Eltham College 2019 Paper 2

IndependentCo-ed

23 questions
2 sections

Original PDFWorked solutions in progress

Questions

Section A
Questions 1–20
1. 1
  What is the difference between the largest and the smallest of the following numbers:
  
  $0.9 \rtqMathsListSeparator 0.17 \rtqMathsListSeparator 0.72 \rtqMathsListSeparator 0.73$
  
  $0.9$
  
  $0.17$
  
  $0.72$
  
  $0.73$
  
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2. 2
  What is the smallest four-digit positive integer which has four different digits?
  
  $1032$
  
  $1021$
  
  $1234$
  
  $1023$
  
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3. 3
  What is $(999 - 99 + 9) \div 9$ ?
  
  $99$
  
  $100$
  
  $101$
  
  $109$
  
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4. 4
  Each block shown in this tower will have a number displayed on it. Some are already done.
  
  For each block above the bottom row, the number on it is the sum of the numbers on the two blocks it stands upon. What number should replace $n$ ?
  
  $\rtqMathsBoxedCellArrayFractionHighStyle \begin{array}{c} \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{65} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{34} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{15} \\ \rtqMathsBoxedCellFourDigitsWideFractionHigh{n} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{9} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{} \rtqMathsBoxedCellSeparator \rtqMathsBoxedCellFourDigitsWideFractionHigh{7} \end{array}$
  
  $6$
  
  $10$
  
  $11$
  
  $13$
  
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5. 5
  The number $987 \rtqMathsDigitGroupSeparator 654 \rtqMathsDigitGroupSeparator 321$ is multiplied by $9$ . How many times does the digit $8$ occur in the result?
  
  $1$
  
  $2$
  
  $3$
  
  $9$
  
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6. 6
  Which of the following has the same remainder when it is divided by $2$ as when it is divided by $3$ ?
  
  $5$
  
  $7$
  
  $9$
  
  $11$
  
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7. 7
  What is the value of $19 + 99 + 19 \times 99$ ?
  
  $1999$
  
  $11701$
  
  $13563$
  
  None of these
  
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8. 8
  In this diagram what is the value of $x$ ?
  The triangle has a horizontal base extended to the left. The 100-degree label at the left base vertex and x-degree label at the top are text-only sectors. A visible major reflex arc at the right base vertex is labelled 324 degrees.
  
  $36$
  
  $64$
  
  $100$
  
  $144$
  
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9. 9
  How many triangles of any size are there in this diagram?
  Both diagonals and the horizontal line meet at the rectangle's centre, dividing the rectangle into several triangular regions.
  
  $8$
  
  $10$
  
  $12$
  
  $14$
  
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10. 10
  Which of these calculations produces a multiple of $5$ ?
  
  $1 + 2 \times 3 + 4$
  
  $1 \times 2 + 3 \times 4$
  
  $1 + 2 \times 3 \times 4$
  
  $1 \times 2 \times 3 \times 4$
  
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11. 11
  It was reported recently that in an average lifetime of $70 \rtqMathsUnit{years}$ , each human is likely to swallow about $8$ spiders while sleeping. Supposing that the population of the UK is around $60 \rtqMathsUnit{million}$ , what is the best estimate of the number of spiders that are consumed in this way in the UK each year?
  
  $600 \rtqMathsDigitGroupSeparator 000$
  
  $7 \rtqMathsDigitGroupSeparator 000 \rtqMathsDigitGroupSeparator 000$
  
  $80 \rtqMathsDigitGroupSeparator 000 \rtqMathsDigitGroupSeparator 000$
  
  $900 \rtqMathsDigitGroupSeparator 000 \rtqMathsDigitGroupSeparator 000$
  
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12. 12
  Which of the following is divisible by all of the numbers from $1$ to $10$ inclusive?
  
  $34 \times 45$
  
  $45 \times 56$
  
  $56 \times 27$
  
  $67 \times 78$
  
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13. 13
  Which one of these calculations is incorrect?
  
  $4 \times 5 + 67 = 45 + 6 \times 7$
  
  $3 \times 7 + 48 = 37 + 4 \times 8$
  
  $2 \times 5 + 69 = 25 + 6 \times 9$
  
  $9 \times 6 + 73 = 96 + 7 \times 3$
  
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14. 14
  If the following fractions are arranged in increasing order of size, which one is the smallest?
  
  $\dfrac{1}{2}$
  
  $\dfrac{3}{5}$
  
  $\dfrac{4}{7}$
  
  $\dfrac{5}{9}$
  
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15. 15
  In the sequence which begins $2, 3, 5, 10, \rtqMathsSequenceEllipsis$ each number after the second is the sum of all the previous numbers in the sequence.
  
  What is the $10^\text{th}$ number in the sequence?
  
  $47$
  
  $170$
  
  $640$
  
  $1280$
  
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16. 16
  Which of the following calculation is correct for the area of the shape?
  The L-shaped figure has a top side labelled 5 m, a left side labelled 10 m, an inner vertical side labelled 6 m and a bottom side labelled 9 m.
  
  $10 \times 6 + 5 \times 4$
  
  $10 \times 5 + 9 \times 6$
  
  $9 \times 10 - 6 \times 4$
  
  They are all correct
  
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17. 17
  When $x = 1.5$ what is the value of the perimeter of this triangular area?
  The triangle points to the left. Its upper sloping side is labelled 3x plus 1, its short right side 2x minus 2, and its lower sloping side 4x.
  
  $12$
  
  $12.5$
  
  $13$
  
  $13.5$
  
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18. 18
  Kieran thinks of a number. He doubles it and adds $6$ . He then divides it by $2$ . The answer is $8$ . What was his original number?
  
  $5$
  
  $11$
  
  $20$
  
  $-2$
  
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19. 19
  Which image completes the symmetric figure using the dashed line of symmetry?
  An eight-by-eight square grid has a dashed diagonal line from the top-left corner to the bottom-right corner. Counting intersections from the bottom-left, the open solid outline follows (2, 6), (2, 5), (1, 5), (1, 4), (2, 4), (2, 3), (4, 3) and ends at (4, 4). Both open endpoints lie on the diagonal.
  
  An eight-by-eight square grid has a dashed diagonal from top left to bottom right. Counting intersections from the bottom-left, the closed outline follows (3,7), (4,7), (4,6), (5,6), (5,4), (4,4), (4,3), (2,3), (2,4), (1,4), (1,5), (2,5), (2,6) and (3,6).
  
  An eight-by-eight square grid has a dashed diagonal from top left to bottom right. Counting intersections from the bottom-left, the closed outline follows (4,7), (5,7), (5,4), (4,4), (4,3), (2,3), (2,4), (1,4), (1,5), (2,5), (2,6) and (4,6).
  
  An eight-by-eight square grid has a dashed diagonal from top left to bottom right. Counting intersections from the bottom-left, the closed outline follows (2,6), (4,6), (4,3), (2,3), (2,4), (1,4), (1,5) and (2,5).
  
  An eight-by-eight square grid has a dashed diagonal from top left to bottom right. Counting intersections from the bottom-left, the closed outline follows (3,7), (4,7), (4,5), (5,5), (5,4), (4,4), (4,3), (2,3), (2,4), (1,4), (1,5), (2,5), (2,6) and (3,6).
  
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20. 20
  I choose three numbers from this number square, including one number from each row and one number from each column.
  
  I then multiply the three numbers together.
  
  What is the largest possible product?
  
  $1$ $2$ $3$
  $4$ $5$ $6$
  $7$ $8$ $9$
  
  $96$
  
  $105$
  
  $162$
  
  $504$
  
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Section B
Questions 1–3
1. 1
  A swimming pool has a length that is four times its width.
  
  The length and width are both multiples of $5$ .
  
  The perimeter is less than $150 \rtqMathsUnit{m}$ .
  
  How many different widths could it have?
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2. 2
  The numbers from $1$ to $9$ inclusive are to be placed, one number in each square, into the shape shown below, so that the total of the three numbers in each of the four lines is the same.
  Nine equal square cells join edge to edge in a W-shaped strip. From left to right along the strip, the cells contain: blank, blank, 1, an asterisk, 4, blank, 2, blank, blank. Each sloping run contains three cells; neighbouring runs share an end cell.
  Which number should replace $\rtqMathsSymbolAsterisk$ ?
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3. 3
  $\rtqMathsColumnarArithmeticStyle \begin{array}{ccccc} & F & O & U & R \\ & F & O & U & R \\ {}+ & F & O & U & R \\ \hline T & H & R & E & E \end{array}$
  
  In this word sum, each letter represents a different digit. What digit does each letter represent?
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