Built in the openQuestions and original PDFs available now. We’re adding worked solutions.

The North London Independent Girls’ Schools’ Consortium 2010 Group 2

IndependentGirls

42 questions

Original PDFWorked solutions in progress

Questions

1. 1
  $\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 3 & 9 & 7 & 4 \\ {}+ & & 2 & 5 & 8 \\ \hline\\ \hline \end{array}$
  Worked solution
  Being written
2. 2
  $\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 7 & 3 & 2 \\ {}- & 3 & 5 & 7 \\ \hline\\ \hline \end{array}$
  Worked solution
  Being written
3. 3
  Write in numbers thirty-two thousand and twenty-seven.
  Worked solution
  Being written
4. 4
  $\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 7 & 2 & 9 \\ \times & & & 7 \\ \hline & & & \end{array}$
  Worked solution
  Being written
5. 5
  Long-division question showing 34024 divided by 8 in division-bracket notation.
  Worked solution
  Being written
6. 6
  There is some coloured water in the jar.
  A vertical two-litre measuring cylinder has major, midpoint and smaller graduation ticks. The liquid level is halfway between one litre and one and a half litres.
  How much more water is needed to make $2 \rtqMathsUnit{litres}$ ?
  Worked solution
  Being written
7. 7
  Fill in the gaps in these number patterns:
  7.a
  $37 \rtqMathsListSeparator 34 \rtqMathsListSeparator 31 \rtqMathsListSeparator \rtqMathsSequenceEllipsis \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  7.b
  $0.8 \rtqMathsListSeparator 0.4 \rtqMathsListSeparator 0.2 \rtqMathsListSeparator \rtqMathsSequenceEllipsis \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  7.c
  $1 \rtqMathsListSeparator 3 \rtqMathsListSeparator 9 \rtqMathsListSeparator 27 \rtqMathsListSeparator \rtqMathsSequenceEllipsis \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  Worked solution
  Being written
8. 8
  The shape below is made up of square tiles. Which of tiles $A, B, C, D$ or $E$ could be removed so that the perimeter remained the same?
  
  Circle your answer.
  
  Worked solution
  Being written
9. 9
  Five bags of apples cost $\rtqMathsSymbolPound 3.25$ .
  
  How much would seven bags of apples cost?
  Worked solution
  Being written
10. 10
  Circle the numbers which are larger than $\dfrac{1}{3}$
  
  $0.25 \rtqMathsListSeparator \dfrac{2}{9} \rtqMathsListSeparator 0.039 \rtqMathsListSeparator \dfrac{4}{5} \rtqMathsListSeparator \dfrac{3}{8}$
  Worked solution
  Being written
11. 11
  Write down the number which is $21$ less than $2000$ .
  Worked solution
  Being written
12. 12
  These are the start and finish times on a DVD recorder:
  
  $\begin{array}{ll} \text{START} & 14 \rtqMathsTimeSeparator 48 \\\\ \text{FINISH} & 17 \rtqMathsTimeSeparator 25 \end{array}$
  
  For how long was the video recording?
  Worked solution
  Being written
13. 13
  There were $500$ cats in a survey about two new cat foods, Moggy Nosh and Feline Fodder.
  
  $220$ were Persians and the rest were Siamese.
  
  $80$ cats preferred Moggy Nosh.
  
  Of these, $42$ were Persians.
  
  Use this informaation to complete this table.
  
  Persian Siamese
  Prefer Feline Fodder
  Prefer Moggy Nosh
  Worked solution
  Being written
14. 14
  Find the missing digit to make the calculation correct:
  
  $\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 4 & A \\ \times & & A \\ \hline 3 & 2 & 9 \end{array}$
  Worked solution
  Being written
15. 15
  The pupils in a Mathematics class were asked which sport they enjoyed the most. The answers given are shown in the bar graph below:
  
  15.a
  How many more pupils answered Netball than Badminton?
  15.b
  Two pupils in the class were away the day the question was asked.
  
  How many pupils in total are in the class?
  Worked solution
  Being written
16. 16
  Jenn's fish tank was filled half way. She added $9 \rtqMathsUnit{gallons}$ of water to the tank and found that it was then $\dfrac{7}{8}$ full.
  
  How much water can the tank hold altogether?
  Worked solution
  Being written
17. 17
  17.a
  The area of the small shaded square is $1 \rtqMathsUnit{square centimetre}$ .
  
  What is the area of the larger shaded square?
  
  17.b
  In the grid below, draw a square with an area of $2 \rtqMathsSpaceQuarterEm \text{cm}^2$ .
  
  Worked solution
  Being written
18. 18
  The pie chart shows the results of the $96$ games played by a school football team. They lost $25\%$ of their games and won and drew an equal number of games.
  
  How many games were:
  18.a
  lost
  18.b
  won
  Worked solution
  Being written
19. 19
  Two girls were on a sponsored walk from Pangbourne to Goring.
  
  One of them gave up $5 \rtqMathsUnit{km}$ after she had passed the half-way check-point.
  
  She was then $10 \rtqMathsUnit{km}$ from Goring.
  
  How far apart are the towns?
  Worked solution
  Being written
20. 20
  Mrs Jones prints books.
  
  PRINT CHARGES
  $3 \rtqMathsUnitCurrencyPence$ per page
  $75 \rtqMathsUnitCurrencyPence$ for the cover
  
  Jon pays $\rtqMathsSymbolPound 4.35$ for his book, including the cover.
  
  How many pages are in his book?
  Worked solution
  Being written
21. 21
  This is a right angled triangular tile:
  
  Write how many of these tiles you can fit into each of the following shapes.
  21.a
  21.b
  Worked solution
  Being written
22. 22
  Numbers are placed in a triangle.
  
  The numbers in the middle of the sides are the sum of the numbers at the ends.
  
  Fill in the missing numbers for this triangle:
  
  Worked solution
  Being written
23. 23
  23.a
  Find the angle between the hands of a clock at $11 \rtqMathsTimeAm$ .
  23.b
  How many degrees has the minute hand moved between $3.55 \rtqMathsTimePm$ and $5.15 \rtqMathsTimePm$ .
  Worked solution
  Being written
24. 24
  A piece of wire $36 \rtqMathsUnit{cm}$ long is bent into the shape of a rectangle.
  
  If the rectangle is twice as long as it is wide, what is the area?
  Worked solution
  Being written
25. 25
  A boy ate $100$ cookies in five days. Each day he ate $6$ more than the day before.
  
  How many cookies did he eat on the first day?
  Worked solution
  Being written
26. 26
  The diagram shows the number of paths from Queton to Toytown through Rowton or Seton.
  
  How many different ways are there of getting from Queton to Toytown if you can only go from left to right?
  Worked solution
  Being written
27. 27
  Here is a number pattern:
  
  $\text{A}$ $\text{B}$ $\text{C}$ $\text{D}$
  shaded $1$ $2$ $3$
  $6$ $5$ $4$ shaded
  shaded $7$ $8$ $9$
  $12$ $11$ $10$ shaded
  shaded
  shaded
  27.a
  Complete the next two rows of the table.
  27.b
  If the pattern continued, write down the correct column letter for each of these numbers:
  27.b.i
  $29$
  27.b.ii
  $54$
  27.b.iii
  $141$
  Worked solution
  Being written
28. 28
  Here are some number cards:
  
  $\rtqMathsSizeEight{\rtqMathsBoxedValue{3}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{9}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{2}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{7}}$
  
  You can use each card once to make the number $3927$ , like this:
  
  $\rtqMathsSizeEight{\rtqMathsBoxedValue{3}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{9}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{2}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{7}}$
  
  Use the four number cards to make numbers that are as close as possible to the numbers written below.
  
  Example:
  
  $8000 \rightarrow \rtqMathsSizeEight{\rtqMathsBoxedValue{7}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{9}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{3}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{2}}$
  
  You must not use the same card more than once in each answer.
  28.a
  $3000 \rightarrow \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide}$
  28.b
  $7000 \rightarrow \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide}$
  28.c
  $3800 \rightarrow \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide}$
  Worked solution
  Being written
29. 29
  Jemima has five cards which are numbered from $1$ to $5$ on one side, and have either a square, a circle, a triangle or a star drawn on the other side.
  
  She knows that there is at least one card with each shape and that the odd numbered cards do not have squares on them. Card number $4$ has a circle on it, and two cards that have a sum of $6$ both have stars on them.
  
  What shape is on card $3$ ?
  Worked solution
  Being written
30. 30
  A number of children are standing in a circle. They are evenly spaced and the $7^{\text{th}}$ child is directly opposite the $18^{\text{th}}$ child.
  
  How many children are there altogether?
  Worked solution
  Being written
31. 31
  Four years ago the combined age of $3$ dogs was $24$ years.
  
  What will the combined age be in $2$ years' time?
  Worked solution
  Being written
32. 32
  A Year $6$ class has $30$ pupils. There are $21$ who are right-handed. There are $16$ girls in the class.
  
  Not all the girls are right-handed.
  
  What is the smallest number of girls who are right-handed?
  Worked solution
  Being written
33. 33
  A wheel has $3$ different colours painted on its rim, red ( $\text{R}$ ), green ( $\text{G}$ ) and yellow ( $\text{Y}$ ).
  
  As it turns, a pattern is left on the ground.
  
  The first mark is yellow, and the second mark is red, so the pattern left on the ground will be:
  
  $\text{Y} \rtqMathsListSeparator \text{R} \rtqMathsListSeparator \text{G} \rtqMathsListSeparator \text{Y} \rtqMathsListSeparator \text{R} \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  33.a
  What is the colour of the $20^{\text{th}}$ mark?
  33.b
  Another wheel makes the pattern:
  
  $\text{G} \rtqMathsListSeparator \text{Y} \rtqMathsListSeparator \text{Y} \rtqMathsListSeparator \text{R} \rtqMathsListSeparator \text{G} \rtqMathsListSeparator \text{Y} \rtqMathsListSeparator \text{Y} \rtqMathsListSeparator \text{R} \rtqMathsListSeparator \text{G} \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  
  What is the colour of the $38^{\text{th}}$ mark?
  33.c
  Another wheel has $6$ different colours. No colour is repeated.
  
  If red is the $83^{\text{rd}}$ colour in the pattern, how many colours are at the start of the pattern before red occurs?
  Worked solution
  Being written
34. 34
  Some marbles are released through this network from $\text{S}$ .
  
  At each of the junctions, half of the marbles flow in each direction.
  
  34.a
  What fraction of the marbles go through $\text{E}$ ?
  34.b
  If $120$ marbles are released through the network, how many do not reach $\text{F}$ ?
  Worked solution
  Being written
35. 35
  It takes two decorators $8$ days to paint a house.
  
  One is lazy and one is energetic.
  
  The energetic one could paint the house in $12$ days on his own.
  
  How many days would it take the lazy one to paint the house on his own?
  Worked solution
  Being written
36. 36
  Work out the perimeter of the following shape.
  
  All the interior angles are right angles.
  
  The shape is not drawn accurately.
  
  Worked solution
  Being written
37. 37
  Three ducks and two ducklings weigh $32 \rtqMathsUnit{kg}$ . Four ducks and three ducklings weigh $44 \rtqMathsUnit{kg}$ . All ducks weigh the same as each other and all ducklings weigh the same as each other.
  
  What is the weight of two ducks and one duckling?
  Worked solution
  Being written
38. 38
  Use each number from $1$ to $8$ once in the boxes to make all the calculations correct:
  
  Worked solution
  Being written
39. 39
  39.a
  In a game two discs are tossed and the numbers landing uppermost are added together.
  
  The red disc has the number $3$ on one side and $5$ on the other side; whereas the blue disc has $4$ on one side and $7$ on the other.
  
  If they land so that $3$ and $7$ are showing, the score is $10$ .
  
  Write down the other possible scores for this game.
  39.b
  In a new game a green disc has $6$ on one side and $4$ on the other. A yellow disc has $1$ on one side and $3$ on the other. The rules are the same.
  
  Find the score which you are most likely to get.
  39.c
  In another game a pink disc has $8$ on one side, but on the other side is a mystery number, and a purple disc has $4$ on one side with a different mystery number on the back.
  
  The four possible total scores are $12, 13, 14, 15$ .
  
  Find two possible pairs of values for the mystery numbers.
  Worked solution
  Being written
40. 40
  Each of the symbols has a different value associated with it. When you add up the value of all the symbols you get the total value for that row or column.
  
  Find the value of each symbol.
  
  $99$
  $99$
  $154$
  $99$
  $142$ $99$ $\rtqMathsQuestionMarkPlaceholder$ $99$ shaded
  Worked solution
  Being written
41. 41
  A square grid is separated into $16$ small squares.
  
  How many ways can two squares be shaded so that the grid has symmetry about the diagonal line $AC$ if:
  
  41.a
  The two squares must not include the diagonal line?
  41.b
  The two squares must include the diagonal line?
  41.c
  On the grids below, show all the ways exactly two squares can be shaded so that the grid has symmetry about the two diagonal lines, $AC$ and $BD$ .
  
  (You may not need to use all the grids).
  
  Worked solution
  Being written
42. 42
  On the planet Arithmetica, the natives have a special sort of arithmetic using the symbol $\rtqMathsSymbolTaurus$ .
  
  For example, $5 \rtqMathsBinaryOperatorTaurus 3$ means double $5$ then subtract $3$ .
  
  So,
  
  $\begin{aligned} 5 \rtqMathsBinaryOperatorTaurus 3 &= 2 \times 5 - 3 \\\\ &= 10 - 3 \\\\ &= 7 \end{aligned}$
  42.a
  Work out $8 \rtqMathsBinaryOperatorTaurus 6$
  42.b
  They also use this symbol twice:
  
  For example,
  
  $\begin{aligned} (5 \rtqMathsBinaryOperatorTaurus 3) \rtqMathsBinaryOperatorTaurus 2 &= (2 \times 5 - 3) \rtqMathsBinaryOperatorTaurus 2 \\\\ &= 7 \rtqMathsBinaryOperatorTaurus 2 \\\\ &= 2 \times 7 - 2 \\\\ &= 14 - 2 \\\\ &= 12 \end{aligned}$
  
  Work out $(9 \rtqMathsBinaryOperatorTaurus 4) \rtqMathsBinaryOperatorTaurus 3$
  42.c
  If $(6 \rtqMathsBinaryOperatorTaurus n) \rtqMathsBinaryOperatorTaurus 10 = 8$ , what is the number $n$ ?
  Worked solution
  Being written