Bancroft's School 2018 Paper 1

IndependentCo-ed

37 questions
2 sections

Original PDFWorked solutions in progress

Questions

Section A
Questions 1–30
1. 1
  Fill in the missing numbers in the boxes.
  1.a
  $2018 - \rtqMathsBoxedEmptyValueFourDigitsWide = 1989$
  1.b
  $0.5 \div \dfrac{1}{2} = \rtqMathsBoxedEmptyValueFourDigitsWide$
  1.c
  $18 + \rtqMathsBoxedEmptyValueFourDigitsWide + 23 = 67$
  1.d
  $\rtqMathsBoxedEmptyValueFourDigitsWide \times 5 \times 10 = 4500$
  1.e
  $\dfrac{3}{4}$ of $36 = \rtqMathsBoxedEmptyValueFourDigitsWide$
  1.f
  Write in figures the number two million, two hundred and two.
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2. 2
  Subtract $2018$ from $8102$ .
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3. 3
  Divide $(2018 - 20 + 18)$ by $8$ .
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4. 4
  Multiply $2018$ by $17$ .
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5. 5
  What number (written in digits) is twenty less than twenty thousand?
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6. 6
  6.a
  I thought of a number, halved it and then subtracted $9$ .
  
  I got an answer of $12$ .
  
  What was my original number?
  6.b
  Fawzan went shopping with $\rtqMathsSymbolPound 100$ in his wallet.
  
  He spent $10 \%$ of his money on a book and $20 \%$ of the rest on a DVD. How much money did he then have left?
  6.c
  Abdul is making some small snacks for a party.
  
  He cuts $1.2 \rtqMathsUnit{kg}$ of cheese into a number of $30 \rtqMathsUnit{g}$ pieces.
  
  How many pieces does he have?
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7. 7
  7.a
  The sum of three consecutive whole numbers is $60$ .
  
  What is the largest of the three numbers?
  7.b
  What is the smallest positive whole number that divides exactly by $1, 2, 3, 4$ and $5$ ?
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8. 8
  What is the name of the special quadrilateral that has $4$ lines of symmetry (or “mirror lines”)?
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9. 9
  A right angled triangle has an angle of $55 \degree$ .
  
  What is the size of the smallest angle in the triangle?
  An unshaded triangle has a horizontal base and a vertical left side meeting at a marked right angle. The hypotenuse slopes down from the upper left to the lower right. No angle value is shown in the diagram.
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10. 10
  10.a
  $\dfrac{3}{4}$ $\dfrac{2}{3}$ $\dfrac{7}{10}$
  
  For the three fractions in the table above, write down:
  10.a.i
  the largest fraction.
  10.a.ii
  the smallest fraction.
  10.b
  Write (as a decimal) the difference between $\dfrac{3}{4}$ and $\dfrac{7}{10}$ .
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11. 11
  11.a
  My flask holds $480 \rtqMathsUnit{ml}$ when it is one quarter empty.
  
  How much does it hold when it is one quarter full?
  11.b
  In the diagram, the small squares are all the same size.
  
  What fraction of the large square is shaded?
  Nine equal smaller squares, each turned through 45 degrees, are arranged in three rows of three. Neighbouring small squares meet at their corners, and the outermost corners meet the sides of the large square. The small squares are shaded; the spaces between them are unshaded.
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12. 12
  12.a
  I set off with a $\rtqMathsSymbolPound 10$ note to buy a book costing $\rtqMathsSymbolPound 4.95$ , a cake costing $\rtqMathsSymbolPound 1.30$ and a new pen. I got $\rtqMathsSymbolPound 2.25$ change.
  
  How much did the pen cost?
  12.b
  Six children each had an equal share of a sum of money.
  
  They each received $\rtqMathsSymbolPound 3.18$ and there was $2 \rtqMathsUnitCurrencyPence$ left over.
  
  How much was the sum of money?
  12.c
  Auntie Jean is saving all her $5 \rtqMathsUnitCurrencyPence$ coins in a jar.
  
  The total amount of money in the jar is $\rtqMathsSymbolPound 18.55$ .
  
  How many coins are in the jar?
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13. 13
  What is the missing number in each of these sequences?
  13.a
  $6, \rtqMathsListSeparator 12, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 48, \rtqMathsListSeparator 96$
  13.b
  $3, \rtqMathsListSeparator 13, \rtqMathsListSeparator 24, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 49, \rtqMathsListSeparator 63$
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14. 14
  I write down a sequence of numbers.
  
  My first number is $160000$ and then I divide by $4$ to get the next number each time. What is the $5^\text{th}$ number in my sequence?
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15. 15
  A pattern that repeats every six symbols starts like this:
  
  , , , , , , , , , , ,
  15.a
  What is the $100 ^ \text{th}$ symbol in the sequence?
  15.b
  What is the $107 ^ \text{th}$ symbol in the sequence?
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16. 16
  Ben makes a stack of identical cans with $6$ on the bottom row, $5$ above that, then $4$ , then $3$ , then $2$ , then $1$ on top.
  
  Jamal makes a stack twice as high.
  
  How many cans are there in Jamal's stack?
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17. 17
  17.a
  Freya puts a casserole in the oven at $11.40 \rtqMathsTimeAm$ .
  
  It needs $1 \rtqMathsUnit{hour}$ and $45 \rtqMathsUnit{minutes}$ to cook.
  
  At what time will it be cooked?
  17.b
  How many minutes are there from $11.11$ until $23.23$ on the same day?
  17.c
  Archie is $20$ years, $20$ months, $20$ weeks and $20$ days old.
  
  What age will he be on his next birthday?
  17.d
  Gemma had a baby born on $1 ^ \text{st}$ February $2017$ .
  
  On what date will the baby be $400$ days old?
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18. 18
  The faces of a cube are painted so that any two faces with an edge in common are painted different colours.
  
  What is the smallest number of colours needed?
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19. 19
  A solid wooden cube is painted blue on the outside.
  
  The cube is then cut into eight smaller cubes of equal size.
  
  What is the the total number of faces of the smaller cubes that have blue paint on them?
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20. 20
  Chi is facing North East.
  
  In which direction will he be facing if he turns clockwise through $3$ right angles?
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21. 21
  21.a
  A group of $30$ adults and $16$ children paid $\rtqMathsSymbolPound 408$ in total to watch a football match. Each child ticket cost $\rtqMathsSymbolPound 3$ .
  
  What was the cost of each adult ticket?
  21.b
  In a sale, prices are reduced by $15 \%$ .
  
  What is the sale price of a hoody that originally cost $\rtqMathsSymbolPound 30$ ?
  21.c
  Guy has twice as many stickers as Asif and five more than Kayal.
  
  They have $35$ stickers altogether.
  
  How many stickers does Guy have?
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22. 22
  A cube has each of its faces covered by one face of an identical cube, making the solid shape shown.
  
  The volume of the solid shape is $875 \rtqMathsUnit{cm}^3$ .
  A central cube has one identical cube attached face-to-face to each of its six faces. The cubes extend in three perpendicular directions, with parts of the rear cubes obscured in this view.
  22.a
  What is the volume of one of the cubes?
  22.b
  What is the length of one side of a cube?
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23. 23
  The card is grey on the front and black on the back.
  
  When piece $A$ is turned over, which one of the shapes below shows its black side?
  
  Put a ring around the correct answer.
  A grey concave polygon has a tall body on the right, matching sloping upper and lower left shoulders, and a rectangular tab projecting from its upper-left side. The centred two-line label reads front of, piece A. A narrow black silhouette with a rectangular tab projecting from the lower-left middle and pointed upper and lower shoulders. A black silhouette retaining the upper-left rectangular tab of the card front. A black silhouette with a long upper-left point, a short lower-left shoulder and no rectangular tab. A black silhouette with the rectangular tab on the lower-left side. A black silhouette with upper and lower left diagonals surrounding a rectangular notch.
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24. 24
  Maria and Kay ran a $1500 \rtqMathsUnit{metres}$ race.
  
  The graph shows information about the race.
  The horizontal axis is Time (minutes), labelled from 0 to 8 in steps of 1. The vertical axis is Distance (metres), labelled from 0 to 1500 in steps of 300. Both axes have arrowheads and the plot has reading grid lines. The key identifies Maria by a dotted curve and Kay by a solid curve. Both curves start at the origin and rise, with changing steepness, to the 1500-metre grid line.
  24.a
  For how many minutes was Kay in the lead?
  24.b
  After how many metres were they level during the race?
  24.c
  Who won the race?
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25. 25
  The diagram shows the coordinates of three points $A, B$ and $C$ .
  
  Shape $ABCD$ is a kite.
  Sparse horizontal x and vertical y axes have arrowheads and an origin labelled 0, with no numbered ticks or background grid. The unshaded kite has four filled vertex markers joined A to B to C to D to A. A is the left vertex, labelled (3, 4); B is the upper vertex, labelled (5, 6); C is the right vertex, labelled (10, 4). The lower vertex is labelled D without a coordinate pair.
  What are the coordinates of point $D$ ?
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26. 26
  Given that,
  
  $\begin{aligned} \rtqMathsSymbolBlackTriangle + \rtqMathsSymbolBlackTriangle &= \rtqMathsSymbolBlackSquare \\\\ \rtqMathsSymbolBlackSquare + \rtqMathsSymbolBlackTriangle &= \rtqMathsSymbolBlackCircle \\\\ \rtqMathsSymbolBlackLozenge &= \rtqMathsSymbolBlackCircle + \rtqMathsSymbolBlackSquare + \rtqMathsSymbolBlackTriangle \end{aligned}$
  
  How many $\rtqMathsSymbolBlackTriangle$ s are equal to $\rtqMathsSymbolBlackLozenge$ ?
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27. 27
  $5$ toffees weigh the same as $6$ maltesers and $3$ toffees.
  
  How many maltesers would weigh the same as $9$ toffees?
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28. 28
  In a game you need to get three coloured discs (green, blue and red) in the correct order.
  
  Three attempts have been made and are shown below, with the number of discs that are in the correct positions.
  
  What is the correct order for the three coloured discs?
  
  POSITION 1 POSITION 2 POSITION 3 NUMBER CORRECT
  Red Blue Green One
  Red Green Blue None
  Green Blue Red None
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29. 29
  Given that $44 \times 382 = 16808$ , use this information to work these out:
  29.a
  $16808 \div 382$
  29.b
  $88 \times 191$
  29.c
  $1680.8 \div 44$
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30. 30
  The diagram shows a pentagonal prism.
  
  Write the letter of the one shape below that is a net for the pentagonal prism.
  A perspective wireframe pentagonal prism has a regular pentagonal front face and a longer prism body receding upwards and to the right toward a smaller rear face. Four rectangular side faces form a horizontal strip. Two pentagonal end faces are attached above and below the fourth rectangle. Five rectangular side faces form a horizontal strip. Both pentagonal end faces are attached below the strip, under the second and fifth rectangles. Four rectangles form a horizontal strip. One pentagon is attached below the third rectangle, and a fifth rectangle extends diagonally from the pentagon. There is no second pentagonal end face. Five rectangles attach one to each edge of a central pentagon. A second pentagon attaches to the outer edge of one rectangle. Five rectangles and two pentagons form a bent arrangement. Three rectangles branch around a central sloping rectangle, while two rectangles extend to the right from the lower pentagon.
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Section D
Questions 1–7
1. 1
  Dave has a lot of tables.
  
  Each rectangular table seats $8$ people.
  
  Each round table seats $5$ people.
  
  What is the smallest number of tables of each type that Dave needs to use to seat $35$ friends and himself, without any empty seats?
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2. 2
  2.a
  Which one of the following numbers is three less than a multiple of $5$ and three more than a multiple of $6$ ?
  
  $12$
  
  $17$
  
  $21$
  
  $22$
  
  $27$
  
  2.b
  What is the smallest four-digit positive whole number which has four different digits?
  2.c
  How many odd three-digits numbers is it possible to make, using just the numbers $7, 8$ and $9$ ?
  
  (You are allowed to use each of the numbers more than once in a particular three-digit number.)
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3. 3
  3.a
  Fill in each box with either $+$ or $-$ to make the answer of $100$ .
  
  $123 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \ 45 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 67 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 89 = \rtqMathsSpaceQuarterEm 100$
  3.b
  Last year, $275$ of the $500$ pupils at Woodgreen School were boys.
  
  This year, there are $540$ pupils in the school but the proportion of boys is the same as last year.
  
  How many boys are at the school this year?
  3.c
  Maya cuts a $6 \rtqMathsUnit{metre}$ piece of string into three different pieces.
  
  The longest piece is $40 \rtqMathsUnit{cm}$ longer than the middle piece.
  
  The middle piece is $70 \rtqMathsUnit{cm}$ longer than the shorter piece.
  
  How long (in centimetres) is the longest piece?
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4. 4
  The symbol $\rtqMathsSymbolAsterisk$ is used like this:
  
  $\begin{aligned} a \rtqMathsBinaryOperatorAsterisk b &= 5 \text{ times } a, \text{ plus } b \end{aligned}$
  
  For example,
  
  $\begin{aligned} 2 \rtqMathsBinaryOperatorAsterisk 7 &= (5 \times 2) + 7 \\\\ &= 17 \end{aligned}$
  4.a
  Find the value of $9 \rtqMathsBinaryOperatorAsterisk 8$ .
  4.b
  What number does $m$ stand for, if $m \rtqMathsBinaryOperatorAsterisk 6 = 41$ ?
  4.c
  If $n \rtqMathsBinaryOperatorAsterisk 4 = 8 \rtqMathsBinaryOperatorAsterisk n$ , what number does $n$ stand for?
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5. 5
  Rob, Bertie and Dom ran a race.
  
  Just one of the following four statements is true.
  
  Which one is it?
  
  Rob came $1 ^ \text{st}$
  
  Bertie came $1 ^ \text{st}$
  
  Dom came $2 ^ \text{nd}$
  
  Dom did not come $2 ^ \text{nd}$
  
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6. 6
  6.a
  Write down the answers to the calculations (Hint: there is a quick way!)
  6.a.i
  $(49 \times 37018) + (51 \times 37018)$
  6.a.ii
  $(26 \times 37018) - (25 \times 37018)$
  6.b
  How many triangles are there in this diagram?
  Two straight lines run from the upper vertex to different points on the horizontal base. A third line, parallel to the base, joins the sloping outer sides and crosses both internal lines. The intervals along the base are unequal. No regions are shaded.
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7. 7
  Given that none of $A, B$ or $C$ is zero, work out what number each of the letters stands for in these two calculations.
  7.a
  $\rtqMathsColumnarArithmeticStyle \begin{array}{cccc} & & B & C \\ {}\times & & B & C \\ \hline & A & B & C \end{array}$
  7.b
  $\rtqMathsColumnarArithmeticStyle \begin{array}{cccc} & D & E & F \\ & D & E & F \\ {}+ & D & E & F \\ \hline & E & E & E \end{array}$
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