Kent College Canterbury Paper 1

IndependentCo-ed

23 questions

Original PDFWorked solutions in progress

Questions

1. 1
  Calculate and show all your working,
  1.a
  $465 + 67 =$
  1.b
  $4177 - 1315$
  1.c
  $67 \times 7 =$
  1.d
  $402 \div 6 =$
  1.e
  $\rtqMathsSymbolPound 20 - \rtqMathsSymbolPound 12.53$
  1.f
  $41 × 63 =$
  Worked solution
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2. 2
  Write down the answer to each of the following.
  2.a
  $201 \times 10$
  2.b
  $700 \div 10$
  2.c
  $201 \times 2000$
  2.d
  $52 \rtqMathsSpaceQuarterEm 000 \div 200$
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3. 3
  Calculate $2943 \div 27$ . Show your working.
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4. 4
  Work out
  4.a
  $12 + 6 \div 3$
  4.b
  $26 -(19+4)$
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5. 5
  5.a
  Find $\dfrac{1}{2}$ of $72$ .
  5.b
  Find $\dfrac{3}{4}$ of $28$ .
  5.c
  Find $\dfrac{3}{5}$ of $40$ .
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6. 6
  A balloon pump and three packs of balloons cost $\rtqMathsSymbolPound 9$ altogether.
  
  A balloon pump and four packs of balloons cost $\rtqMathsSymbolPound 11$ altogether.
  6.a
  How much does a pack of balloons cost?
  6.b
  How much does a balloon pump and eight packs of balloons cost?
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7. 7
  Draw an extra line to give each shape below one line of symmetry.
  7.a
  An unnumbered eight-column by seven-row grid has no bottom boundary. A bold horizontal line spans three cells from (2, 3) to (5, 3), and a bold one-cell branch rises from (4, 3) to (4, 4), using the bottom-left corner as (0, 0). Only the supplied lines are shown.
  7.b
  An unnumbered eight-column by seven-row grid has no bottom boundary. A bold open line runs from (3, 4) down to (3, 3), right to (4, 3), up to (4, 4), then right to (5, 4), using the bottom-left corner as (0, 0). Only the supplied line is shown.
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8. 8
  Place the following sets of numbers in order, smallest first.
  8.a
  $47, \rtqMathsListSeparator 63, \rtqMathsListSeparator 18, \rtqMathsListSeparator 103, \rtqMathsListSeparator 70$
  8.b
  $0.731, \rtqMathsListSeparator 0.8, \rtqMathsListSeparator 0.73 , \rtqMathsListSeparator 0.711$
  8.c
  $1 \rtqMathsUnit{m} \rtqMathsSpaceQuarterEm 43 \rtqMathsUnit{cm}, \rtqMathsListSeparator 140 \rtqMathsUnit{cm}, \rtqMathsListSeparator 1 \rtqMathsUnit{m} \rtqMathsSpaceQuarterEm 6 \rtqMathsUnit{cm}, \rtqMathsListSeparator 1423 \rtqMathsUnit{mm}$
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9. 9
  9.a
  What fraction of this shape is shaded?
  The upper-left two-by-two block is shaded, together with the cell directly below its left-hand column.
  9.b
  How much of this square is shaded? Write your answer as a decimal.
  The first three columns are fully shaded, together with the upper five cells of the fourth column.
  Worked solution
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10. 10
  Fill in the gaps in the sequences.
  10.a
  $7, \rtqMathsListSeparator 15, \rtqMathsListSeparator 23, \rtqMathsListSeparator 31, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  10.b
  $42, \rtqMathsListSeparator 33, \rtqMathsListSeparator 24, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 6, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
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11. 11
  Write in the missing numbers.
  11.a
  $12 - \rtqMathsBoxedEmptyValueTwoDigitsWide = -1$
  11.b
  $5 \times \rtqMathsBoxedEmptyValueTwoDigitsWide = 460$
  11.c
  $52 \div \rtqMathsBoxedEmptyValueTwoDigitsWide = 13$
  11.d
  $\dfrac{2}{5} \rtqMathsBinaryOperatorOf \rtqMathsBoxedEmptyValueTwoDigitsWide = 12$
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12. 12
  12.a
  Work out $50 \%$ of $58 \rtqMathsUnit{m}$ .
  12.b
  Work out $75 \%$ of $\rtqMathsSymbolPound 24$ .
  12.c
  Work out $10 \%$ of $130$ .
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13. 13
  A number line starts at $-9$ and finishes at $11$ .
  
  What number is $\dfrac{2}{5}$ of the way along the number line?
  Only the endpoint ticks and labels minus 9 and 11 are shown. A downward pointer marks a position two-fifths of the way from the left endpoint to the right endpoint.
  Show your working.
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14. 14
  A train leaves Carlisle station at $3.37 \rtqMathsTimePm$ and arrives in London at $6.48 \rtqMathsTimePm$ .
  
  How long did the journey take?
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15. 15
  15.a
  Look at this information about recycling:
  
  “ $25$ large plastic bottles can be recycled to make $1$ fleece jacket.”
  
  Write the missing number in this sentence.
  
  $200$ large plastic bottles can be recycled to make $\rtqMathsUnderlineEmptyValueLong$ fleece jackets.
  15.b
  In a survey, $9$ out of $10$ people said they would like to recycle more.
  
  What percentage of people said they would like to recycle more?
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16. 16
  The diagram shows four identical white rectangles around a shaded square.
  Four identical white rectangles form a pinwheel around one lightly shaded central square. One rectangle is labelled 8 cm along its long side and 3 cm along its short side. A caption says Not drawn accurately.
  Not drawn accurately
  
  What is the area of the shaded square?
  Worked solution
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17. 17
  I put square tiles on a large grid so that the tiles touch at the corners.
  
  The diagram shows part of my diagonal pattern.
  A square coordinate grid extends from 0 to 7.5 on both axes, with labelled ticks from 0 to 7. Seven complete filled unit-square tiles form a diagonal staircase from tile 1 in the lower-left to tile 7 in the upper-right. The visible lower-left quarter of tile 8 continues beyond the cropped upper-right edge. A filled point marks the shared corner at (2, 1).
  17.a
  The bottom right-hand corner of tile $2$ is marked with a ●
  
  Write the coordinates of this point.
  17.b
  Tile $4$ touches two other tiles.
  
  Write the coordinates of the points where tile $4$ touches two other tiles.
  17.c
  Write the coordinates of the points where tile $17$ touches two other tiles.
  17.d
  I have $30$ tiles to make a pattern on a grid.
  
  The pattern is a series of squares.
  
  I have used some of the $30$ tiles to make my pattern.
  
  Do I have enough tiles left to make the next square, of side length $4$ ?
  
  Show working to explain your answer.
  A square coordinate grid extends from 0 to 7.5 on both axes, with labelled ticks from 0 to 7. A filled one-unit square occupies 0 to 1 on each axis. A filled two-by-two square occupies x=1 to 3 and y=1 to 3. A filled three-by-three square occupies x=3 to 6 and y=3 to 6. Internal unit boundaries remain visible, and an empty half-cell continuation remains beyond the final labelled grid lines.
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18. 18
  Tom is making patterns with matches.
  Pattern 1 contains four matchsticks arranged as the first stage of the repeated matchstick pattern. Pattern 2 contains eight matchsticks arranged as the second stage of the repeated matchstick pattern. Pattern 3 contains twelve matchsticks arranged as the third stage of the repeated matchstick pattern.
  18.a
  How many more matches will Tom need to make pattern $4$ ?
  18.b
  How many matches altogether will Tom need to make pattern $5$ ?
  18.c
  How many matches will Tom need to make pattern $12$ ?
  18.d
  Tom has a box containing $99$ matches. What is the largest pattern number he can make?
  
  Show any working.
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19. 19
  Mark is $3 \rtqMathsUnit{years}$ older than David. The sum of their ages is $89$ .
  
  How old is Mark?
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20. 20
  Some people use this rule to work out how many hours' sleep each night young children need.
  
  “Subtract the child's age in years from $30$ , then divide the result by $2$ ”
  20.a
  Sanjay is $8 \rtqMathsUnit{years}$ old.
  
  Use the rule to work out how many hours' sleep he needs.
  20.b
  Lisa is $6 \rtqMathsUnit{years}$ old.
  
  She wakes up every morning at $7 \rtqMathsTimeAm$ .
  
  Use the rule to work out what time she needs to go to sleep.
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21. 21
  Tariq wants to use four planks of wood to make the top of a table.
  
  Each plank of wood is $14 \rtqMathsUnit{cm}$ wide.
  
  He wants the table to be $65 \rtqMathsUnit{cm}$ wide with equal spaces between the planks of wood.
  Four identical horizontal planks are separated by three equal spaces. A dimension marks each plank as 14 cm wide, and another marks the complete arrangement as 65 cm wide.
  How much space should he leave between each of the planks of wood?
  
  Show your working.
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22. 22
  One way to make a magic square is to substitute numbers into this algebra grid.
  
  $a + b$ $a - b + c$ $a - c$
  $a - b -c$ $a$ $a +b+c$
  $a + c$ $a + b - c$ $a - b$
  22.a
  Complete the magic square below using the values $a = 10, b = 3, c = 5$ .
  
  $5$
  $10$
  $15$
  22.b
  Here is the algebra grid again.
  
  $a + b$ $a - b + c$ $a - c$
  $a - b -c$ $a$ $a +b+c$
  $a + c$ $a + b - c$ $a - b$
  
  I use different values for $a, b$ and $c$ to complete the magic square.
  
  $20$ $21$ $7$
  $3$ $16$ $29$
  $25$ $11$ $12$
  
  What values for $a, b$ and $c$ did I use?
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23. 23
  In this subtraction, $P, Q, R, S$ and $T$ represent single digits.
  
  $\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 7 & Q & 2 & S & T \\ {}- & P & 3 & R & 9 & 6 \\ \hline & 2 & 2 & 2 & 2 & 2 \end{array}$
  
  What is the value of $P + Q + S + T$ ?
  Worked solution
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$a + b$	$a - b + c$	$a - c$
$a - b -c$	$a$	$a +b+c$
$a + c$	$a + b - c$	$a - b$

		$5$
	$10$
$15$

$20$	$21$	$7$
$3$	$16$	$29$
$25$	$11$	$12$

		$5$
	$10$
$15$

$20$	$21$	$7$
$3$	$16$	$29$
$25$	$11$	$12$