrac{4}{9}$ of the area of the larger triangle.
  
  Calculate the area of the larger triangle.
  Worked solution
  Being written
19. 19
  $17$ multiplied by itself gives a $3$ -digit answer:
  
  $\rtqMathsSizeEight{\rtqMathsBoxedValue{1}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{7}} \rtqMathsSpaceQuarterEm \times \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{1}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{7}} \rtqMathsSpaceQuarterEm = \rtqMathsSizeEight{\rtqMathsBoxedValue{2}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{8}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{9}}$
  
  Find the smallest $2$ -digit number that can be multiplied by itself to give a $4$ -digit answer, and put all the numbers in the boxes below:
  
  $\rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \times \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm = \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide}$
  Worked solution
  Being written
20. 20
  Write in the missing digits (one digit in each space):
  
  $323 \times \rtqMathsEllipsisEmptyValueOneDigitWide \rtqMathsSpaceOneSixthEm 7 = 1518 \rtqMathsSpaceOneSixthEm \rtqMathsEllipsisEmptyValueOneDigitWide$
  Worked solution
  Being written
Section B
Questions 1–10
1. 1
  In the diagram below, we want to complete the pattern of $3$ shaded and $4$ unshaded hexagons.
  
  Which hexagon do I shade for my final pattern to have exactly $2$ lines of symmetry?
  
  Worked solution
  Being written
2. 2
  In the grid below, each letter represents a number. The numbers on the right hand side represent the total of each row, and the numbers at the bottom show the totals of each column.
  
  Which numbers should replace each of the letters?
  
  $A$ $D$ $D$ $D$ $29$
  $B$ $A$ $B$ $D$ $27$
  $C$ $B$ $C$ $B$ $x$
  $A$ $A$ $A$ $A$ $32$
  $31$ $y$ $30$ $28$
  Worked solution
  Being written
3. 3
  I am thinking of a number that when I multiply it by two and divide the result by four, then multiply the result of that by itself, gives me a number that when I subtract four and divide by ten, gives me six.
  
  What is the number that I originally thought of?
  Worked solution
  Being written
4. 4
  My watch is set to show the correct time at $12$ noon on Wednesday.
  
  It gains $4 \rtqMathsUnit{minutes}$ every $3 \rtqMathsUnit{hours}$ .
  4.a
  What time does the watch show when the correct time is $12$ noon on Friday, assuming the watch has not been reset again?
  4.b
  The watch is reset again to show the correct time at $12$ noon on Friday.
  
  What is the correct time when the watch is showing $19 \rtqMathsTimeSeparator 40$ on Friday night?
  Worked solution
  Being written
5. 5
  Three apples and a banana cost $32 \rtqMathsUnitCurrencyPence$ . Six apples and a banana cost $53 \rtqMathsUnitCurrencyPence$ .
  
  How much does one banana cost?
  Worked solution
  Being written
6. 6
  The combined age of Alan and Ben is forty three.
  
  The combined age of Alan and Carl is fifty five and the combined age of Ben and Carl is sixty-six.
  6.a
  What is the combined age of Alan, Ben and Carl?
  6.b
  How old is Alan?
  Worked solution
  Being written
7. 7
  A palindromic number is a number that can be read the same forwards and backwards, e.g. $33$ and $797$ .
  
  How many of such numbers are there between $10$ and $1000$ ?
  Worked solution
  Being written
8. 8
  After a card game, four gamblers had $\rtqMathsSymbolPound 234$ between them. Harry had $\rtqMathsSymbolPound 20$ more than Dana, Charlotte had $\rtqMathsSymbolPound 53$ more than Dana and Sid had $\rtqMathsSymbolPound 71$ more than Dana.
  
  How much did each of them have?
  Worked solution
  Being written
9. 9
  There are $6 \rtqMathsUnit{fangos}$ in a rango and $15 \rtqMathsUnit{rangos}$ in a bango.
  9.a
  Alex has $9 \rtqMathsUnit{rangos}$ and $4 \rtqMathsUnit{fangos}$ . Barbara has $7 \rtqMathsUnit{rangos}$ and $3 \rtqMathsUnit{fangos}$ .
  
  How many fangos do they both have in total?
  9.b
  What fraction of a bango do $12 \rtqMathsUnit{fangos}$ represent?
  9.c
  How many whole bangos are there in $274 \rtqMathsUnit{fangos}$ ?
  
  How many fangos are left over?
  Worked solution
  Being written
10. 10
  Four of the five jigsaw pieces shown below fit together to make a square.
  
  Which one of these diagrams does not fit?
  
  Worked solution
  Being written

Section C

Questions 1–5

The numbers $1$ to $500$ are arranged in order in a table:

	Column $1$	Column $2$	Column $3$	Column $4$	Column $5$	Column $6$	Column $7$
Row $1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Row $2$	$8$	$9$	$10$	$11$	$12$	$13$	$14$
Row $3$	$15$	$16$	$17$	$18$	$19$	$20$	$21$
Row $4$	$22$	$23$	$24$	$25$	$26$	$27$	$28$

Only rows $1, 2, 3$ and $4$ are shown, but there are many more rows.

1.a
What do you notice about the numbers in column $7$ ?
1.b
What is the last number in row $8$ ?
1.c
What is the last number in row $100$ ?
1.d
$77$ is the last number in which row?
1.e
What is the number in row $12$ and column $3$ ?
1.f
What row and column will contain the number $400$ ?

Worked solution

Being written

2
You are told that:

$N_{5}$ means “add up the first $5$ counting numbers”, so $N_{5} = 1 + 2 + 3 + 4 + 5 = 15$

$O_{3}$ means “add up the first $3$ odd numbers”, so $O_{3} = 1 + 3 + 5 = 9$

$E_{4}$ means “add up the first $4$ even numbers”, so $E_{4} = 2 + 4 + 6 + 8 = 20$ and so on.
1. 2.a
  Work out the following:
  2.a.i
  $E_{7} =$
  2.a.ii
  $N_{8} =$
  2.a.iii
  $N_{9} =$
2. 2.b
  Find the value of $N_{401} - N_{400}$ .
3. 2.c
  There is a different way of finding, for example, $O_{7}$ :
  
  $\begin{aligned} O_1 &= 1 = 1^2 \\\\ O_2 &= 1 + 3 = 4 = 2^2 \\\\ O_3 &= 1 + 3 + 5 = 9 =3^2 \\ & \vdots \\ O_7 &= 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 = 7^2 \end{aligned}$
  
  Find the value of:
  
  $O_{13} =$
4. 2.d
  Notice that $N_{6}$ can be split into $2$ parts to make the calculation easier:
  
  $N_{6} = 1 + \rtqMathsHighlight{2} + 3 + \rtqMathsHighlight{4} + 5 + \rtqMathsHighlight{6} = O_{3} + \rtqMathsHighlight{E_{3}}$
  
  Complete the following line by filling in the boxes.
  
  $N_{10} = \rtqMathsSpaceQuarterEm O_{ \rtqMathsBoxedEmptyValueOneDigitWide } \rtqMathsSpaceQuarterEm + \rtqMathsSpaceQuarterEm E_{ \rtqMathsBoxedEmptyValueOneDigitWide }$
5. 2.e
  You are told that $N_{200} = 20100$ and $N_{401} = 80601$ .
  
  Use this information to work out the following:
  2.e.i
  $E_{100} =$
  2.e.ii
  $E_{200} =$
Worked solution
Being written
3
The letters on the $7$ cards below have a number $1, 2, 3, 4, 5, 6$ or $7$ on the back, but not in that order.

$\rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{S}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{t}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{P}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{a}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{u}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{l}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{s}}$

If $\rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{s}}$ has the number $1$ on the back and the cards

$\rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{s}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{a}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{t}}$ add up to $8$ ,

$\rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{s}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{a}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{P}}$ add up to $9$ ,

$\rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{l}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{a}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{P}}$ add up to $11$ .
1. 3.a
  What does $\rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{s}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{a}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{l}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{t}}$ add up to?
2. 3.b
  What does $\rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{s}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{P}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{l}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{a}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedCellTwoDigitsWideOneDigitHigh{t}}$ add up to?
Worked solution
Being written
4
You are told that the opposite sides of a cube add up to $13$ .

Find the sum of the faces that border with the marked corner:

For example, the sum of the faces $= 3 + 5 + 9 = 17$ .
1. 4.a
  Find the sum of the faces that border with the marked corner for the following:
  4.a.i
  4.a.ii
2. 4.b
  The same cube is rolled so a $10$ is on top.
  
  Fill in the missing sides so that the sum of the faces that border with the marked corner is $27$ .
3. 4.c
  The same cube is rolled so an $8$ is on top.
  
  Write down all possibilities for the sum of the missing faces that border with the marked corner.
  
  You MUST show your working.
Worked solution
Being written
5
On the island of Mathia the people use patterns instead of numbers like ours.

Here are some facts about Mathian numbers:

$\begin{aligned} \rtqMathsSymbolCircledReverseSolidus + \rtqMathsSymbolCircledReverseSolidus &= \rtqMathsSymbolWhiteSquare \\\\ \rtqMathsSymbolCircledReverseSolidus + \rtqMathsSymbolBlackSquare &= \rtqMathsSymbolWhiteSquare + \rtqMathsSymbolCircledDot \\\\ \rtqMathsSymbolCircledDot + \rtqMathsSymbolBoxTimes &= \rtqMathsSymbolWhiteSquare + \rtqMathsSymbolBlackSquare \end{aligned}$

Now answer these questions.

(Give your answer in Mathian numbers using just ONE symbol).
1. 5.a
  $\rtqMathsSymbolWhiteSquare - \rtqMathsSymbolCircledReverseSolidus =$
2. 5.b
  $\rtqMathsSymbolCircledReverseSolidus + \rtqMathsSymbolWhiteSquare =$
3. 5.c
  $\rtqMathsSymbolCircledReverseSolidus + \rtqMathsSymbolCircledDot =$
Worked solution
Being written

$A$	$D$	$D$	$D$	$29$
$B$	$A$	$B$	$D$	$27$
$C$	$B$	$C$	$B$	$x$
$A$	$A$	$A$	$A$	$32$
$31$	$y$	$30$	$28$

St Paul's Girls' School Paper 1

Questions

Section A

Section B

Section C